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Imagine spending months or even years developing a new feature only to find out it doesn’t resonate with your users, argh! This kind of situation could be any worst Product manager’s nightmare.
There's a way to fix this problem called the Value Hypothesis . This idea helps builders to validate whether the ideas they’re working on are worth pursuing and useful to the people they want to sell to.
This guide will teach you what you need to know about Value Hypothesis and a step-by-step process on how to create a strong one. At the end of this post, you’ll learn how to create a product that satisfies your users.
Are you ready? Let’s get to it!
Scrutinizing this hypothesis helps you as a developer to come up with a product that your customers like and love to use.
Product managers use the Value Hypothesis as a north star, ensuring focus on client needs and avoiding wasted resources. For more on this, read about the product management process .
Let's get into the step-by-step process, but first, we need to understand the basics of the Value Hypothesis:
A Value Hypothesis is like a smart guess you can test to see if your product truly solves a problem for your customers. It’s your way of predicting how well your product will address a particular issue for the people you’re trying to help.
You need to know what a Value Hypothesis is, what it covers, and its key parts before you use it. To learn more about finding out what customers need, take a look at our guide on discovering features .
The Value Hypothesis does more than just help with the initial launch, it guides the whole development process. This keeps teams focused on what their users care about helping them choose features that their audience will like.
A strong Value Hypothesis rests on three key components:
Value Proposition: The Value Proposition spells out the main advantage your product gives to customers. It explains the "what" and "why" of your product showing how it eases a particular pain point.
This proposition targets a specific group of consumers. To learn more, check out our guide on roadmapping .
Customer Segmentation: Knowing and grasping your target audience is essential. This involves studying their demographics, needs, behaviors, and problems. By dividing your market, you can shape your value proposition to address the unique needs of each group.
Customer feedback surveys can prove priceless in this process. Find out more about this in our customer feedback surveys guide.
Problem Statement : The Problem Statement defines the exact issue your product aims to fix. It should zero in on a real fixable pain point your target users face. For hands-on applications, see our product launch communication plan .
Here are some key questions to guide you:
What are the primary challenges and obstacles faced by your target users?
What existing solutions are available, and where do they fall short?
What unmet needs or desires does your target audience have?
For a structured approach to prioritizing features based on customer needs, consider using a feature prioritization matrix .
Now that we've covered the basics, let's look at how to build a convincing Value Hypothesis. Here's a two-step method, along with value hypothesis templates, to point you in the right direction:
To start with, you need to carry out market research. By carrying out proper market research, you will have an understanding of existing solutions and identify areas in which customers' needs are yet to be met. This is integral to effective idea tracking .
Next, use customer interviews, surveys, and support data to understand your target audience's problems and what they want. Check out our list of tools for getting customer feedback to help with this.
Once you've completed your research, it's crucial to identify your customers' needs. By merging insights from market research with direct user feedback, you can pinpoint the key requirements of your customers.
Here are some key questions to think about:
What are the most significant challenges that your target users encounter daily?
Which current solutions are available to them, and how do these solutions fail to fully address their needs?
What specific pain points are your target users struggling with that aren't being resolved?
Are there any gaps or shortcomings in the existing products or services that your customers use?
What unfulfilled needs or desires does your target audience express that aren't currently met by the market?
To prioritize features based on customer needs in a structured way, think about using a feature prioritization matrix .
Once you've created your Value Hypothesis with a template, you need to check if it holds up. Here's how you can do this:
Build a minimum viable product (MVP)—a basic version of your product with essential functions. This lets you test your value proposition with actual users and get feedback without spending too much. To achieve the best outcomes, look into the best practices for customer feedback software .
Build mock-ups to show your product idea. Use these mock-ups to get user input on the user experience and overall value offer.
After you've gathered data about your hypothesis, it's time to examine it. Here are some metrics you can use:
User Engagement : Monitor stats like time on the platform, feature use, and return visits to see how much users interact with your MVP or mock-up.
Conversion Rates : Check conversion rates for key actions like sign-ups, buys, or feature adoption. These numbers help you judge if your value offer clicks with users. To learn more, read our article on SaaS growth benchmarks .
The Value Hypothesis framework shines because you can keep making it better. Here's how to fine-tune your hypothesis:
Set up an ongoing system to gather user data as you develop your product.
Look at what users say to spot areas that need work then update your value proposition based on what you learn.
Read about managing product updates to keep your hypotheses current.
The market keeps changing, and your Value Hypothesis should too. Stay up to date on what's happening in your industry and watch how users' habits change. Tweak your value proposition to stay useful and ahead of the competition.
Here are some ways to keep your Value Hypothesis fresh:
Do market research often to keep up with what's happening in your industry and what your competitors are up to.
Keep an eye on what users are saying to spot new problems or things they need but don't have yet.
Try out different value statements and features to see which ones your audience likes best.
To keep your guesses up-to-date, check out our guide on handling product changes .
While the Value Hypothesis approach is powerful, it's key to steer clear of these common traps:
Avoid Confirmation Bias : People tend to focus on data that backs up their initial guesses. But it's key to look at feedback that goes against your ideas and stay open to different views.
Watch out for Shiny Object Syndrome : Don't let the newest fads sway you unless they solve a main customer problem. Your value proposition should fix actual issues for your users.
Don't Cling to Your First Hypothesis : As the market changes, your value proposition should too. Be ready to shift your hypothesis when new evidence and user feedback comes in.
Don't Mix Up Busywork with Real Progress : Getting user feedback is key, but making sense of it brings real value. Look at the data to find useful insights that can shape your product. To learn more about this, check out our guide on handling customer feedback .
To build a product that succeeds, you need to know your target users inside out and understand how you help them. The Value Hypothesis framework gives you a step-by-step way to do this.
If you follow the steps in this guide, you can create a strong value proposition, check if it works, and keep improving it to ensure your product stays useful and important to your customers.
Keep in mind, a good Value Hypothesis changes as your product and market change. When you use data and put customers first, you're on the right track to create a product that works.
Want to put the Value Hypothesis framework into action? Check out our top templates for creating product roadmaps to streamline your process. Think about using featureOS to manage customer feedback. This tool makes it easier to collect, examine, and put user feedback to work.
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We introduce a projection-based test for assessing logistic regression models using the empirical residual marked empirical process and suggest a model-based bootstrap procedure to calculate critical values. We comprehensively compare this test and Stute and Zhu’s test with several commonly used goodness-of-fit (GoF) tests: the Hosmer–Lemeshow test, modified Hosmer–Lemeshow test, Osius–Rojek test, and Stukel test for logistic regression models in terms of type I error control and power performance in small ( \(n=50\) ), moderate ( \(n=100\) ), and large ( \(n=500\) ) sample sizes. We assess the power performance for two commonly encountered situations: nonlinear and interaction departures from the null hypothesis. All tests except the modified Hosmer–Lemeshow test and Osius–Rojek test have the correct size in all sample sizes. The power performance of the projection based test consistently outperforms its competitors. We apply these tests to analyze an AIDS dataset and a cancer dataset. For the former, all tests except the projection-based test do not reject a simple linear function in the logit, which has been illustrated to be deficient in the literature. For the latter dataset, the Hosmer–Lemeshow test, modified Hosmer–Lemeshow test, and Osius–Rojek test fail to detect the quadratic form in the logit, which was detected by the Stukel test, Stute and Zhu’s test, and the projection-based test.
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Chen, K., Hu, I., Ying, Z.: Strong consistency of maximum quasi-likelihood estimators in generalized linear models with fixed and adaptive designs. Ann. Stat. 27 (4), 1155–1163 (1999)
Article MathSciNet Google Scholar
Dardis, C.: LogisticDx: diagnostic tests and plots for logistic regression models. R package version 0.3 (2022)
Dikta, G., Kvesic, M., Schmidt, C.: Bootstrap approximations in model checks for binary data. J. Am. Stat. Assoc. 101 , 521–530 (2006)
Ekanem, I.A., Parkin, D.M.: Five year cancer incidence in Calabar, Nigeria (2009–2013). Cancer Epidemiol. 42 , 167–172 (2016)
Article Google Scholar
Escanciano, J.C.: A consistent diagnostic test for regression models using projections. Economet. Theor. 22 , 1030–1051 (2006)
Härdle, W., Mammen, E., Müller, M.: Testing parametric versus semiparametric modeling in generalized linear models. J. Am. Stat. Assoc. 93 , 1461–1474 (1998)
MathSciNet Google Scholar
Harrell, F.E.: rms: Regression modeling strategies. R package version 6.3-0 (2022)
Hosmer, D.W., Hjort, N.L.: Goodness-of-fit processes for logistic regression: simulation results. Stat. Med. 21 (18), 2723–2738 (2002)
Hosmer, D.W., Lemesbow, S.: Goodness of fit tests for the multiple logistic regression model. Commun Stat Theory Methods 9 , 1043–1069 (1980)
Hosmer, D.W., Hosmer, T., Le Cessie, S., Lemeshow, S.: A comparison of goodness-of-fit tests for the logistic regression model. Stat. Med. 16 (9), 965–980 (1997)
Hosmer, D., Lemeshow, S., Sturdivant, R.: Applied Logistic Regression. Wiley Series in Probability and Statistics, Wiley, New York (2013)
Book Google Scholar
Jones, L.K.: On a conjecture of Huber concerning the convergence of projection pursuit regression. Ann. Stat. 15 , 880–882 (1987)
Kohl, M.: MKmisc: miscellaneous functions from M. Kohl. R package version, vol. 1, p. 8 (2021)
Kosorok, M.R.: Introduction to Empirical Processes and Semiparametric Inference, vol. 61. Springer, New York (2008)
Lee, S.-M., Tran, P.-L., Li, C.-S.: Goodness-of-fit tests for a logistic regression model with missing covariates. Stat. Methods Med. Res. 31 , 1031–1050 (2022)
Lindsey, J.K.: Applying Generalized Linear Models. Springer, Berlin (2000)
McCullagh, P., Nelder, J.A.: Generalized Linear Models, vol. 37. Chapman and Hall (1989)
Nelder, J.A., Wedderburn, R.W.M.: Generalized linear models. J. R. Stat. Soc. Ser. A 135 , 370–384 (1972)
Oguntunde, P.E., Adejumo, A.O., Okagbue, H.I.: Breast cancer patients in Nigeria: data exploration approach. Data Brief 15 , 47 (2017)
Osius, G., Rojek, D.: Normal goodness-of-fit tests for multinomial models with large degrees of freedom. J. Am. Stat. Assoc. 87 (420), 1145–1152 (1992)
Rady, E.-H.A., Abonazel, M.R., Metawe’e, M.H.: A comparison study of goodness of fit tests of logistic regression in R: simulation and application to breast cancer data. Appl. Math. Sci. 7 , 50–59 (2021)
Google Scholar
Stukel, T.A.: Generalized logistic models. J. Am. Stat. Assoc. 83 (402), 426–431 (1988)
Stute, W., Zhu, L.-X.: Model checks for generalized linear models. Scand. J. Stat. Theory Appl. 29 , 535–545 (2002)
van der Vaart, A.W., Wellner, J.A.: Weak Convergence and Empirical Processes. Springer (1996)
van Heel, M., Dikta, G., Braekers, R.: Bootstrap based goodness-of-fit tests for binary multivariate regression models. J. Korean Stat. Soc. 51 (1), 308–335 (2022)
Yin, C., Zhao, L., Wei, C.: Asymptotic normality and strong consistency of maximum quasi-likelihood estimates in generalized linear models. Sci. China Ser. A Math. 49 , 145–157 (2006)
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Li’s research was partially supported by NNSFC grant 11871294. Härdle gratefully acknowledges support through the European Cooperation in Science & Technology COST Action grant CA19130 - Fintech and Artificial Intelligence in Finance - Towards a transparent financial industry; the project “IDA Institute of Digital Assets”, CF166/15.11.2022, contract number CN760046/ 23.05.2024 financed under the Romanias National Recovery and Resilience Plan, Apel nr. PNRR-III-C9-2022-I8; and the Marie Skłodowska-Curie Actions under the European Union’s Horizon Europe research and innovation program for the Industrial Doctoral Network on Digital Finance, acronym DIGITAL, Project No. 101119635
Authors and affiliations.
Department of Statistics, South China University of Technology, Guangzhou, China
Huiling Liu
School of Mathematics and Statistics, Qingdao University, Shandong, 266071, China
Center for Statistics and Data Science, Beijing Normal University, Zhuhai, 519087, China
Feifei Chen
BRC Blockchain Research Center, Humboldt-Universität zu Berlin, 10178, Berlin, Germany
Wolfgang Härdle
Dept Information Management and Finance, National Yang Ming Chiao Tung U, Hsinchu, Taiwan
IDA Institute Digital Assets, Bucharest University of Economic Studies, Bucharest, Romania
Department of Statistics, George Washington University, Washington, DC, 20052, USA
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LHL, LXM and LH wrote the main manuscript text, LHL and CFF program, HW commented on the methodological section. All authors reviewed the manuscript.
Correspondence to Hua Liang .
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Liu, H., Li, X., Chen, F. et al. A comprehensive comparison of goodness-of-fit tests for logistic regression models. Stat Comput 34 , 175 (2024). https://doi.org/10.1007/s11222-024-10487-5
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DOI : https://doi.org/10.1007/s11222-024-10487-5
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Table of contents. Step 1: State your null and alternate hypothesis. Step 2: Collect data. Step 3: Perform a statistical test. Step 4: Decide whether to reject or fail to reject your null hypothesis. Step 5: Present your findings. Other interesting articles. Frequently asked questions about hypothesis testing.
6. Write a null hypothesis. If your research involves statistical hypothesis testing, you will also have to write a null hypothesis. The null hypothesis is the default position that there is no association between the variables. The null hypothesis is written as H 0, while the alternative hypothesis is H 1 or H a.
The treatment group's mean is 58.70, compared to the control group's mean of 48.12. The mean difference is 10.67 points. Use the test's p-value and significance level to determine whether this difference is likely a product of random fluctuation in the sample or a genuine population effect.. Because the p-value (0.000) is less than the standard significance level of 0.05, the results are ...
Hypothesis testing is a scientific method used for making a decision and drawing conclusions by using a statistical approach. It is used to suggest new ideas by testing theories to know whether or not the sample data supports research. A research hypothesis is a predictive statement that has to be tested using scientific methods that join an ...
Photo from StepUp Analytics. Hypothesis testing is a method of statistical inference that considers the null hypothesis H₀ vs. the alternative hypothesis Ha, where we are typically looking to assess evidence against H₀. Such a test is used to compare data sets against one another, or compare a data set against some external standard. The former being a two sample test (independent or ...
Hypothesis testing is a crucial procedure to perform when you want to make inferences about a population using a random sample. These inferences include estimating population properties such as the mean, differences between means, proportions, and the relationships between variables. This post provides an overview of statistical hypothesis testing.
In hypothesis testing, the goal is to see if there is sufficient statistical evidence to reject a presumed null hypothesis in favor of a conjectured alternative hypothesis.The null hypothesis is usually denoted \(H_0\) while the alternative hypothesis is usually denoted \(H_1\). An hypothesis test is a statistical decision; the conclusion will either be to reject the null hypothesis in favor ...
Hypothesis testing is a fundamental technique in statistics, used to determine if there is enough evidence in a sample of data to infer that a certain condition holds for the entire population.
What is Hypothesis Testing? In simple terms, hypothesis testing is a method used to make decisions or inferences about population parameters based on sample data. Imagine being handed a dice and asked if it's biased. By rolling it a few times and analyzing the outcomes, you'd be engaging in the essence of hypothesis testing.
Step 5: Phrase your hypothesis in three ways. To identify the variables, you can write a simple prediction in if … then form. The first part of the sentence states the independent variable and the second part states the dependent variable. If a first-year student starts attending more lectures, then their exam scores will improve.
A test statistic is a numerical summary of a sample. It is a random variable as it is derived from a random sample. In hypothesis tests, it compares the sample statistic to the expected result of the null hypothesis. The selection of the test statistic is dependent on: Parametric vs. non-parametric; Number of samples (one, two, multiple)
5.2 - Writing Hypotheses. The first step in conducting a hypothesis test is to write the hypothesis statements that are going to be tested. For each test you will have a null hypothesis ( H 0) and an alternative hypothesis ( H a ). When writing hypotheses there are three things that we need to know: (1) the parameter that we are testing (2) the ...
If the biologist set her significance level \(\alpha\) at 0.05 and used the critical value approach to conduct her hypothesis test, she would reject the null hypothesis if her test statistic t* were less than -1.6939 (determined using statistical software or a t-table):s-3-3. Since the biologist's test statistic, t* = -4.60, is less than -1.6939, the biologist rejects the null hypothesis.
State and check the assumptions for a hypothesis test. A random sample of size n is taken. The population standard derivation is known. The sample size is at least 30 or the population of the random variable is normally distributed. Find the sample statistic, test statistic, and p-value. Conclusion; Interpretation; Solution. 1. x = life of battery
6. Test Statistic: The test statistic measures how close the sample has come to the null hypothesis. Its observed value changes randomly from one random sample to a different sample. A test statistic contains information about the data that is relevant for deciding whether to reject the null hypothesis or not.
3. One-Sided vs. Two-Sided Testing. When it's time to test your hypothesis, it's important to leverage the correct testing method. The two most common hypothesis testing methods are one-sided and two-sided tests, or one-tailed and two-tailed tests, respectively. Typically, you'd leverage a one-sided test when you have a strong conviction ...
The null hypothesis, denoted as H 0, is the hypothesis that the sample data occurs purely from chance. The alternative hypothesis, denoted as H 1 or H a, is the hypothesis that the sample data is influenced by some non-random cause. Hypothesis Tests. A hypothesis test consists of five steps: 1. State the hypotheses. State the null and ...
Hypothesis Testing. Investigators conducting studies need research questions and hypotheses to guide analyses. Starting with broad research questions (RQs), investigators then identify a gap in current clinical practice or research. ... With very large sample sizes, the p-value can be very low significant differences in the reduction of ...
7 Statistical hypothesis. A statistical hypothesis is when you test only a sample of a population and then apply statistical evidence to the results to draw a conclusion about the entire population. Instead of testing everything, you test only a portion and generalize the rest based on preexisting data. Examples:
Step 2: State the Alternate Hypothesis. The claim is that the students have above average IQ scores, so: H 1: μ > 100. The fact that we are looking for scores "greater than" a certain point means that this is a one-tailed test. Step 3: Draw a picture to help you visualize the problem. Step 4: State the alpha level.
Hypothesis tests # Formal hypothesis testing is perhaps the most prominent and widely-employed form of statistical analysis. It is sometimes seen as the most rigorous and definitive part of a statistical analysis, but it is also the source of many statistical controversies. The currently-prevalent approach to hypothesis testing dates to developments that took place between 1925 and 1940 ...
Hypothesis testing is a technique that is used to verify whether the results of an experiment are statistically significant. It involves the setting up of a null hypothesis and an alternate hypothesis. There are three types of tests that can be conducted under hypothesis testing - z test, t test, and chi square test.
Data from a sample is used in hypothesis testing to examine a given hypothesis. We must have a postulated parameter to conduct hypothesis testing. Bootstrap distributions and randomization distributions are created using comparable simulation techniques. The observed sample statistic is the focal point of a bootstrap distribution, whereas the ...
Hypothesis testing is a statistical method used to draw conclusions about populations from sample data, typically represented in tables. With the prevalence of graph representations in real-life applications, hypothesis testing on graphs is gaining importance. In this work, we formalize node, edge, and path hypotheses on attributed graphs.
How a Value Hypothesis Helps Product Managers. Scrutinizing this hypothesis helps you as a developer to come up with a product that your customers like and love to use. Product managers use the Value Hypothesis as a north star, ensuring focus on client needs and avoiding wasted resources. For more on this, read about the product management process.
We assess the power performance for two commonly encountered situations: nonlinear and interaction departures from the null hypothesis. All tests except the modified Hosmer-Lemeshow test and Osius-Rojek test have the correct size in all sample sizes. The power performance of the projection based test consistently outperforms its competitors.