hypothesis framework

Hypothesis Testing Framework

Now that we've seen an example and explored some of the themes for hypothesis testing, let's specify the procedure that we will follow.

Hypothesis Testing Steps

The formal framework and steps for hypothesis testing are as follows:

• Identify and define the parameter of interest
• Define the competing hypotheses to test
• Set the evidence threshold, formally called the significance level
• Generate or use theory to specify the sampling distribution and check conditions
• Calculate the test statistic and p-value
• Evaluate your results and write a conclusion in the context of the problem.

We'll discuss each of these steps below.

Identify Parameter of Interest

First, I like to specify and define the parameter of interest. What is the population that we are interested in? What characteristic are we measuring?

By defining our population of interest, we can confirm that we are truly using sample data. If we find that we actually have population data, our inference procedures are not needed. We could proceed by summarizing our population data.

By identifying and defining the parameter of interest, we can confirm that we use appropriate methods to summarize our variable of interest. We can also focus on the specific process needed for our parameter of interest.

In our example from the last page, the parameter of interest would be the population mean time that a host has been on Airbnb for the population of all Chicago listings on Airbnb in March 2023. We could represent this parameter with the symbol $\mu$. It is best practice to fully define $\mu$ both with words and symbol.

Define the Hypotheses

For hypothesis testing, we need to decide between two competing theories. These theories must be statements about the parameter. Although we won't have the population data to definitively select the correct theory, we will use our sample data to determine how reasonable our "skeptic's theory" is.

The first hypothesis is called the null hypothesis, $H_0$. This can be thought of as the "status quo", the "skeptic's theory", or that nothing is happening.

Examples of null hypotheses include that the population proportion is equal to 0.5 ($p = 0.5$), the population median is equal to 12 ($M = 12$), or the population mean is equal to 14.5 ($\mu = 14.5$).

The second hypothesis is called the alternative hypothesis, $H_a$ or $H_1$. This can be thought of as the "researcher's hypothesis" or that something is happening. This is what we'd like to convince the skeptic to believe. In most cases, the desired outcome of the researcher is to conclude that the alternative hypothesis is reasonable to use moving forward.

Examples of alternative hypotheses include that the population proportion is greater than 0.5 ($p > 0.5$), the population median is less than 12 ($M < 12$), or the population mean is not equal to 14.5 ($\mu \neq 14.5$).

There are a few requirements for the hypotheses:

• the hypotheses must be about the same population parameter,
• the hypotheses must have the same null value (provided number to compare to),
• the null hypothesis must have the equality (the equals sign must be in the null hypothesis),
• the alternative hypothesis must not have the equality (the equals sign cannot be in the alternative hypothesis),
• there must be no overlap between the null and alternative hypothesis.

You may have previously seen null hypotheses that include more than an equality (e.g. $p \le 0.5$). As long as there is an equality in the null hypothesis, this is allowed. For our purposes, we will simplify this statement to ($p = 0.5$).

To summarize from above, possible hypotheses statements are:

$H_0: p = 0.5$ vs. $H_a: p > 0.5$

$H_0: M = 12$ vs. $H_a: M < 12$

$H_0: \mu = 14.5$ vs. $H_a: \mu \neq 14.5$

In our second example about Airbnb hosts, our hypotheses would be:

$H_0: \mu = 2100$ vs. $H_a: \mu > 2100$.

Set Threshold (Significance Level)

There is one more step to complete before looking at the data. This is to set the threshold needed to convince the skeptic. This threshold is defined as an $\alpha$ significance level. We'll define exactly what the $\alpha$ significance level means later. For now, smaller $\alpha$s correspond to more evidence being required to convince the skeptic.

A few common $\alpha$ levels include 0.1, 0.05, and 0.01.

For our Airbnb hosts example, we'll set the threshold as 0.02.

Determine the Sampling Distribution of the Sample Statistic

The first step (as outlined above) is the identify the parameter of interest. What is the best estimate of the parameter of interest? Typically, it will be the sample statistic that corresponds to the parameter. This sample statistic, along with other features of the distribution will prove especially helpful as we continue the hypothesis testing procedure.

However, we do have a decision at this step. We can choose to use simulations with a resampling approach or we can choose to rely on theory if we are using proportions or means. We then also need to confirm that our results and conclusions will be valid based on the available data.

Required Condition

The one required assumption, regardless of approach (resampling or theory), is that the sample is random and representative of the population of interest. In other words, we need our sample to be a reasonable sample of data from the population.

Using Simulations and Resampling

If we'd like to use a resampling approach, we have no (or minimal) additional assumptions to check. This is because we are relying on the available data instead of assumptions.

We do need to adjust our data to be consistent with the null hypothesis (or skeptic's claim). We can then rely on our resampling approach to estimate a plausible sampling distribution for our sample statistic.

Recall that we took this approach on the last page. Before simulating our estimated sampling distribution, we adjusted the mean of the data so that it matched with our skeptic's claim, shown in the code below.

We'll see a few more examples on the next page.

Using Theory

On the other hand, we could rely on theory in order to estimate the sampling distribution of our desired statistic. Recall that we had a few different options to rely on:

• the CLT for the sampling distribution of a sample mean
• the binomial distribution for the sampling distribution of a proportion (or count)
• the Normal approximation of a binomial distribution (using the CLT) for the sampling distribution of a proportion

If relying on the CLT to specify the underlying sampling distribution, you also need to confirm:

• having a random sample and
• having a sample size that is less than 10% of the population size if the sampling is done without replacement
• having a Normally distributed population for a quantitative variable OR
• having a large enough sample size (usually at least 25) for a quantitative variable
• having a large enough sample size for a categorical variable (defined by $np$ and $n(1-p)$ being at least 10)

If relying on the binomial distribution to specify the underlying sampling distribution, you need to confirm:

• having a set number of trials, $n$
• having the same probability of success, $p$ for each observation

After determining the appropriate theory to use, we should check our conditions and then specify the sampling distribution for our statistic.

For the Airbnb hosts example, we have what we've assumed to be a random sample. It is not taken with replacement, so we also need to assume that our sample size (700) is less than 10% of our population size. In other words, we need to assume that the population of Chicago Airbnbs in March 2023 was at least 7000. Since we do have our (presumed) population data available, we can confirm that there were at least 7000 Chicago Airbnbs in the population in 2023.

Additionally, we can confirm that normality of the sampling distribution applies for the CLT to apply. Our sample size is more than 25 and the parameter of interest is a mean, so this meets our necessary criteria for the normality condition to be valid.

With the conditions now met, we can estimate our sampling distribution. From the CLT, we know that the distribution for the sample mean should be $\bar{X} \sim N(\mu, \frac{\sigma}{\sqrt{n}})$.

Now, we face our next challenge -- what to plug in as the mean and standard error for this distribution. Since we are adopting the skeptic's point of view for the purpose of this approach, we can plug in the value of $\mu_0 = 2100$. We also know that the sample size $n$ is 700. But what should we plug in for the population standard deviation $\sigma$?

When we don't know the value of a parameter, we will generally plug in our best estimate for the parameter. In this case, that corresponds to plugging in $\hat{\sigma}$, or our sample standard deviation.

Now, our estimated sampling distribution based on the CLT is: $\bar{X} \sim N(2100, 41.4045)$.

If we compare to our corresponding skeptic's sampling distribution on the last page, we can confirm that the theoretical sampling distribution is similar to the simulated sampling distribution based on resampling.

Assumptions not met

What do we do if the necessary conditions aren't met for the sampling distribution? Because the simulation-based resampling approach has minimal assumptions, we should be able to use this approach to produce valid results as long as the provided data is representative of the population.

The theory-based approach has more conditions, and we may not be able to meet all of the necessary conditions. For example, if our parameter is something other than a mean or proportion, we may not have appropriate theory. Additionally, we may not have a large enough sample size.

• First, we could consider changing approaches to the simulation-based one.
• Second, we might look at how we could meet the necessary conditions better. In some cases, we may be able to redefine groups or make adjustments so that the setup of the test is closer to what is needed.
• As a last resort, we may be able to continue following the hypothesis testing steps. In this case, your calculations may not be valid or exact; however, you might be able to use them as an estimate or an approximation. It would be crucial to specify the violation and approximation in any conclusions or discussion of the test.

Calculate the evidence with statistics and p-values

Now, it's time to calculate how much evidence the sample contains to convince the skeptic to change their mind. As we saw above, we can convince the skeptic to change their mind by demonstrating that our sample is unlikely to occur if their theory is correct.

How do we do this? We do this by calculating a probability associated with our observed value for the statistic.

For example, for our situation, we want to convince the skeptic that the population mean is actually greater than 2100 days. We do that by calculating the probability that a sample mean would be as large or larger than what we observed in our actual sample, which was 2188 days. Why do we need the larger portion? We use the larger portion because a sample mean of 2200 days also provides evidence that the population mean is larger than 2100 days; it isn't limited to exactly what we observed in our sample. We call this specific probability the p-value.

That is, the p-value is the probability of observing a test statistic as extreme or more extreme (as determined by the alternative hypothesis), assuming the null hypothesis is true.

Our observed p-value for the Airbnb host example demonstrates that the probability of getting a sample mean host time of 2188 days (the value from our sample) or more is 1.46%, assuming that the true population mean is 2100 days.

Test statistic

Notice that the formal definition of a p-value mentions a test statistic . In most cases, this word can be replaced with "statistic" or "sample" for an equivalent statement.

Oftentimes, we'll see that our sample statistic can be used directly as the test statistic, as it was above. We could equivalently adjust our statistic to calculate a test statistic. This test statistic is often calculated as:

$\text{test statistic} = \frac{\text{estimate} - \text{hypothesized value}}{\text{standard error of estimate}}$

P-value Calculation Options

Note also that the p-value definition includes a probability associated with a test statistic being as extreme or more extreme (as determined by the alternative hypothesis . How do we determine the area that we consider when calculating the probability. This decision is determined by the inequality in the alternative hypothesis.

For example, when we were trying to convince the skeptic that the population mean is greater than 2100 days, we only considered those sample means that we at least as large as what we observed -- 2188 days or more.

If instead we were trying to convince the skeptic that the population mean is less than 2100 days ($H_a: \mu < 2100$), we would consider all sample means that were at most what we observed - 2188 days or less. In this case, our p-value would be quite large; it would be around 99.5%. This large p-value demonstrates that our sample does not support the alternative hypothesis. In fact, our sample would encourage us to choose the null hypothesis instead of the alternative hypothesis of $\mu < 2100$, as our sample directly contradicts the statement in the alternative hypothesis.

If we wanted to convince the skeptic that they were wrong and that the population mean is anything other than 2100 days ($H_a: \mu \neq 2100$), then we would want to calculate the probability that a sample mean is at least 88 days away from 2100 days. That is, we would calculate the probability corresponding to 2188 days or more or 2012 days or less. In this case, our p-value would be roughly twice the previously calculated p-value.

We could calculate all of those probabilities using our sampling distributions, either simulated or theoretical, that we generated in the previous step. If we chose to calculate a test statistic as defined in the previous section, we could also rely on standard normal distributions to calculate our p-value.

Evaluate your results and write conclusion in context of problem

Once you've gathered your evidence, it's now time to make your final conclusions and determine how you might proceed.

In traditional hypothesis testing, you often make a decision. Recall that you have your threshold (significance level $\alpha$) and your level of evidence (p-value). We can compare the two to determine if your p-value is less than or equal to your threshold. If it is, you have enough evidence to persuade your skeptic to change their mind. If it is larger than the threshold, you don't have quite enough evidence to convince the skeptic.

Common formal conclusions (if given in context) would be:

• I have enough evidence to reject the null hypothesis (the skeptic's claim), and I have sufficient evidence to suggest that the alternative hypothesis is instead true.
• I do not have enough evidence to reject the null hypothesis (the skeptic's claim), and so I do not have sufficient evidence to suggest the alternative hypothesis is true.

The only decision that we can make is to either reject or fail to reject the null hypothesis (we cannot "accept" the null hypothesis). Because we aren't actively evaluating the alternative hypothesis, we don't want to make definitive decisions based on that hypothesis. However, when it comes to making our conclusion for what to use going forward, we frame this on whether we could successfully convince someone of the alternative hypothesis.

A less formal conclusion might look something like:

Based on our sample of Chicago Airbnb listings, it seems as if the mean time since a host has been on Airbnb (for all Chicago Airbnb listings) is more than 5.75 years.

Significance Level Interpretation

We've now seen how the significance level $\alpha$ is used as a threshold for hypothesis testing. What exactly is the significance level?

The significance level $\alpha$ has two primary definitions. One is that the significance level is the maximum probability required to reject the null hypothesis; this is based on how the significance level functions within the hypothesis testing framework. The second definition is that this is the probability of rejecting the null hypothesis when the null hypothesis is true; in other words, this is the probability of making a specific type of error called a Type I error.

Why do we have to be comfortable making a Type I error? There is always a chance that the skeptic was originally correct and we obtained a very unusual sample. We don't want to the skeptic to be so convinced of their theory that no evidence can convince them. In this case, we need the skeptic to be convinced as long as the evidence is strong enough . Typically, the probability threshold will be low, to reduce the number of errors made. This also means that a decent amount of evidence will be needed to convince the skeptic to abandon their position in favor of the alternative theory.

p-value Limitations and Misconceptions

In comparison to the $\alpha$ significance level, we also need to calculate the evidence against the null hypothesis with the p-value.

The p-value is the probability of getting a test statistic as extreme or more extreme (in the direction of the alternative hypothesis), assuming the null hypothesis is true.

Recently, p-values have gotten some bad press in terms of how they are used. However, that doesn't mean that p-values should be abandoned, as they still provide some helpful information. Below, we'll describe what p-values don't mean, and how they should or shouldn't be used to make decisions.

Factors that affect a p-value

What features affect the size of a p-value?

• the null value, or the value assumed under the null hypothesis
• the effect size (the difference between the null value under the null hypothesis and the true value of the parameter)
• the sample size

More evidence against the null hypothesis will be obtained if the effect size is larger and if the sample size is larger.

Misconceptions

We gave a definition for p-values above. What are some examples that p-values don't mean?

• A p-value is not the probability that the null hypothesis is correct
• A p-value is not the probability that the null hypothesis is incorrect
• A p-value is not the probability of getting your specific sample
• A p-value is not the probability that the alternative hypothesis is correct
• A p-value is not the probability that the alternative hypothesis is incorrect
• A p-value does not indicate the size of the effect

Our p-value is a way of measuring the evidence that your sample provides against the null hypothesis, assuming the null hypothesis is in fact correct.

Using the p-value to make a decision

Why is there bad press for a p-value? You may have heard about the standard $\alpha$ level of 0.05. That is, we would be comfortable with rejecting the null hypothesis once in 20 attempts when the null hypothesis is really true. Recall that we reject the null hypothesis when the p-value is less than or equal to the significance level.

Consider what would happen if you have two different p-values: 0.049 and 0.051.

In essence, these two p-values represent two very similar probabilities (4.9% vs. 5.1%) and very similar levels of evidence against the null hypothesis. However, when we make our decision based on our threshold, we would make two different decisions (reject and fail to reject, respectively). Should this decision really be so simplistic? I would argue that the difference shouldn't be so severe when the sample statistics are likely very similar. For this reason, I (and many other experts) strongly recommend using the p-value as a measure of evidence and including it with your conclusion.

Putting too much emphasis on the decision (and having a significant result) has created a culture of misusing p-values. For this reason, understanding your p-value itself is crucial.

Searching for p-values

The other concern with setting a definitive threshold of 0.05 is that some researchers will begin performing multiple tests until finding a p-value that is small enough. However, with a p-value of 0.05, we know that we will have a p-value less than 0.05 1 time out of every 20 times, even when the null hypothesis is true.

This means that if researchers start hunting for p-values that are small (sometimes called p-hacking), then they are likely to identify a small p-value every once in a while by chance alone. Researchers might then publish that result, even though the result is actually not informative. For this reason, it is recommended that researchers write a definitive analysis plan to prevent performing multiple tests in search of a result that occurs by chance alone.

Best Practices

With all of this in mind, what should we do when we have our p-value? How can we prevent or reduce misuse of a p-value?

• Report the p-value along with the conclusion
• Specify the effect size (the value of the statistic)
• Define an analysis plan before looking at the data
• Interpret the p-value clearly to specify what it indicates
• Consider using an alternate statistical approach, the confidence interval, discussed next, when appropriate

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“A fact is a simple statement that everyone believes. It is innocent, unless found guilty. A hypothesis is a novel suggestion that no one wants to believe. It is guilty until found effective.”

– Edward Teller, Nuclear Physicist

During my first brainstorming meeting on my first project at McKinsey, this very serious partner, who had a PhD in Physics, looked at me and said, “So, Joe, what are your main hypotheses.” I looked back at him, perplexed, and said, “Ummm, my what?” I was used to people simply asking, “what are your best ideas, opinions, thoughts, etc.” Over time, I began to understand the importance of hypotheses and how it plays an important role in McKinsey’s problem solving of separating ideas and opinions from facts.

What is a Hypothesis?

“Hypothesis” is probably one of the top 5 words used by McKinsey consultants. And, being hypothesis-driven was required to have any success at McKinsey. A hypothesis is an idea or theory, often based on limited data, which is typically the beginning of a thread of further investigation to prove, disprove or improve the hypothesis through facts and empirical data.

The first step in being hypothesis-driven is to focus on the highest potential ideas and theories of how to solve a problem or realize an opportunity.

Let’s go over an example of being hypothesis-driven.

Let’s say you own a website, and you brainstorm ten ideas to improve web traffic, but you don’t have the budget to execute all ten ideas. The first step in being hypothesis-driven is to prioritize the ten ideas based on how much impact you hypothesize they will create.

The second step in being hypothesis-driven is to apply the scientific method to your hypotheses by creating the fact base to prove or disprove your hypothesis, which then allows you to turn your hypothesis into fact and knowledge. Running with our example, you could prove or disprove your hypothesis on the ideas you think will drive the most impact by executing:

1. An analysis of previous research and the performance of the different ideas 2. A survey where customers rank order the ideas 3. An actual test of the ten ideas to create a fact base on click-through rates and cost

While there are many other ways to validate the hypothesis on your prioritization , I find most people do not take this critical step in validating a hypothesis. Instead, they apply bad logic to many important decisions . An idea pops into their head, and then somehow it just becomes a fact.

One of my favorite lousy logic moments was a CEO who stated,

“I’ve never heard our customers talk about price, so the price doesn’t matter with our products , and I’ve decided we’re going to raise prices.”

Luckily, his management team was able to do a survey to dig deeper into the hypothesis that customers weren’t price-sensitive. Well, of course, they were and through the survey, they built a fantastic fact base that proved and disproved many other important hypotheses.

Why is being hypothesis-driven so important?

Imagine if medicine never actually used the scientific method. We would probably still be living in a world of lobotomies and bleeding people. Many organizations are still stuck in the dark ages, having built a house of cards on opinions disguised as facts, because they don’t prove or disprove their hypotheses. Decisions made on top of decisions, made on top of opinions, steer organizations clear of reality and the facts necessary to objectively evolve their strategic understanding and knowledge. I’ve seen too many leadership teams led solely by gut and opinion. The problem with intuition and gut is if you don’t ever prove or disprove if your gut is right or wrong, you’re never going to improve your intuition. There is a reason why being hypothesis-driven is the cornerstone of problem solving at McKinsey and every other top strategy consulting firm.

How do you become hypothesis-driven?

Most people are idea-driven, and constantly have hypotheses on how the world works and what they or their organization should do to improve. Though, there is often a fatal flaw in that many people turn their hypotheses into false facts, without actually finding or creating the facts to prove or disprove their hypotheses. These people aren’t hypothesis-driven; they are gut-driven.

The conversation typically goes something like “doing this discount promotion will increase our profits” or “our customers need to have this feature” or “morale is in the toilet because we don’t pay well, so we need to increase pay.” These should all be hypotheses that need the appropriate fact base, but instead, they become false facts, often leading to unintended results and consequences. In each of these cases, to become hypothesis-driven necessitates a different framing.

• Instead of “doing this discount promotion will increase our profits,” a hypothesis-driven approach is to ask “what are the best marketing ideas to increase our profits?” and then conduct a marketing experiment to see which ideas increase profits the most.

• Instead of “our customers need to have this feature,” ask the question, “what features would our customers value most?” And, then conduct a simple survey having customers rank order the features based on value to them.

• Instead of “morale is in the toilet because we don’t pay well, so we need to increase pay,” conduct a survey asking, “what is the level of morale?” what are potential issues affecting morale?” and what are the best ideas to improve morale?”

Beyond, watching out for just following your gut, here are some of the other best practices in being hypothesis-driven:

Listen to Your Intuition

Your mind has taken the collision of your experiences and everything you’ve learned over the years to create your intuition, which are those ideas that pop into your head and those hunches that come from your gut. Your intuition is your wellspring of hypotheses. So listen to your intuition, build hypotheses from it, and then prove or disprove those hypotheses, which will, in turn, improve your intuition. Intuition without feedback will over time typically evolve into poor intuition, which leads to poor judgment, thinking, and decisions.

Constantly Be Curious

I’m always curious about cause and effect. At Sports Authority, I had a hypothesis that customers that received service and assistance as they shopped, were worth more than customers who didn’t receive assistance from an associate. We figured out how to prove or disprove this hypothesis by tying surveys to transactional data of customers, and we found the hypothesis was true, which led us to a broad initiative around improving service. The key is you have to be always curious about what you think does or will drive value, create hypotheses and then prove or disprove those hypotheses.

Validate Hypotheses

You need to validate and prove or disprove hypotheses. Don’t just chalk up an idea as fact. In most cases, you’re going to have to create a fact base utilizing logic, observation, testing (see the section on Experimentation ), surveys, and analysis.

Be a Learning Organization

The foundation of learning organizations is the testing of and learning from hypotheses. I remember my first strategy internship at Mercer Management Consulting when I spent a good part of the summer combing through the results, findings, and insights of thousands of experiments that a banking client had conducted. It was fascinating to see the vastness and depth of their collective knowledge base. And, in today’s world of knowledge portals, it is so easy to disseminate, learn from, and build upon the knowledge created by companies.

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Home » What is a Hypothesis – Types, Examples and Writing Guide

What is a Hypothesis – Types, Examples and Writing Guide

Table of Contents

In research, a hypothesis is a clear, testable statement predicting the relationship between variables or the outcome of a study. Hypotheses form the foundation of scientific inquiry, providing a direction for investigation and guiding the data collection and analysis process. Hypotheses are typically used in quantitative research but can also inform some qualitative studies by offering a preliminary assumption about the subject being explored.

A hypothesis is a specific, testable prediction or statement that suggests an expected relationship between variables in a study. It acts as a starting point, guiding researchers to examine whether their predictions hold true based on collected data. For a hypothesis to be useful, it must be clear, concise, and based on prior knowledge or theoretical frameworks.

Key Characteristics of a Hypothesis :

• Testable : Must be possible to evaluate or observe the outcome through experimentation or analysis.
• Specific : Clearly defines variables and the expected relationship or outcome.
• Predictive : States an anticipated effect or association that can be confirmed or refuted.

Example : “Increasing the amount of daily physical exercise will lead to a reduction in stress levels among college students.”

Types of Hypotheses

Hypotheses can be categorized into several types, depending on their structure, purpose, and the type of relationship they suggest. The most common types include null hypothesis , alternative hypothesis , directional hypothesis , and non-directional hypothesis .

1. Null Hypothesis (H₀)

Definition : The null hypothesis states that there is no relationship between the variables being studied or that any observed effect is due to chance. It serves as the default position, which researchers aim to test against to determine if a significant effect or association exists.

Purpose : To provide a baseline that can be statistically tested to verify if a relationship or difference exists.

Example : “There is no difference in academic performance between students who receive additional tutoring and those who do not.”

2. Alternative Hypothesis (H₁ or Hₐ)

Definition : The alternative hypothesis proposes that there is a relationship or effect between variables. This hypothesis contradicts the null hypothesis and suggests that any observed result is not due to chance.

Purpose : To present an expected outcome that researchers aim to support with data.

Example : “Students who receive additional tutoring will perform better academically than those who do not.”

3. Directional Hypothesis

Definition : A directional hypothesis specifies the direction of the expected relationship between variables, predicting either an increase, decrease, positive, or negative effect.

Purpose : To provide a more precise prediction by indicating the expected direction of the relationship.

Example : “Increasing the duration of daily exercise will lead to a decrease in stress levels among adults.”

4. Non-Directional Hypothesis

Definition : A non-directional hypothesis states that there is a relationship between variables but does not specify the direction of the effect.

Purpose : To allow for exploration of the relationship without committing to a particular direction.

Example : “There is a difference in stress levels between adults who exercise regularly and those who do not.”

Examples of Hypotheses in Different Fields

• Null Hypothesis : “There is no difference in anxiety levels between individuals who practice mindfulness and those who do not.”
• Alternative Hypothesis : “Individuals who practice mindfulness will report lower anxiety levels than those who do not.”
• Directional Hypothesis : “Providing feedback will improve students’ motivation to learn.”
• Non-Directional Hypothesis : “There is a difference in motivation levels between students who receive feedback and those who do not.”
• Null Hypothesis : “There is no association between diet and energy levels among teenagers.”
• Alternative Hypothesis : “A balanced diet is associated with higher energy levels among teenagers.”
• Directional Hypothesis : “An increase in employee engagement activities will lead to improved job satisfaction.”
• Non-Directional Hypothesis : “There is a relationship between employee engagement activities and job satisfaction.”
• Null Hypothesis : “The introduction of green spaces does not affect urban air quality.”
• Alternative Hypothesis : “Green spaces improve urban air quality.”

Writing Guide for Hypotheses

Writing a clear, testable hypothesis involves several steps, starting with understanding the research question and selecting variables. Here’s a step-by-step guide to writing an effective hypothesis.

Step 1: Identify the Research Question

Start by defining the primary research question you aim to investigate. This question should be focused, researchable, and specific enough to allow for hypothesis formation.

Example : “Does regular physical exercise improve mental well-being in college students?”

Step 2: Conduct Background Research

Review relevant literature to gain insight into existing theories, studies, and gaps in knowledge. This helps you understand prior findings and guides you in forming a logical hypothesis based on evidence.

Example : Research shows a positive correlation between exercise and mental well-being, which supports forming a hypothesis in this area.

Step 3: Define the Variables

Identify the independent and dependent variables. The independent variable is the factor you manipulate or consider as the cause, while the dependent variable is the outcome or effect you are measuring.

• Independent Variable : Amount of physical exercise
• Dependent Variable : Mental well-being (measured through self-reported stress levels)

Step 4: Choose the Hypothesis Type

Select the hypothesis type based on the research question. If you predict a specific outcome or direction, use a directional hypothesis. If not, a non-directional hypothesis may be suitable.

Example : “Increasing the frequency of physical exercise will reduce stress levels among college students” (directional hypothesis).

Step 5: Write the Hypothesis

Formulate the hypothesis as a clear, concise statement. Ensure it is specific, testable, and focuses on the relationship between the variables.

Example : “College students who exercise at least three times per week will report lower stress levels than those who do not exercise regularly.”

Step 6: Test and Refine (Optional)

In some cases, it may be necessary to refine the hypothesis after conducting a preliminary test or pilot study. This ensures that your hypothesis is realistic and feasible within the study parameters.

Tips for Writing an Effective Hypothesis

• Use Clear Language : Avoid jargon or ambiguous terms to ensure your hypothesis is easily understandable.
• Be Specific : Specify the expected relationship between the variables, and, if possible, include the direction of the effect.
• Ensure Testability : Frame the hypothesis in a way that allows for empirical testing or observation.
• Focus on One Relationship : Avoid complexity by focusing on a single, clear relationship between variables.
• Make It Measurable : Choose variables that can be quantified or observed to simplify data collection and analysis.

Common Mistakes to Avoid

• Vague Statements : Avoid vague hypotheses that don’t specify a clear relationship or outcome.
• Unmeasurable Variables : Ensure that the variables in your hypothesis can be observed, measured, or quantified.
• Overly Complex Hypotheses : Keep the hypothesis simple and focused, especially for beginner researchers.
• Using Personal Opinions : Avoid subjective or biased language that could impact the neutrality of the hypothesis.

Examples of Well-Written Hypotheses

• Psychology : “Adolescents who spend more than two hours on social media per day will report higher levels of anxiety than those who spend less than one hour.”
• Business : “Increasing customer service training will improve customer satisfaction ratings among retail employees.”
• Health : “Consuming a diet rich in fruits and vegetables is associated with lower cholesterol levels in adults.”
• Education : “Students who participate in active learning techniques will have higher retention rates compared to those in traditional lecture-based classrooms.”
• Environmental Science : “Urban areas with more green spaces will report lower average temperatures than those with minimal green coverage.”

A well-formulated hypothesis is essential to the research process, providing a clear and testable prediction about the relationship between variables. Understanding the different types of hypotheses, following a structured writing approach, and avoiding common pitfalls help researchers create hypotheses that effectively guide data collection, analysis, and conclusions. Whether working in psychology, education, health sciences, or any other field, an effective hypothesis sharpens the focus of a study and enhances the rigor of research.

• Creswell, J. W., & Creswell, J. D. (2018). Research Design: Qualitative, Quantitative, and Mixed Methods Approaches (5th ed.). SAGE Publications.
• Field, A. (2013). Discovering Statistics Using IBM SPSS Statistics (4th ed.). SAGE Publications.
• Trochim, W. M. K. (2006). The Research Methods Knowledge Base (3rd ed.). Atomic Dog Publishing.
• McLeod, S. A. (2019). What is a Hypothesis? Retrieved from https://www.simplypsychology.org/what-is-a-hypotheses.html
• Walliman, N. (2017). Research Methods: The Basics (2nd ed.). Routledge.

About the author

Muhammad Hassan

Researcher, Academic Writer, Web developer

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Introducing our hypothesis framework

• Stephen Pavlovich
• Dec 09, 2016
• 5 minute read

Download printable versions of our hypothesis framework here .

Experiments are the building blocks of optimization programs. Each experiment will at minimum teach us more about the audience – what makes them more or less likely to convert – and will often drive a significant uplift on key metrics.

At the heart of each experiment is the hypothesis – the statement that the experiment is built around.

But hypotheses can range in quality. In fact, many wouldn’t even qualify as a hypothesis: eg “What if we removed the registration step from checkout”. That might be fine to get an idea across, but it’s going to underperform as a test hypothesis.

For us, an effective hypothesis is made up of eight key components. If it’s reduced to just one component showing what you’ll change (the “test concept”), you’ll not just weaken the potential impact of the test – you’ll undermine the entire testing program.

That’s why we created our hypothesis framework. Based on almost 10 years’ experience in optimization and testing, we’ve created a simple framework that’s applicable to any industry.

• Introduction

Conversion.com’s hypothesis framework

What makes this framework effective, terminology, taking this further.

It’s a simple framework – but there are three factors that make it so effective.

• Putting data first . Quantitative and qualitative data is literally the first element in the framework. It focuses the optimizer on understanding why visitors aren’t converting, rather than brainstorming solutions and hoping there’ll be a problem to match.
• Separating lever and concept . This distinction is relatively rare – but for us, it’s crucial. A lever is the core theme for a test (eg “emphasising urgency”), whereas the concept is the application of that lever to a specific area (eg “showing the number of available rooms on the hotel page”). It’s important to make the distinction as it affects what happens after a test completes. If a test wins, you can apply the same lever to other areas, as well as testing bolder creative on the original area. If it loses, then it’s important to question whether the lever or the concept was at fault – ie did you run a lousy test, or were users just not affected by the lever after all?
• Validating success criteria upfront : The KPI and duration elements are crucial factors in any test, and are often the most overlooked. Many experiments fail by optimizing for a KPI that’s not a priority – eg increasing add-to-baskets without increasing sales. Likewise the duration should not be an afterthought, but instead the result of statistical analysis on the current conversion rate, volume of traffic, and the minimum detectable uplift. All too often, a team will define, build and start an experiment, before realising that its likely duration will be several months.

Quant and qual data

What’s the data and insight that supports the test? This can come from a huge number of sources, like web analytics, sales data, form analysis, session replay, heatmapping, onsite surveys, offsite surveys, focus groups and usability tests. Eg “We know that 96% of visitors to the property results page don’t contact an agent. In usability tests, all users wanted to see the results on a map, rather than just as a list.”

What’s the core theme of the test, if distilled down to a simple phrase? Each lever can have multiple implementations or test concepts, so it’s important to distinguish between the lever and the concept. Eg a lever might be “emphasising urgency” or “simplifying the form”.

What’s the audience or segment that will be included in the test? Like with the area, make sure the audience has sufficient potential and traffic to merit being tested. Eg an audience may be “all visitors” or “returning visitors” or “desktop visitors”.

What’s the goal for the test? It’s important to prioritize the goals, as this will affect the KPIs. Eg the goal may be “increase orders” or “increase profit” or “increase new accounts”.

Test concept

What’s the implementation of the lever? This shows how you’re applying the lever in this test. Eg “adding a map of the local area that integrates with the search filters”.

What’s the flow, page or element that the test is focused on? You’ll need to make sure there’s sufficient potential in the area (ie that an increase will have a meaningful impact) as well as sufficient traffic too (ie that the test can be completed within a reasonable duration – see below). Eg the area may be “the header”, “the application form” or “the search results page”.

The KPI defines how we’ll measure the goal. Eg the KPI could be “the number of successful applications” or “the average profit per order”.

Finally, the duration is how long you expect the test to run. It’s important to calculate this in advance – then stick to it. Eg the duration may be “2 weeks”.

This hypothesis framework isn’t limited to A/B tests on your website – it can apply anywhere: to your advertising creative and channels, even to your SEO, product and pricing strategy. Any change and any experience can be optimized – and to do that effectively requires a data-driven and controlled framework like this.

Don’t forget – you can download printable versions of the hypothesis framework here .

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• How to Write a Strong Hypothesis | Guide & Examples

How to Write a Strong Hypothesis | Guide & Examples

Published on 6 May 2022 by Shona McCombes .

A hypothesis is a statement that can be tested by scientific research. If you want to test a relationship between two or more variables, you need to write hypotheses before you start your experiment or data collection.

Table of contents

What is a hypothesis, developing a hypothesis (with example), hypothesis examples, frequently asked questions about writing hypotheses.

A hypothesis states your predictions about what your research will find. It is a tentative answer to your research question that has not yet been tested. For some research projects, you might have to write several hypotheses that address different aspects of your research question.

A hypothesis is not just a guess – it should be based on existing theories and knowledge. It also has to be testable, which means you can support or refute it through scientific research methods (such as experiments, observations, and statistical analysis of data).

Variables in hypotheses

Hypotheses propose a relationship between two or more variables . An independent variable is something the researcher changes or controls. A dependent variable is something the researcher observes and measures.

In this example, the independent variable is exposure to the sun – the assumed cause . The dependent variable is the level of happiness – the assumed effect .

Prevent plagiarism, run a free check.

Step 1: ask a question.

Writing a hypothesis begins with a research question that you want to answer. The question should be focused, specific, and researchable within the constraints of your project.

Step 2: Do some preliminary research

Your initial answer to the question should be based on what is already known about the topic. Look for theories and previous studies to help you form educated assumptions about what your research will find.

At this stage, you might construct a conceptual framework to identify which variables you will study and what you think the relationships are between them. Sometimes, you’ll have to operationalise more complex constructs.

Step 3: Formulate your hypothesis

Now you should have some idea of what you expect to find. Write your initial answer to the question in a clear, concise sentence.

Step 4: Refine your hypothesis

You need to make sure your hypothesis is specific and testable. There are various ways of phrasing a hypothesis, but all the terms you use should have clear definitions, and the hypothesis should contain:

• The relevant variables
• The specific group being studied
• The predicted outcome of the experiment or analysis

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.

In academic research, hypotheses are more commonly phrased in terms of correlations or effects, where you directly state the predicted relationship between variables.

If you are comparing two groups, the hypothesis can state what difference you expect to find between them.

Step 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 .

Hypothesis testing is a formal procedure for investigating our ideas about the world using statistics. It is used by scientists to test specific predictions, called hypotheses , by calculating how likely it is that a pattern or relationship between variables could have arisen by chance.

A hypothesis is not just a guess. It should be based on existing theories and knowledge. It also has to be testable, which means you can support or refute it through scientific research methods (such as experiments, observations, and statistical analysis of data).

A research hypothesis is your proposed answer to your research question. The research hypothesis usually includes an explanation (‘ x affects y because …’).

A statistical hypothesis, on the other hand, is a mathematical statement about a population parameter. Statistical hypotheses always come in pairs: the null and alternative hypotheses. In a well-designed study , the statistical hypotheses correspond logically to the research hypothesis.

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How To Write a Strong Research Hypothesis

Are you looking to take your research project to the next level? Have you heard of the power of a hypothesis but need to figure out how to formulate one that will unlock potential discoveries? We can help!

So get ready; it's time to dive into unlocking the power of research! This blog post will explore what makes a well-crafted and powerful hypothesis - from identifying a research question to developing supporting evidence.

By learning how to craft a compelling hypothesis, you'll have more tremendous success in every step of your research project.

What are hypotheses, and why are they important?

A hypothesis is an educated guess or a proposition based on limited evidence as a starting point for further investigation. It provides a framework for research and allows researchers to refine their ideas, collect data, and draw conclusions. Hypotheses are essential to the process because they will enable us to organize our thoughts and test theories properly.

Hypotheses are used in many fields , from medicine to psychology to economics. In each area, developing hypotheses based on observations enable researchers to make predictions about their data and guide them toward finding meaningful results.

For example, in medicine, hypotheses can be used to predict which treatments will be most effective for particular conditions or which drugs may have adverse effects when taken together. This allows doctors to make better decisions when caring for patients.

In psychology, hypotheses are often used in experiments to determine whether certain variables influence behavior or mental processes. By testing different combinations of variables, psychologists can identify patterns and understand why people behave the way they do.

In economics, hypotheses provide economists with a framework for analyzing the relationship between economic variables such as wages and consumer spending habits. By understanding these relationships, economists can better understand how economic forces affect the economy.

Overall, hypotheses play an essential role in helping scientists develop new ideas and draw meaningful conclusions from the collected data. Without taking the step to create hypotheses, it would be difficult for researchers to make sense of the vast amounts of information available today and use it effectively in their investigations.

How to determine an effective research question to form your hypothesis

When conducting research, having a compelling research question is critical . Properly formulating this question will allow the researcher to develop their hypothesis. A research question provides a clear and focused goal for your research study and also gives direction on how to get there. A compelling research question should be specific, answerable in the context of your field of study, significant, novel (not already answered by previous studies), and timely – that is, relevant to current events or trends.

Before determining the best research question, you must first understand your topic. Think about the area of knowledge that interests you most and narrow it down to a single theme or concept within this topic. Focus on what interests you most within this theme, and make sure there is room for further exploration and analysis. Once you have chosen a specific topic and narrowed down your focus, you can begin formulating questions related to your project.

To ensure relevance and impact to your field of study, choose questions that address essential issues in the literature or suggest solutions to existing problems. Avoid overly broad topics with unclear objectives; instead, opt for focused questions to enable targeted data collection and analysis with concrete results.

Additionally, consider time frames when formulating questions. If the issue has been discussed extensively in the past but has not been revisited recently, then it's likely not worthy of a new investigation.

Once you have developed some potential questions related to your topic, review them carefully and decide which question best captures the essence of what you want to learn through researching this topic.

Ask yourself:

• Is this question answerable?
• Does it fit within my field of study?
• Is it significant enough?
• Would its findings be novel?

If so, then congratulations! You have identified a compelling research question.

Tips for crafting a well-crafted hypothesis

Once you have formulated the official research question, you may develop the formal hypothesis. When composing a hypothesis, it's essential to think carefully about the question you are trying to answer.

A solid hypothesis should be testable, meaning that it can be verified or disproved through research. It should also be specific and focused on one issue at a time. Here are some tips for crafting a well-crafted hypothesis:

• Consider the goal of your research: Think about what it is that you want to learn or determine from your experiment and make sure that your hypothesis reflects this goal.
• Create an educated guess as to why something is happening: Your hypothesis should explain why something is occurring based on what evidence you already have and direct further investigation into the matter. For example, if you hypothesize that increased carbon dioxide levels in the atmosphere will lead to global warming, your research should focus on examining this relationship further.
• Define any variables or parameters involved in the experiment: This includes things like temperature or chemical composition that could potentially affect the outcome of any experiments done in pursuit of testing your hypothesis.
• Use clear and precise language: Make sure your hypothesis is written with clear and precise language so that anyone reading it can understand exactly what you are attempting to investigate or explain. Avoid complex words and keep sentences short whenever possible.

Following these simple tips will help ensure that your hypothesis is well-crafted and ready for testing!

Examples of evidence that can support your hypothesis

When it comes to developing a hypothesis, supporting evidence is essential for making sure it holds up. This evidence helps strengthen the argument that is being driven by providing facts and logical reasoning that support the hypothesis.

Examples of evidence that can be used to back up a hypothesis include using data from experiments, case studies, and other research projects. Data from experiments can provide insight into how certain variables interact to form a particular outcome.

Case studies may offer greater depth in understanding a specific phenomenon's cause and effect; research projects may yield results that confirm or refute existing theories on a subject.

In addition to these traditional forms of evidence, personal experiences or observations can also help to support a hypothesis. For example, if someone's daily commute has been consistently faster since they changed routes, they could use their personal experience to argue that making this change resulted in shorter commutes.

Similarly, suppose someone has witnessed how two variables consistently coincide (i.e., when one goes up, another goes down). In that case, this could be used to support the notion that there is some correlation between these two aspects.

Overall, evidence to support your hypothesis is crucial for ensuring its validity and credibility. While conducting experiments or researching may seem like time-consuming processes, having solid supporting evidence will make it much easier to defend your ideas convincingly when challenged.

Therefore, it is crucial to take the time necessary to gather credible sources of information to provide the most substantial possible backing for your hypotheses.

Understanding the potential of hypotheses and how they can help your research project progress

The power of research lies in the ability to develop and test hypotheses. A hypothesis is a statement or an idea that can be tested to determine its validity.

Essentially, it is a form of educated guesswork that helps researchers form conclusions about their data. By developing a hypothesis for a research project, you are effectively setting up the framework for further exploration.

When developing a hypothesis, you must consider both the expected outcomes and possible alternative explanations. This will help you focus on testing the possible results without getting sidetracked by irrelevant information. Once you have established a concrete hypothesis, it can then be used as a basis for further research and experimentation.

The process of testing hypotheses is an integral part of the scientific method and can help researchers build confidence in their findings and conclusions. Through careful observation and experimentation, researchers can compare their results against what they initially hypothesized, allowing them to draw more accurate conclusions about their data. As such, hypotheses play an essential role in helping researchers connect the dots between different pieces of evidence and form meaningful conclusions.

Overall, understanding how hypotheses can be used in research projects can be immensely beneficial in helping progress towards reaching meaningful insights from their data. By setting up expectations ahead of time and then testing them against real-world conditions, researchers can gain valuable insights that could potentially change the way we understand our world – now that's something worth exploring!

Final thoughts

A hypothesis is a proposed explanation for an observable phenomenon. It's important to note that hypotheses are not the same thing as theories–a theory is a much broader and well-established frame of reference that explains multiple phenomena.

Generally, scientists form a research question and then narrow it down to a testable hypothesis. After making observations and conducting experiments to gather data, researchers can use evidence to support or reject the hypothesis.

By following these steps to formulate a solid hypothesis, you will be on your way to developing a successful research project. Happy researching!

Header image by Bnenin .