testing hypothesis in statistics calculator

Hypothesis Testing Calculator

Type II Error

The first step in hypothesis testing is to calculate the test statistic. The formula for the test statistic depends on whether the population standard deviation (σ) is known or unknown. If σ is known, our hypothesis test is known as a z test and we use the z distribution. If σ is unknown, our hypothesis test is known as a t test and we use the t distribution. Use of the t distribution relies on the degrees of freedom, which is equal to the sample size minus one. Furthermore, if the population standard deviation σ is unknown, the sample standard deviation s is used instead. To switch from σ known to σ unknown, click on $\boxed{\sigma}$ and select $\boxed{s}$ in the Hypothesis Testing Calculator.

Next, the test statistic is used to conduct the test using either the p-value approach or critical value approach. The particular steps taken in each approach largely depend on the form of the hypothesis test: lower tail, upper tail or two-tailed. The form can easily be identified by looking at the alternative hypothesis (H a ). If there is a less than sign in the alternative hypothesis then it is a lower tail test, greater than sign is an upper tail test and inequality is a two-tailed test. To switch from a lower tail test to an upper tail or two-tailed test, click on $\boxed{\geq}$ and select $\boxed{\leq}$ or $\boxed{=}$, respectively.

In the p-value approach, the test statistic is used to calculate a p-value. If the test is a lower tail test, the p-value is the probability of getting a value for the test statistic at least as small as the value from the sample. If the test is an upper tail test, the p-value is the probability of getting a value for the test statistic at least as large as the value from the sample. In a two-tailed test, the p-value is the probability of getting a value for the test statistic at least as unlikely as the value from the sample.

To test the hypothesis in the p-value approach, compare the p-value to the level of significance. If the p-value is less than or equal to the level of signifance, reject the null hypothesis. If the p-value is greater than the level of significance, do not reject the null hypothesis. This method remains unchanged regardless of whether it's a lower tail, upper tail or two-tailed test. To change the level of significance, click on $\boxed{.05}$. Note that if the test statistic is given, you can calculate the p-value from the test statistic by clicking on the switch symbol twice.

In the critical value approach, the level of significance ($\alpha$) is used to calculate the critical value. In a lower tail test, the critical value is the value of the test statistic providing an area of $\alpha$ in the lower tail of the sampling distribution of the test statistic. In an upper tail test, the critical value is the value of the test statistic providing an area of $\alpha$ in the upper tail of the sampling distribution of the test statistic. In a two-tailed test, the critical values are the values of the test statistic providing areas of $\alpha / 2$ in the lower and upper tail of the sampling distribution of the test statistic.

To test the hypothesis in the critical value approach, compare the critical value to the test statistic. Unlike the p-value approach, the method we use to decide whether to reject the null hypothesis depends on the form of the hypothesis test. In a lower tail test, if the test statistic is less than or equal to the critical value, reject the null hypothesis. In an upper tail test, if the test statistic is greater than or equal to the critical value, reject the null hypothesis. In a two-tailed test, if the test statistic is less than or equal the lower critical value or greater than or equal to the upper critical value, reject the null hypothesis.

When conducting a hypothesis test, there is always a chance that you come to the wrong conclusion. There are two types of errors you can make: Type I Error and Type II Error. A Type I Error is committed if you reject the null hypothesis when the null hypothesis is true. Ideally, we'd like to accept the null hypothesis when the null hypothesis is true. A Type II Error is committed if you accept the null hypothesis when the alternative hypothesis is true. Ideally, we'd like to reject the null hypothesis when the alternative hypothesis is true.

Hypothesis testing is closely related to the statistical area of confidence intervals. If the hypothesized value of the population mean is outside of the confidence interval, we can reject the null hypothesis. Confidence intervals can be found using the Confidence Interval Calculator . The calculator on this page does hypothesis tests for one population mean. Sometimes we're interest in hypothesis tests about two population means. These can be solved using the Two Population Calculator . The probability of a Type II Error can be calculated by clicking on the link at the bottom of the page.

Hypothesis Testing Calculator Online

Hypothesis testing is a foundational method used in statistics to infer the validity of a hypothesis about a population parameter. The Hypothesis Testing Calculator facilitates this process by automating the computations necessary for the t-test , a method used to compare sample means against a hypothesized mean or against each other. Let’s delve into the formulas this calculator uses to execute one-sample and two-sample t-tests.

One-Sample t-Test

Two-Sample t-Test

Equal variances:, unequal variances (welch’s t-test):, table of critical t-values.

These values are crucial in hypothesis testing as they help define the threshold for significance, assisting users of the calculator in interpreting their results accurately.

The calculated t-value is 3.00. Using the critical t-values table, at 95% confidence level and 35 degrees of freedom, the critical value is approximately 2.030. Since 3.00 > 2.030, the null hypothesis is reject, indicating a significant difference from the hypothesize mean.

Most Common FAQs

Yes, while the t-test is specifically design for means, the principles of hypothesis testing apply to other parameters such as proportions and variances. Which can also be tested using appropriate versions of hypothesis tests such as the z-test and F-test.

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t-test Calculator

Table of contents

Welcome to our t-test calculator! Here you can not only easily perform one-sample t-tests , but also two-sample t-tests , as well as paired t-tests .

Do you prefer to find the p-value from t-test, or would you rather find the t-test critical values? Well, this t-test calculator can do both! 😊

What does a t-test tell you? Take a look at the text below, where we explain what actually gets tested when various types of t-tests are performed. Also, we explain when to use t-tests (in particular, whether to use the z-test vs. t-test) and what assumptions your data should satisfy for the results of a t-test to be valid. If you've ever wanted to know how to do a t-test by hand, we provide the necessary t-test formula, as well as tell you how to determine the number of degrees of freedom in a t-test.

When to use a t-test?

A t-test is one of the most popular statistical tests for location , i.e., it deals with the population(s) mean value(s).

There are different types of t-tests that you can perform:

• A one-sample t-test;
• A two-sample t-test; and
• A paired t-test.

In the next section , we explain when to use which. Remember that a t-test can only be used for one or two groups . If you need to compare three (or more) means, use the analysis of variance ( ANOVA ) method.

The t-test is a parametric test, meaning that your data has to fulfill some assumptions :

• The data points are independent; AND
• The data, at least approximately, follow a normal distribution .

If your sample doesn't fit these assumptions, you can resort to nonparametric alternatives. Visit our Mann–Whitney U test calculator or the Wilcoxon rank-sum test calculator to learn more. Other possibilities include the Wilcoxon signed-rank test or the sign test.

Which t-test?

Your choice of t-test depends on whether you are studying one group or two groups:

One sample t-test

Choose the one-sample t-test to check if the mean of a population is equal to some pre-set hypothesized value .

The average volume of a drink sold in 0.33 l cans — is it really equal to 330 ml?

The average weight of people from a specific city — is it different from the national average?

Two-sample t-test

Choose the two-sample t-test to check if the difference between the means of two populations is equal to some pre-determined value when the two samples have been chosen independently of each other.

In particular, you can use this test to check whether the two groups are different from one another .

The average difference in weight gain in two groups of people: one group was on a high-carb diet and the other on a high-fat diet.

The average difference in the results of a math test from students at two different universities.

This test is sometimes referred to as an independent samples t-test , or an unpaired samples t-test .

Paired t-test

A paired t-test is used to investigate the change in the mean of a population before and after some experimental intervention , based on a paired sample, i.e., when each subject has been measured twice: before and after treatment.

In particular, you can use this test to check whether, on average, the treatment has had any effect on the population .

The change in student test performance before and after taking a course.

The change in blood pressure in patients before and after administering some drug.

How to do a t-test?

So, you've decided which t-test to perform. These next steps will tell you how to calculate the p-value from t-test or its critical values, and then which decision to make about the null hypothesis.

Decide on the alternative hypothesis :

Use a two-tailed t-test if you only care whether the population's mean (or, in the case of two populations, the difference between the populations' means) agrees or disagrees with the pre-set value.

Use a one-tailed t-test if you want to test whether this mean (or difference in means) is greater/less than the pre-set value.

Compute your T-score value :

Formulas for the test statistic in t-tests include the sample size , as well as its mean and standard deviation . The exact formula depends on the t-test type — check the sections dedicated to each particular test for more details.

Determine the degrees of freedom for the t-test:

The degrees of freedom are the number of observations in a sample that are free to vary as we estimate statistical parameters. In the simplest case, the number of degrees of freedom equals your sample size minus the number of parameters you need to estimate . Again, the exact formula depends on the t-test you want to perform — check the sections below for details.

The degrees of freedom are essential, as they determine the distribution followed by your T-score (under the null hypothesis). If there are d degrees of freedom, then the distribution of the test statistics is the t-Student distribution with d degrees of freedom . This distribution has a shape similar to N(0,1) (bell-shaped and symmetric) but has heavier tails . If the number of degrees of freedom is large (>30), which generically happens for large samples, the t-Student distribution is practically indistinguishable from N(0,1).

💡 The t-Student distribution owes its name to William Sealy Gosset, who, in 1908, published his paper on the t-test under the pseudonym "Student". Gosset worked at the famous Guinness Brewery in Dublin, Ireland, and devised the t-test as an economical way to monitor the quality of beer. Cheers! 🍺🍺🍺

p-value from t-test

Recall that the p-value is the probability (calculated under the assumption that the null hypothesis is true) that the test statistic will produce values at least as extreme as the T-score produced for your sample . As probabilities correspond to areas under the density function, p-value from t-test can be nicely illustrated with the help of the following pictures:

The following formulae say how to calculate p-value from t-test. By cdf t,d we denote the cumulative distribution function of the t-Student distribution with d degrees of freedom:

p-value from left-tailed t-test:

p-value = cdf t,d (t score )

p-value from right-tailed t-test:

p-value = 1 − cdf t,d (t score )

p-value from two-tailed t-test:

p-value = 2 × cdf t,d (−|t score |)

or, equivalently: p-value = 2 − 2 × cdf t,d (|t score |)

However, the cdf of the t-distribution is given by a somewhat complicated formula. To find the p-value by hand, you would need to resort to statistical tables, where approximate cdf values are collected, or to specialized statistical software. Fortunately, our t-test calculator determines the p-value from t-test for you in the blink of an eye!

t-test critical values

Recall, that in the critical values approach to hypothesis testing, you need to set a significance level, α, before computing the critical values , which in turn give rise to critical regions (a.k.a. rejection regions).

Formulas for critical values employ the quantile function of t-distribution, i.e., the inverse of the cdf :

Critical value for left-tailed t-test: cdf t,d -1 (α)

critical region:

(-∞, cdf t,d -1 (α)]

Critical value for right-tailed t-test: cdf t,d -1 (1-α)

[cdf t,d -1 (1-α), ∞)

Critical values for two-tailed t-test: ±cdf t,d -1 (1-α/2)

(-∞, -cdf t,d -1 (1-α/2)] ∪ [cdf t,d -1 (1-α/2), ∞)

To decide the fate of the null hypothesis, just check if your T-score lies within the critical region:

If your T-score belongs to the critical region , reject the null hypothesis and accept the alternative hypothesis.

If your T-score is outside the critical region , then you don't have enough evidence to reject the null hypothesis.

How to use our t-test calculator

Choose the type of t-test you wish to perform:

A one-sample t-test (to test the mean of a single group against a hypothesized mean);

A two-sample t-test (to compare the means for two groups); or

A paired t-test (to check how the mean from the same group changes after some intervention).

Two-tailed;

Left-tailed; or

Right-tailed.

This t-test calculator allows you to use either the p-value approach or the critical regions approach to hypothesis testing!

Enter your T-score and the number of degrees of freedom . If you don't know them, provide some data about your sample(s): sample size, mean, and standard deviation, and our t-test calculator will compute the T-score and degrees of freedom for you .

Once all the parameters are present, the p-value, or critical region, will immediately appear underneath the t-test calculator, along with an interpretation!

One-sample t-test

The null hypothesis is that the population mean is equal to some value μ 0 \mu_0 μ 0 ​ .

The alternative hypothesis is that the population mean is:

• different from μ 0 \mu_0 μ 0 ​ ;
• smaller than μ 0 \mu_0 μ 0 ​ ; or
• greater than μ 0 \mu_0 μ 0 ​ .

One-sample t-test formula :

• μ 0 \mu_0 μ 0 ​ — Mean postulated in the null hypothesis;
• n n n — Sample size;
• x ˉ \bar{x} x ˉ — Sample mean; and
• s s s — Sample standard deviation.

Number of degrees of freedom in t-test (one-sample) = n − 1 n-1 n − 1 .

The null hypothesis is that the actual difference between these groups' means, μ 1 \mu_1 μ 1 ​ , and μ 2 \mu_2 μ 2 ​ , is equal to some pre-set value, Δ \Delta Δ .

The alternative hypothesis is that the difference μ 1 − μ 2 \mu_1 - \mu_2 μ 1 ​ − μ 2 ​ is:

• Different from Δ \Delta Δ ;
• Smaller than Δ \Delta Δ ; or
• Greater than Δ \Delta Δ .

In particular, if this pre-determined difference is zero ( Δ = 0 \Delta = 0 Δ = 0 ):

The null hypothesis is that the population means are equal.

The alternate hypothesis is that the population means are:

• μ 1 \mu_1 μ 1 ​ and μ 2 \mu_2 μ 2 ​ are different from one another;
• μ 1 \mu_1 μ 1 ​ is smaller than μ 2 \mu_2 μ 2 ​ ; and
• μ 1 \mu_1 μ 1 ​ is greater than μ 2 \mu_2 μ 2 ​ .

Formally, to perform a t-test, we should additionally assume that the variances of the two populations are equal (this assumption is called the homogeneity of variance ).

There is a version of a t-test that can be applied without the assumption of homogeneity of variance: it is called a Welch's t-test . For your convenience, we describe both versions.

Two-sample t-test if variances are equal

Use this test if you know that the two populations' variances are the same (or very similar).

Two-sample t-test formula (with equal variances) :

where s p s_p s p ​ is the so-called pooled standard deviation , which we compute as:

• Δ \Delta Δ — Mean difference postulated in the null hypothesis;
• n 1 n_1 n 1 ​ — First sample size;
• x ˉ 1 \bar{x}_1 x ˉ 1 ​ — Mean for the first sample;
• s 1 s_1 s 1 ​ — Standard deviation in the first sample;
• n 2 n_2 n 2 ​ — Second sample size;
• x ˉ 2 \bar{x}_2 x ˉ 2 ​ — Mean for the second sample; and
• s 2 s_2 s 2 ​ — Standard deviation in the second sample.

Number of degrees of freedom in t-test (two samples, equal variances) = n 1 + n 2 − 2 n_1 + n_2 - 2 n 1 ​ + n 2 ​ − 2 .

Two-sample t-test if variances are unequal (Welch's t-test)

Use this test if the variances of your populations are different.

Two-sample Welch's t-test formula if variances are unequal:

• s 1 s_1 s 1 ​ — Standard deviation in the first sample;
• s 2 s_2 s 2 ​ — Standard deviation in the second sample.

The number of degrees of freedom in a Welch's t-test (two-sample t-test with unequal variances) is very difficult to count. We can approximate it with the help of the following Satterthwaite formula :

Alternatively, you can take the smaller of n 1 − 1 n_1 - 1 n 1 ​ − 1 and n 2 − 1 n_2 - 1 n 2 ​ − 1 as a conservative estimate for the number of degrees of freedom.

🔎 The Satterthwaite formula for the degrees of freedom can be rewritten as a scaled weighted harmonic mean of the degrees of freedom of the respective samples: n 1 − 1 n_1 - 1 n 1 ​ − 1 and n 2 − 1 n_2 - 1 n 2 ​ − 1 , and the weights are proportional to the standard deviations of the corresponding samples.

As we commonly perform a paired t-test when we have data about the same subjects measured twice (before and after some treatment), let us adopt the convention of referring to the samples as the pre-group and post-group.

The null hypothesis is that the true difference between the means of pre- and post-populations is equal to some pre-set value, Δ \Delta Δ .

The alternative hypothesis is that the actual difference between these means is:

Typically, this pre-determined difference is zero. We can then reformulate the hypotheses as follows:

The null hypothesis is that the pre- and post-means are the same, i.e., the treatment has no impact on the population .

The alternative hypothesis:

• The pre- and post-means are different from one another (treatment has some effect);
• The pre-mean is smaller than the post-mean (treatment increases the result); or
• The pre-mean is greater than the post-mean (treatment decreases the result).

Paired t-test formula

In fact, a paired t-test is technically the same as a one-sample t-test! Let us see why it is so. Let x 1 , . . . , x n x_1, ... , x_n x 1 ​ , ... , x n ​ be the pre observations and y 1 , . . . , y n y_1, ... , y_n y 1 ​ , ... , y n ​ the respective post observations. That is, x i , y i x_i, y_i x i ​ , y i ​ are the before and after measurements of the i -th subject.

For each subject, compute the difference, d i : = x i − y i d_i := x_i - y_i d i ​ := x i ​ − y i ​ . All that happens next is just a one-sample t-test performed on the sample of differences d 1 , . . . , d n d_1, ... , d_n d 1 ​ , ... , d n ​ . Take a look at the formula for the T-score :

Δ \Delta Δ — Mean difference postulated in the null hypothesis;

n n n — Size of the sample of differences, i.e., the number of pairs;

x ˉ \bar{x} x ˉ — Mean of the sample of differences; and

s s s  — Standard deviation of the sample of differences.

Number of degrees of freedom in t-test (paired): n − 1 n - 1 n − 1

t-test vs Z-test

We use a Z-test when we want to test the population mean of a normally distributed dataset, which has a known population variance . If the number of degrees of freedom is large, then the t-Student distribution is very close to N(0,1).

Hence, if there are many data points (at least 30), you may swap a t-test for a Z-test, and the results will be almost identical. However, for small samples with unknown variance, remember to use the t-test because, in such cases, the t-Student distribution differs significantly from the N(0,1)!

🙋 Have you concluded you need to perform the z-test? Head straight to our z-test calculator !

What is a t-test?

A t-test is a widely used statistical test that analyzes the means of one or two groups of data. For instance, a t-test is performed on medical data to determine whether a new drug really helps.

What are different types of t-tests?

Different types of t-tests are:

• One-sample t-test;
• Two-sample t-test; and
• Paired t-test.

How to find the t value in a one sample t-test?

To find the t-value:

• Subtract the null hypothesis mean from the sample mean value.
• Divide the difference by the standard deviation of the sample.
• Multiply the resultant with the square root of the sample size.

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ol{padding-top:0;}.css-1dtpypy ul:not(:first-child),.css-1dtpypy ol:not(:first-child){padding-top:4px;} Test setup

Choose test type

t-test for the population mean, μ, based on one independent sample . Null hypothesis H 0 : μ = μ 0  

Alternative hypothesis H 1

Test details

Significance level α

The probability that we reject a true H 0 (type I error).

Degrees of freedom

Calculated as sample size minus one.

Test results

One sample t test calculator

The One Sample t Test Calculator allows you to determine p-values, critical values, test statistics, and conclusions using the one-sample t test method.

Related Calculators :

• List of all calculator
• P-value calculator
• Critical value Calculator
• One sample z test calculator

How to Use the One Sample t Test Calculator

• Select Data Type: Choose whether to input summary statistics directly or provide a data set.
• Input Your Data: Enter the required values such as population mean, sample size, sample mean, and sample standard deviation.
• Set Hypotheses: Specify the null and alternative hypotheses.
• Calculate: Click the "Calculate" button to see the test statistic, p-value, and other relevant results.

Interpreting the Results

To interpret the results of a one-sample t-test, you must first grasp several crucial components: the test statistic (t-value), degrees of freedom, p-value, and confidence interval. Here's a step-by-step way to interpreting these findings:

Components of One-Sample t-Test Results

Test Statistic (t-value) :

This result indicates the amount of standard deviations your sample mean is from the population mean under the null hypothesis. A larger absolute value of t indicates a wider divergence between the sample mean and the population average.

Degrees of Freedom (df):

This is normally the sample size less one (n-1). The degrees of freedom are utilized to calculate the critical value of t using the t-distribution table.

This represents the likelihood of receiving a test statistic as extreme as the one observed, assuming the null hypothesis is correct. A low p-value ( less than 0.05) indicates that the observed data are unlikely to support the null hypothesis, resulting in its rejection.

Confidence Interval:

This defines a range of values within which the genuine population mean is expected to fall. If the confidence interval excludes the population mean stated in the null hypothesis, it supports the conclusion that the sample mean differs considerably from the population mean.

Steps to Interpret the Results

State the Hypotheses:

Null Hypothesis (H₀): The population mean is equal to a specified value (e.g. \( \mu=\mu_0 \) ).

Alternative Hypothesis (H₁): The population mean is different from the specified value (e.g. \( \mu \ne \mu_0 \) ).

Check the t-value:

Compare the t-value to the crucial value from the t-distribution table based on the specified significance level (α, typically 0.05) and degrees of freedom.

If |t-value| > critical value, reject the null hypothesis.

Examine the P-value:

• If the p-value is less than the chosen significance level \( \alpha \), reject the null hypothesis.
• A p-value less than \(0.05\) typically indicates strong evidence against the null hypothesis.

Review the Confidence Interval:

Check to see if the confidence interval for the sample mean includes the population mean under the null hypothesis.

If the interval excludes the population mean, it indicates that the sample mean is significantly different than the population mean.

Requirements and Assumptions for a one sample t test

To effectively execute and interpret a one-sample t-test, you must first grasp the test's requirements and assumptions. Meeting these parameters assures that the test results are legitimate and reliable.

Requirements for a One-Sample t-Test

You will need a sample of the population you are studying.

To compare the sample mean to the population mean (μ₀), you must have a known population mean.

A suitable sample size is necessary. While the t-test performs well with small sample sizes, higher sample sizes yield more accurate results.

Assumptions of a One-Sample t-Test

Random Sampling:

Data should be acquired from the population using random sampling. This guarantees that the sample is representative of the population and minimises bias.

Scale of Measurement:

The data must be continuous (interval or ratio scale). This means that the data points may be meaningfully arranged, and the differences between them are consistent and observable.

The data should follow a roughly normal distribution. This assumption is particularly essential for small sample sizes (n < 30). For bigger samples, the Central Limit Theorem predicts that the sample mean distribution will be essentially normal, regardless of the distribution of the data.

Independence :

Observations in the sample must be independent of one another. This means that the value of one observation should not affect or predict the value of another.

Unknown Population Standard Deviation: :

The test assumes that the population standard deviation \(\alpha\) is unknown and needs to be determined from the sample.

Applications of the One Sample t Test

This test is widely used in various fields including:

• Education: Assessing whether the average test scores of a class differ from the national average.
• Healthcare: Comparing the mean blood pressure level of a group of patients to a known population mean.
• Business: Evaluating if the average sales of a product differ from the company's historical sales data.

Frequently Asked Questions (FAQs)

What is a one-sample t test.

A one-sample t test is a statistical approach for determining whether a sample's mean differs significantly from a known population mean.

When should I use a one-sample t test?

Use this test when the population standard deviation is unknown and the sample size is small (typically n < 30).

How do I interpret the p-value in a t test?

The p-value indicates the probability of observing the test results under the null hypothesis. A low p-value less than the significance level equal to \( \alpha \) suggests rejecting the null hypothesis.

Why Use Our One Sample t Test Calculator?

Our calculator offers several advantages:

• Accuracy: Provides precise calculations for your hypothesis testing needs.
• User-Friendly Interface: Easy to navigate and input your data.
• Educational Value: Offers detailed explanations and step-by-step guides to help you understand the results.
• Time-Saving: Quickly computes results, allowing you to focus on analysis and interpretation.
• Versatility: Suitable for various fields such as education, healthcare, and business, making it a valuable tool for a wide range of users.

Start your hypothesis testing today with our One Sample t Test Calculator and achieve accurate and reliable results effortlessly.

For optimal use, please visit DATAtab on your desktop PC!

Metric Variables:

Ordinal variables:, nominal variables:, hypothesis test calculator.

Do you want to calculate a hypothesis test such as a t-test , Chi Square test or an ANOVA ? You can do that easily here in the browser.

If you want to use your own data just clear the upper table

• Clear the table in the Hypothesis test calculator.
• Copy your data into the table.
• Select the variables.

In the hypothesis test calculator you can calculate e.g. a t-test, a chi-square test, a binomial test or an analysis of variance. If you need a more detailed explanation, you can find more information in the tutorials.

In order to use the hypothesis test calculator, you must first formulate your hypothesis and collect your data. DATAtab will then suggest the hypothesis test you need based on the data entered into the statistics calculator.

p value calculator

With the p value calculator you can calculate the p value for different tests. There is a wide range of methods for this. Just click on the variables you want to evaluate above and DATAtab will give you the tests you can use.

For example, if you select a metric and a categorical variable, the Independent t-Test calculator is automatically selected. If your data is not normally distributed, simply use the Mann-Whitney U-test calculator.

H0 and H1 calculator

With the h0 and h1 calculator for the different hypothesis test you can calculate the p-value which gives you an indication if you can reject the H0 or not.

Cite DATAtab: DATAtab Team (2024). DATAtab: Online Statistics Calculator. DATAtab e.U. Graz, Austria. URL https://datatab.net

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Test Statistic Calculator

Choose the method, enter the values into the test statistic calculator, and click on the “Calculate” button to calculate the statistical value for hypothesis evaluation.

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This test statistic calculator helps to find the static value for hypothesis testing. The calculated test value shows if there’s enough evidence to reject a null hypothesis. Also, this calculator performs calculations of either for one population mean, comparing two means, single population proportion, and two population proportions.

Our tool is highly useful in various fields like research, experimentation, quality control, and data analysis.

What is Test Statistics?

A test statistic is a numerical value obtained from the sample data set. It summarizes the differences between what you observe within your sample and what would be expected if a hypothesis were true. 

The t-test statistic also shows how closely your data matches the predicted distribution among the sample tests you perform. 

How to Calculate Test Statistics Value?

• Collect the data from the populations
• Use the data to find the standard deviation of the population
• Calculate the mean (μ) of the population using this data
• Determine the z-value or sample size 
• Use the suitable test statistic formula and get the results

Test Statistic For One Population Mean:

Test statistics for a single population mean is calculated when a variable is numeric and involves one population or a group. 

x̄ - µ 0 σ / √n

• x̄ = Mean of your sample data
• µ 0 = Hypothesized population mean that you are comparing to your sample mean
• σ = Population standard deviation
• n = number of observations (sample size) in your data set

Suppose we want to test if the average height of adult males in a city is 70 inches. We take a sample of 25 adult males and find the sample mean height to be 71 inches with a sample standard deviation of 3 inches. We use a significance level of 0.05.

t = 70 - 71 3√25

Test Statistic Comparing Two Population Means:

This test is applied when the numeric value is compared across the various populations or groups. To compute the resulting test statistic, two distinct random samples must be chosen, one from each population.

\(\frac{√x̄ - √ȳ}{\sqrt{\frac{\sigma_{1}^{2}}{n_{1}}+\frac{\sigma_{2}^{2}}{n_{2}}}}\)

• ȳ = means of hypothesized population

Suppose we want to test if there is a difference in average test scores between two schools. We take a sample of 30 students from school A with an average score of 85 and a standard deviation of 5, and a sample of 35 students from school B with an average score of 82 and a standard deviation of 6.

t = 85 - 82 √5 2 / 30 + 6 2 / 35

t = 3 √ 25/30 + 36/35

t = 3 √0.833 + 1.029

t = 3 √1.862

Test Statistic For a Single Population Proportion:

This test is used to determine if a single population's proportion differs from a specified standard. The test stat calculator works for a population proportion when dealing with data by having a limit of P₀ because proportions represent parts of a whole and cannot logically exceed the total or be negative.

\(\frac{\hat{p}-p_{0}}{\sqrt{\frac{p_{0}(1-p_{0})}{n}}}\)

• P̂ = Sample proportion
• P 0 = Population proportion

Suppose we want to test if the proportion of left-handed people in a population is 10%. We take a sample of 100 people and find that 8 are left-handed. We use a significance level of 0.05.

= P̂ - P₀ √0.10 (1 - 0.10)/100

= 0.08 - 0.10 √0.10 (1 - 0.10)/100

= -0.02 √0.10 (0.9)/100

= -0.02 √0.009

= -0.02 0.03

= −0.67

Test Statistic For Two Population Proportion:

This test identifies the difference in proportions between two independent groups to assess their significance.

\(\frac{\hat{p}_{1}-\hat{p}_{2}}{\sqrt{\hat{p}(1-\hat{p})(\frac{1}{n_{1}}+\frac{1}{n_{2}})}}\)

• P̂ 1 and P̂ 2 = Sample proportions for two groups

Suppose we want to test if the proportion of smokers is different between two cities. We take a sample of 150 people from City A and find that 30 are smokers, and a sample of 200 people from City B and find that 50 are smokers.

• P̂ 1 = 30 / 150 = 0.20
• P̂ 2 = 50 / 200 = 0.25
• P̂ = 30 + 50 / 150 + 200 = 0.229

Calculation:

= 0.20 - 0.25 √0.229 (1 - 0.229) (1 / 150 + 1/200)

= -0.05 √0.229 (0.771) (1 / 150 + 1 / 200)

= -0.05 √0.176 (1/150 + 1/200)

= -0.05 √0.176 (0.0113)

= -0.05 √0.002

= -0.05 0.045

= −1.11

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P-value Calculator

Please provide any one value below to compute p-value from z-score or vice versa for a normal distribution.

A p-value (probability value) is a value used in statistical hypothesis testing that is intended to determine whether the obtained results are significant. In statistical hypothesis testing, the null hypothesis is a type of hypothesis that states a default position, such as there is no association among groups or relationship between two observations. Assuming that the given null hypothesis is correct, a p-value is the probability of obtaining test results in an experiment that are at least as extreme as the observed results. In other words, determining a p-value helps you determine how likely it is that the observed results actually differ from the null hypothesis.

The smaller the p-value, the higher the significance, and the more evidence there is that the null hypothesis should be rejected for an alternative hypothesis. Typically, a p-value of ≤ 0.05 is accepted as significant and the null hypothesis is rejected, while a p-value > 0.05 indicates that there is not enough evidence against the null hypothesis to reject it.

Given that the data being studied follows a normal distribution, a Z-score table can be used to determine p-values, as in this calculator.

Z-test for two Means, with Known Population Standard Deviations

Instructions: This calculator conducts a Z-test for two population means (\(\mu_1\) and \(\mu_2\)), with known population standard deviations ( \(\sigma_1\) and \(\sigma_2\)). Please select the null and alternative hypotheses, type the significance level, the sample means, the population standard deviations, the sample sizes, and the results of the z-test will be displayed for you:

The Z-test for Two Means

More about the z-test for two means so you can better use the results delivered by this solver: A z-test for two means is a hypothesis test that attempts to make a claim about the population means (\(\mu_1\) and \(\mu_2\)). More specifically, we are interested in assessing whether or not it is reasonable to claim that the two population means the population means \(\mu\) 1 and \(\mu\) 2 are equal, based on the information provided by the samples. The test has two non-overlapping hypotheses, the null and the alternative hypothesis.

The null hypothesis is a statement about the population means, corresponding to the assumption of no effect, and the alternative hypothesis is the complementary hypothesis to the null hypothesis. The main properties of a one sample z-test for two population means are:

• Depending on our knowledge about the "no effect" situation, the z-test can be two-tailed, left-tailed or right-tailed
• The main principle of hypothesis testing is that the null hypothesis is rejected if the test statistic obtained is sufficiently unlikely under the assumption that the null hypothesis is true
• The p-value is the probability of obtaining sample results as extreme or more extreme than the sample results obtained, under the assumption that the null hypothesis is true
• In a hypothesis tests there are two types of errors. Type I error occurs when we reject a true null hypothesis, and the Type II error occurs when we fail to reject a false null hypothesis

How to calculate the test statistic for the two samples? We have that the formula for a z-statistic for two population means is:

The above formula allows you to assess whether or not there is a statistically significant difference between two means. The null hypothesis is rejected when the z-statistic lies on the rejection region, which is determined by the significance level (\(\alpha\)) and the type of tail (two-tailed, left-tailed or right-tailed).

In case that the population standard deviations are not known, you can use a t-test for two sample means calculator .

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Z-Test Calculator

Sample size, n
Population mean, μ
Population standard deviation, σ
Alternative hypothesis H : Sample 1 Sample mean, x̅ Sample size, n Population standard deviation, σ Sample 2 Sample mean, x̅ Sample size, n Population standard deviation, σ   Population mean difference, d Alternative hypothesis H : -μ ≠d -μ <d -μ >d This Z-test calculator computes data for both one-sample and two-sample Z-tests. It also provides a diagram to show the position of the Z-score and the acceptance/rejection regions. When making a two-sample Z-test calculation, the population mean difference, d, represents the difference between the population means of sample one and sample two, which is μ 1 -μ 2 . To use this calculator, simply select the type of calculation from the tab, enter the values, and click the 'Calculate' button. The Z-test is a statistical procedure used to determine whether there is a significant difference between means, either between a sample mean and a known population mean (one-sample Z-test) or between the means of two independent samples (two-sample Z-test). It assumes that the data is normally distributed and is particularly useful when the sample sizes are large (>30) and the population standard deviations are known. When analyzing data to make informed decisions, statistical hypothesis tests are indispensable tools used to determine if evidence exists to reject a prevailing assumption or theory, known as the null hypothesis. The Z-test is one of these tests. One-Sample Z-Test The one-sample Z-test is used when you want to compare the mean of a single sample to a known population mean to see if there is a significant difference. This is particularly common in quality control and other scenarios where the standard deviation of the population is known. Null Hypothesis (H 0 ): The sample mean is equal to the population mean (x̅=μ). Alternative Hypothesis (H 1 ): The sample mean is not equal to the population mean (x̅≠μ). This can also be one-tailed (x̅>μ or x̅<μ) depending on the direction of interest. The formula for the Z-statistic in a one-sample Z-test is: Z =   x̅ - μ   σ √n x̅ is the sample mean μ is the population mean σ is the population standard deviation n is the sample size Example: Suppose a school administrator knows the national average score for a standardized test is 500 with a standard deviation of 50. A sample of 100 students from a new teaching program scores an average of 520. To determine if this program significantly differs from the national average: Z =   520 - 500   50 √100   20   5 This Z-value would then be compared against a critical value from the Z-distribution table typically at a 0.05 significance level. The critical value for a 0.05 significance level is approximately ±1.96. The Z-value of 4 is greater than 1.96. Therefore, the null hypothesis is rejected and the score of this program is considered significantly different from the national average at the 0.05 significance level. Two-Sample Z-Test The two-sample Z-test (or independent samples Z-test) compares the means from two independent groups to determine if there is a statistically significant difference between them. Null Hypothesis (H 0 ): The two population means have a difference of d (μ 1 -μ 2 =d). If d is 0, the null hypothesis states that the two population means are equal (μ 1 =μ 2 ). Alternative Hypothesis (H 1 ): The difference between two population means is not d (μ 1 -μ 2 ≠d), which can also be directional (μ 1 -μ 2 >d or μ 1 -μ 2 <d). If d is 0, the alternative hypothesis becomes μ 1 ≠μ 2 , or μ 1 >μ 2 or μ 1 <μ 2 if it is directional. The formula for calculating the Z-statistic in a two-sample Z-test is: Z =   (x̅ - x̅ ) - (μ - μ )   √ σ n σ n x̅ 1 and x̅ 2 are the sample means of groups 1 and 2, respectively μ 1 and μ 2 are the population means, with μ 1 - μ 2 = d. d is often hypothesized to be zero under the null hypothesis. σ 1 and σ 2 are the population standard deviations n 1 and n 2 are the sample sizes of the two groups Example: Consider two groups of employees from different branches of a company undergoing training. Group A has 50 employees with an average score of 80 and a standard deviation of 10, and Group B has 50 employees with an average score of 75 and a standard deviation of 12. To test if there's a significant difference: Z =   (80 - 75) - 0   √ 10 50 12 50   5   2.21 This Z-value is then compared to the critical Z-values to assess significance. The critical value of a 0.05 significance level is around ±1.95. The Z-value of 2.26 is more than 1.95. Therefore, the two group has significant difference at 0.05 significance level. Significance Level The significance level (α) is a critical concept in hypothesis testing. It represents the probability threshold below which the null hypothesis will be rejected. Common levels are 0.05 (5%) or 0.01 (1%). The choice of α affects the Z-critical value, which is used to determine whether to reject the null hypothesis based on the computed Z-score. Critical Value: This is a point on the Z-distribution that the test statistic must exceed to reject the null hypothesis. For instance, at a 5% significance level in a two-tailed test, the critical values are approximately ±1.96. The significance level (probability) and critical value (Z-score) can be converted with each other the Z-distribution table or use our Z/P converter . Using the above examples, if the computed Z-scores exceed the respective critical values, the null hypotheses in each case would be rejected, indicating a statistically significant difference as per the alternative hypotheses. These examples demonstrate how the Z-test is applied in different scenarios to test hypotheses concerning population means. One Sample T Test Calculator Enter sample data Reporting results in APA style One sample t-test, what is a one sample t-test, how to use the one sample t test calculator, calculators. Null Hypothesis Calculator: Quick & Accurate Statistical Analysis This null hypothesis calculator helps you determine the statistical significance of your data set by calculating the probability of observing your results under the null hypothesis. How to Use the Null Hypothesis Calculator To use the null hypothesis calculator, enter the sample mean, hypothesized population mean, sample standard deviation, and sample size into their respective fields. Then press the “Calculate” button, and the calculator will display the test statistic used to determine if the null hypothesis can be rejected. How It Calculates the Results The calculator computes the test statistic by using the formula: ( z = frac{(bar{x} – mu_0)}{(sigma / sqrt{n})} ) ( bar{x} ) is the sample mean ( mu_0 ) is the hypothesized population mean ( sigma ) is the standard deviation of the sample ( n ) is the sample size This test statistic is then used in statistical hypothesis testing to determine if there is enough evidence to reject the null hypothesis at a certain significance level. Limitations The calculator presumes that the sample data are representative of the population and that the sampling distribution of the mean is approximately normally distributed, especially as the sample size becomes large (Central Limit Theorem). It also assumes that an accurate standard deviation is known and that the sample is drawn randomly. Be aware that for smaller sample sizes, particularly under 30, this calculator may not provide accurate results because the central limit theorem applies better to larger samples. For small samples, other techniques or adjustments (like t-tests) typically need to be used. Other Resources and Tools Empirical Rule Calculator – Quick & Accurate Statistical Analysis F Value Calculator – Quick Statistical Analysis Tool P Value Calculator – Accurate Statistical Analysis AP Stats Calculator – Easy Statistical Analysis Average Deviation Calculator: Quick & Accurate Statistical Tool Calculators Descriptive Statistics Merchandise Which Statistics Test? T Test Calculator for 2 Dependent Means The t -test for dependent means (also called a repeated-measures t -test, paired samples t -test, matched pairs t -test and matched samples t -test) is used to compare the means of two sets of scores that are directly related to each other. So, for example, it could be used to test whether subjects' galvanic skin responses are different under two conditions - first, on exposure to a photograph of a beach scene; second, on exposure to a photograph of a spider. Requirements The data is normally distributed Scale of measurement should be interval or ratio The two sets of scores are paired or matched in some way Null Hypothesis H 0 : U D = U 1 - U 2 = 0, where U D equals the mean of the population of difference scores across the two measurements. Single Proportion Hypothesis Test Calculator Use the calculator below to analyze the results of a single proportion hypothesis test. Enter your null hypothesis's proportion, sample proportion, sample size, test type, and significance level. You will find a description of how to conduct a hypothesis test of a proportion below the calculator. Define the z-test Significance Level Sample Proportion z-score Probability Sample Proportion Under the Null Distribution Conducting single proportion hypothesis tests. A hypothesis test of a sample proportion can help you make inferences about the population from which you drew it. It is a tool to determine what is probably true about an event or phenomena. Testing a Proportion For the results of a hypothesis test to be valid, you should follow these steps: Check Your Conditions State your hypothesis, determine your analysis plan, analyze your sample, interpret your results. To use the testing procedure described below, you should check the following conditions: Binary Outcomes - When conducting a hypothesis test for a proportion, each sample point should consist of only one of two outcomes. We often label one outcome a “success” and one outcome a “failure,” but it does not matter which of the two outcomes gets which label. Success-Failure Rate - Your sample size should be large enough that under the null hypothesis proportion you are likely to see at least 10 “success” and 10 “failures.” For example, if you have null hypothesis proportion with a 10% or 0.1 “success” rate, then you would need a sample of 100 [10 = 100 * 10%] to have a large enough sample to meet this condition. This condition helps ensure that the sampling distribution from which you collect your sample reasonably follows the Normal Distribution. Simple Random Sampling - You should collect your sample with simple random sampling. This type of sampling requires that every occurrence of a category or event in a population has an equal chance of being selected when taking a sample. Sample-to-Population Ratio - The population should be much larger than the sample you collect. As a rule-of-thumb, the sample size should represent no more than 5% of the population. You must state a null hypothesis and an alternative hypothesis to conduct a hypothesis test for a proportion. The null hypothesis, is a skeptical claim that you would like to test. It is defined by a hypothesized proportion, which is often labeled P 0 . The alternative hypothesis represents an alternative claim to the null hypothesis. Your null hypothesis and alternative hypothesis should be stated in one of three mutually exclusive ways listed in the table below. Null Hypothesis Alternative Hypothesis Number of Tails Description Tests whether the population defined by the proportion, P, from which you drew your sample is different from the population defined by the null hypothesis's proportion, P . Tests whether the population defined by the proportion, P, from which you drew your sample is greater than the population defined by the null hypothesis's proportion, P . Tests whether the population defined by the proportion, P, from which you drew your sample is less than the population defined by null hypothesis's proportion, P . Before conducting a hypothesis test, you must determine a reasonable significance level , α, or the probability of rejecting the null hypothesis assuming it is true. The lower your significance level, the more confident you can be of the conclusion of your hypothesis test. Common significance levels are 10%, 5%, and 1%. To evaluate your hypothesis test at the significance level that you set, consider if you are conducting a one or two tail test: Two-tail tests divide the rejection region, or critical region, evenly above and below the null distribution, i.e. to the tails of the null sampling distribution. For example, in a two-tail test with a 5% significance level, your rejection region would be the upper and lower 2.5% of the null distribution. An alternative hypothesis of P ≠ P 0 requires a two-tail test. One-tail tests place the rejection region entirely on one side of the null distribution i.e. to the right or left tail of the null sampling distribution. For example, in a one-tail test evaluating if the sampling distribution is above the null sampling distribution with a 5% significance level, your rejection region would be the upper 5% of the null distribution. P > P 0 and P < P 0 alternative hypotheses require one-tail tests. The graphical results section of the calculator above shades rejection regions blue. After checking your conditions, stating your hypothesis, determining your significance level, α, and collecting your sample, you are ready to analyze your hypothesis. Sample proportions follow the Normal Distribution with the following parameters (i.e. numbers that define the distribution): The Population Proportion, P - The population proportion is assumed to be the proportion given by the null hypothesis in a single proportion hypothesis test. The Standard Error, SE - The standard error can be computed as follows: SE = sqrt((P x (1 - P))/ n), with n being the sample size. It defines how sample proportions are expected to vary around the null hypothesis's proportion given the sample size and under the assumption that the null hypothesis is true. In a single proportion hypothesis test, we calculate the probability that we would observe the sample proportion, p, assuming the null hypothesis is true, also known as the p-value . If the p-value is less than the significance level, then we can reject the null hypothesis. You can determine a precise p-value using the calculator above, but we can find an estimate of the p-value manually by calculating the z-score as follows: z = (p - P) / SE The z-score is a test statistic that tells us how far our observation is from the null hypothesis's proportion under the null distribution. Using any z-score table, we can look up the probability of observing the results under the null distribution. You will need to look up the z-score for the type of test you are conducting, i.e. one or two tail. A hypothesis test for a proportion is sometimes known as a z-test because of the use of a z-score in analyzing results. If we find the probability is below the significance level, we reject the null hypothesis. The conclusion of a hypothesis test for a proportion is always either: Reject the null hypothesis Do not reject the null hypothesis If you reject the null hypothesis, you cannot say that your sample proportion is the true population proportion. If you do not reject the null hypothesis, you cannot say that the null hypothesis is true. A hypothesis test is simply a way to look at a sample and conclude if it provides sufficient evidence to reject the null hypothesis. Example: Hypothesis Test for a Proportion Let’s say you are the Marketing Director of a software company. You have set up a demo request page on your website, and you believe that 40% of visitors to that page will request a demo. You decide to test your claim that 40% of visitors to the demo page will request a demo. So, you decide to run a hypothesis test for a proportion with a sample size of 500 visitors. Let’s go through the steps you would take to run the test. Check the conditions - Your test consists of binary outcomes (i.e. request demo and not request demo), your sample size is large enough to meet the success-failure condition but not too large to violate the sample-to-population ratio condition, and you collect your sample using simple random sampling . So, your test satisfies the conditions for a z-test of a single proportion. State Your Hypothesis - Your null hypothesis is that the true proportion of visitors requesting a demo equals 40%, formally stated P = 40%. Your alternate hypothesis is that the true proportion of vistors requesting a demo does not equal 40%, formally stated P ≠ 40%. Determine Your Analysis Plan - You believe that a 5% significance level is reasonable. As your test is two-tail test, you will evaluate if your sample proportion would occur at the upper or lower 2.5% [2.5% = 5%/2] of the null distribution. Analyze Your Sample - You collect your samle (which you do after steps 1-3). You find that the proportion of visitors request a demo in your sample is 44%. Using the calculator above, you find that a sample proportion of 44% would results in a z-score of 1.83 under the null distribution, which translates to a p-value of 6.79%. Interpret Your Results - Since your p-value of 6.79% is greater than the significance level of 5%, you do not have sufficient evidence to reject the null hypothesis. In this example, you found that you cannot reject your original claim that 40% of your demo webpage vistors request demos. The test does not guarantee that your 40% figure is correct, but it does give you confidence that you do not have sufficient evidence to say otherwise. An Overview of Descriptive vs. Inferential Statistics Statistics serve as the backbone of understanding and interpreting data and gives the ability to analyze and draw conclusions from information in the world. Broadly, there are two types of statistics: descriptive and inferential. This article will delve into the key concepts, techniques, and applications of each type, highlighting their differences and their importance. Understanding Descriptive Statistics Descriptive statistics is used to summarize a given dataset’s basic features to aid in understanding what the data means. It includes measures of central tendency (such as the mean, median, and mode) that are used to describe the center of the dataset. It also includes methods of dispersion (such as the range, variance, and standard deviation) that describe how spread out the data is around those measures of central tendency. Many data visualizations also fall under descriptive statistics, such as histograms or scatterplots.   Descriptive statistics are used extensively to provide a summary of any given dataset. For example, in the field of economics, descriptive statistics would include measures of GDP or unemployment rates. In business, it would include the number of sales per department over the last quarter. Basic correlation analysis can also be included in descriptive statistics. The advantages of descriptive statistics are that they are easy to compute and understand. They provide a clear and concise summary of large datasets. However, they are limited in that descriptive statistics can only describe data. They cannot be used to make predictions or provide support for statistical hypotheses. Understanding Inferential Statistics Inferential statistics are techniques that allow statisticians to use data from a sample to make inferences or predictions for a larger population. Central to inferential statistics is the idea of hypothesis testing where data from a subset of the population is used to provide probabilistic support for a hypothesis about the larger population. Inferential statistics includes a wide range of statistical tests and methods. For example, the t-test can be used to compare the means of two independent groups, or the mean of one group to a hypothesized mean. An analysis of variance test (ANOVA) can compare these means across three or more independent groups. Chi-square tests can determine if there is an association between two categorical variables. There are many other techniques as well, such as regression analysis, factor analysis, and survival analysis. A clear benefit of inferential statistics is that they allow for predictions and generalizations using a sample dataset. However, there are some limitations to consider. Interpreting the results of inferential statistics tests can be difficult. The validity and accuracy of the results also depends strongly on the sample size of the available dataset. Key Differences Between Descriptive and Inferential Statistics Purpose : Descriptive statistics are used to summarize a dataset while the purpose of inferential statistics is to make predictions about a larger population based on a dataset. Scope : Descriptive statistics are limited to only the available data while inferential statistics is designed to extend from the provided sample to the larger population and make probabilistically-informed generalizations. Data Representation : Descriptive statistics utilizes single number summaries, such as the mean or standard deviation, along with graphs and charts. Inferential statistics relies on probabilities and results of hypothesis tests. How to Choose the Right Approach Choosing between descriptive and inferential statistics depends on the research question, the nature of the data, and the objectives of the analysis. Descriptive statistics should be used when the goal is to provide a straightforward summary of the data, or if existing data needs to be presented visually in a clear, understandable format. Descriptives are also critical to the exploratory data analysis stage of any large statistical or data-driven project. Inferential statistics should be used when the goal is to make predictions about a population or if a hypothesis about the data is being tested. It can also provide a more robust understanding of the relationships between variables. Practically, both methods are combined in most statistical applications. There is often a descriptive phase where the basic characteristics of the data are explored and understood. Insights from this phase then drive the inferential phase of statistical analysis. Featured Posts Mehrnaz holds a Masters in Data Analytics and is a full time biostatistician working on complex machine learning development and statistical analysis in healthcare. She has experience with AI and has taught university courses in biostatistics and machine learning at University of the People. Leave a Reply Cancel reply Your email address will not be published. Required fields are marked * Join the Statology Community Sign up to receive Statology's exclusive study resource: 100 practice problems with step-by-step solutions. Plus, get our latest insights, tutorials, and data analysis tips straight to your inbox! By subscribing you accept Statology's Privacy Policy. 187 IMAGES Hypothesis Testing Formula hypothesis test formula statistics Hypothesis Testing Population Mean One Tailed Binomial Hypothesis Testing on Casio fx-CG50 Calculator Hypothesis Testing Statistics Formula Sheet P value from hypothesis test calculator VIDEO What is a hypothesis test? A beginner's guide to hypothesis testing! How to Conduct an Independent Samples t-test in Excel || Independent Samples Hypothesis Testing Hypothesis testing-Null and Alternative hypothesis Hypothesis Testing Hypothesis Testing in 17 Seconds Hypothesis testing: Lower tail test with R COMMENTS Hypothesis Testing Calculator with Steps Hypothesis Testing Calculator. The first step in hypothesis testing is to calculate the test statistic. The formula for the test statistic depends on whether the population standard deviation (σ) is known or unknown. If σ is known, our hypothesis test is known as a z test and we use the z distribution. If σ is unknown, our hypothesis test is ... Hypothesis Test Calculator Calculation Example: There are six steps you would follow in hypothesis testing: Formulate the null and alternative hypotheses in three different ways: H 0: θ = θ 0 v e r s u s H 1: θ ≠ θ 0. H 0: θ ≤ θ 0 v e r s u s H 1: θ > θ 0. H 0: θ ≥ θ 0 v e r s u s H 1: θ < θ 0. Hypothesis testing calculator Hypothesis testing is an important part of statistical analysis because it allows you to make population-level inferences based on sample data. Our calculator makes this process easier by providing user-friendly interfaces and step-by-step directions for performing different tests. Hypothesis Testing Calculator Online Hypothesis testing is a foundational method used in statistics to infer the validity of a hypothesis about a population parameter. The Hypothesis Testing Calculator facilitates this process by automating the computations necessary for the t-test, a method used to compare sample means against a hypothesized mean or against each other.Let's delve into the formulas this calculator uses to ... t-test Calculator Recall, that in the critical values approach to hypothesis testing, you need to set a significance level, α, before computing the critical values, which in turn give rise to critical regions (a.k.a. rejection regions). Formulas for critical values employ the quantile function of t-distribution, i.e., the inverse of the cdf:. Critical value for left-tailed t-test: Online Statistics Calculator: Hypothesis testing, t-test, chi-square Hypothesis Test. Here you will find everything about hypothesis testing: One sample t-test, Unpaired t-test, Paired t-test and Chi-square test. You will also find tutorials for non-parametric statistical procedures such as the Mann-Whitney u-Test and Wilcoxon-Test. mann-whitney-u-test and the Wilcoxon test One sample t test calculator Select Data Type: Choose whether to input summary statistics directly or provide a data set. Input Your Data: Enter the required values such as population mean, sample size, sample mean, and sample standard deviation. Set Hypotheses: Specify the null and alternative hypotheses. Calculate: Click the "Calculate" button to see the test statistic ... Hypothesis Test Calculator: t-test, chi-square, analysis of variance Copy your data into the table. Select the variables. In the hypothesis test calculator you can calculate e.g. a t-test, a chi-square test, a binomial test or an analysis of variance. If you need a more detailed explanation, you can find more information in the tutorials. In order to use the hypothesis test calculator, you must first formulate ... Test Statistic Calculator A particular statistical calculation that figures out the relationship between the sample and its population is known as the test statistics. It's a score that is used in the hypothesis test and informs about how likely the results are under the assumption that the null hypothesis is true. T-Test Calculator for 2 Independent Means This simple t -test calculator, provides full details of the t-test calculation, including sample mean, sum of squares and standard deviation. A t -test is used when you're looking at a numerical variable - for example, height - and then comparing the averages of two separate populations or groups (e.g., males and females). Calculators Phi Coefficient Calculator. Hypothesis Tests One Sample t-test Calculator Two Sample t-test Calculator One Sample Z-Test Calculator Two Sample Z-Test Calculator Welch's t-test Calculator ... Statology makes learning statistics easy by explaining topics in simple and straightforward ways. Our team of writers have over 40 years of experience in ... Single Sample T-Test Calculator A single sample t-test (or one sample t-test) is used to compare the mean of a single sample of scores to a known or hypothetical population mean. So, for example, it could be used to determine whether the mean diastolic blood pressure of a particular group differs from 85, a value determined by a previous study. Requirements. P-value Calculator P-value Calculator. Please provide any one value below to compute p-value from z-score or vice versa for a normal distribution. A p-value (probability value) is a value used in statistical hypothesis testing that is intended to determine whether the obtained results are significant. In statistical hypothesis testing, the null hypothesis is a ... Z-test for One Population Mean Instructions: This calculator conducts a Z-test for one population mean (\ (\mu\)), with known population standard deviation (\ (\sigma\)). Please select the null and alternative hypotheses, type the hypothesized mean, the significance level, the sample mean, the population standard deviation, and the sample size, and the results of the z-test ... Z-test for two Means, with Known Population Standard Deviations Instructions: This calculator conducts a Z-test for two population means ( \mu_1 μ1 and \mu_2 μ2 ), with known population standard deviations ( \sigma_1 σ1 and \sigma_2 σ2 ). Please select the null and alternative hypotheses, type the significance level, the sample means, the population standard deviations, the sample sizes, and the results ... Difference in Means Hypothesis Test Calculator Use the calculator below to analyze the results of a difference in sample means hypothesis test. Enter your sample means, sample standard deviations, sample sizes, hypothesized difference in means, test type, and significance level to calculate your results. You will find a description of how to conduct a two sample t-test below the calculator. Z-Test Calculator The significance level (α) is a critical concept in hypothesis testing. It represents the probability threshold below which the null hypothesis will be rejected. Common levels are 0.05 (5%) or 0.01 (1%). The choice of α affects the Z-critical value, which is used to determine whether to reject the null hypothesis based on the computed Z-score. Test Statistic Calculator The test value calculator transforms the data analysis by simplifying the hypothesis testing. Attach to the guide below to utilize the test statistics calculator. Input: Choose the point that you want to calculate. Put the values according to the chosen value. Tap on "Calculate". One Sample T Test Calculator The one-sample t-test determines if the mean of a single sample is significantly different from a known population mean. The one sample t-test calculator calculates the one sample t-test p-value and the effect size. When you enter the raw data, the one sample t-test calculator provides also the Shapiro-Wilk normality test result and the outliers. Null Hypothesis Calculator: Quick & Accurate Statistical Analysis This test statistic is then used in statistical hypothesis testing to determine if there is enough evidence to reject the null hypothesis at a certain significance level. Limitations The calculator presumes that the sample data are representative of the population and that the sampling distribution of the mean is approximately normally ... T-Test Calculator for 2 Dependent Means Scale of measurement should be interval or ratio. The two sets of scores are paired or matched in some way. Null Hypothesis. H 0: U D = U 1 - U 2 = 0, where U D equals the mean of the population of difference scores across the two measurements. Equation. A T-test calculator that compares 2 dependent population means for statistical significance. Single Proportion Hypothesis Test Calculator A hypothesis test for a proportion is sometimes known as a z-test because of the use of a z-score in analyzing results. If we find the probability is below the significance level, we reject the null hypothesis. Interpret Your Results. The conclusion of a hypothesis test for a proportion is always either: Reject the null hypothesis An Overview of Descriptive vs. Inferential Statistics Inferential statistics are techniques that allow statisticians to use data from a sample to make inferences or predictions for a larger population. Central to inferential statistics is the idea of hypothesis testing where data from a subset of the population is used to provide probabilistic support for a hypothesis about the larger population. assignment essay homework paper phd report resume review speech thesis