Hypothesis Testing Guide

Learning to write proper hypotheses is a fundamental skill in statistics. This interactive guide will walk you through the process with clear steps, detailed explanations, and important reminders. Take your time with each section to build a solid foundation.

Step 1: Identify Your Research Question

Start by clearly stating what you want to investigate. Your question should be specific and focused on a single measurable characteristic of one group.

What Hypothesis Testing Does

Hypothesis testing is a method for making decisions about a population based on a sample. It tells you whether your data is consistent or inconsistent with a particular claim about a population parameter.

Important limitation: Basic hypothesis testing does NOT tell you:

  • Why the parameter has a certain value
  • What causes the parameter to be what it is
  • How one variable affects another variable
  • Whether two variables are related to each other
Good vs. Bad Research Questions
Good research questions for beginners:
  • What is the average height of students at my university?
  • What proportion of registered voters in my city support the new park proposal?
  • Is the average amount of sleep college students get equal to 7 hours per night?

Why these are good: Each question focuses on describing ONE characteristic of ONE defined group.

Questions to avoid as a beginner:
  • Do students who study more get better grades? (implies a relationship between two variables)
  • Does drinking coffee improve test performance? (implies causation)
  • Are men taller than women? (compares two groups, requires different tests)
Step 2: Identify the Population Parameter

A parameter is a numerical characteristic of an entire population. Select which parameter you're studying.

How to choose:

Ask yourself: "Am I calculating an average of numbers (mean) or counting how many have a certain characteristic (proportion)?"

Step 3: Check That Your Data Is Obtainable

Before writing hypotheses, make sure you can realistically collect the data you need.

Ask yourself:
  • Can I survey or measure a sample from this population?
  • Is the information publicly available or can I access it?
  • Do I have the time and resources needed?
  • Is it ethical and legal to collect this data?
  • Can the characteristic be measured objectively?
Examples: Realistic vs. Unrealistic
Realistic examples for students:
  • Surveying students in your classes about their study habits
  • Recording the prices of items at local stores
  • Measuring the height of plants you're growing
  • Counting how many of your friends prefer option A vs. option B
Unrealistic examples for students:
  • Accessing private medical records of hospital patients
  • Surveying all residents of an entire state
  • Data that requires expensive laboratory equipment
  • Information that people are unlikely to answer honestly
Step 4: Write the Null Hypothesis (H₀)

The null hypothesis is your starting assumption. It states that a population parameter equals a specific value.

Key points about the null hypothesis:
  • It uses "equals" only: The null hypothesis ALWAYS uses an equals sign (=). Never use ≠, <, or > in a null hypothesis.
  • It represents the status quo: This is what you assume is true unless your data proves otherwise.
  • It must be specific: You need an exact number, not a range or vague statement.
Where does the specific number come from?
  • Previous research or historical data
  • A claimed value (like a manufacturer's claim)
  • A theoretical expectation
  • A value representing "no effect" or "no preference" (like 0.50 for a 50-50 proportion)

Your Null Hypothesis

Complete the fields above to see your null hypothesis

Examples with Explanations
Example 1: H₀: μ = 30

Translation: "The population mean equals 30"

What this means: We're assuming the true average in the entire population is exactly 30 (units depend on context: 30 minutes, 30 inches, 30 dollars, etc.)

Example 2: H₀: p = 0.50

Translation: "The population proportion equals 0.50" or "50%"

What this means: We're assuming that exactly half (50%) of the population has the characteristic we're studying

Step 5: Write the Alternative Hypothesis (H₁ or Hₐ)

The alternative hypothesis states what you're actually testing for. This is what you suspect might be true instead of the null hypothesis.

Important decision: When in doubt, use a two-tailed test (≠). Only use one-tailed tests when you have a strong reason to look in only one direction.

Your Alternative Hypothesis

Select a test type to see your alternative hypothesis

Examples and When to Use Each Type
Two-tailed example: H₁: μ ≠ 30

Translation: "The population mean is not equal to 30"

When to use: When you want to detect ANY difference, whether it's above or below the null value

Greater than example: H₁: μ > 10

Translation: "The population mean is greater than 10"

Example scenario: A company claims their battery lasts "more than 10 hours"

Less than example: H₁: μ < 200

Translation: "The population mean is less than 200"

Example scenario: A new drug claims to reduce cholesterol "below 200"

Step 6: Select the Appropriate Test Type

Different research questions require different statistical tests. Based on your parameter selection, here's the recommended test:

Recommended Test

Complete the previous steps to see the recommended test type

Quick decision guide:
  • Calculating an average of numbers? → Use t-test for means
  • Counting what percentage has a trait? → Use proportion test
Test Type Details
One-sample t-test (for means)

Use when:

  • Your parameter is μ (a mean/average)
  • You have numerical data (heights, times, prices, scores, etc.)
  • You want to test if the population mean equals a specific value
  • You're examining ONE group only

Example: Testing if the average study time of college students equals 5 hours per week

One-sample proportion test

Use when:

  • Your parameter is p (a proportion/percentage)
  • Your data is categorical (yes/no, success/failure, category A or B)
  • You want to test if the population proportion equals a specific value
  • You're examining ONE group only

Example: Testing if 60% of students prefer online classes

Step 7: Understanding Significance Level (α)

The significance level is the probability of rejecting the null hypothesis when it's actually true. You must choose this BEFORE collecting data.

What α = 0.05 means in plain English:

"I'm willing to accept a 5% chance of concluding the null hypothesis is false when it's actually true."

Or think of it this way: If you repeated your study 100 times and the null hypothesis was actually true every time, you'd expect to incorrectly reject it about 5 times just due to random chance.

Decision rules (after you collect data and calculate a p-value):
  • If p-value ≤ α: Reject the null hypothesis (your data is unlikely if H₀ were true)
  • If p-value > α: Fail to reject the null hypothesis (your data is reasonably consistent with H₀)
What the significance level does NOT mean:
  • It is NOT the probability that the null hypothesis is true
  • It is NOT the probability that your conclusion is wrong
  • It does NOT tell you how important or large the effect is
Step 8: Summary and Final Checklist

Review your complete hypothesis test setup:

Complete Hypothesis Test Setup

Research Question:

Not provided

Population:

Not provided

Parameter:

Not selected

Null Hypothesis (H₀):

Not defined

Alternative Hypothesis (H₁):

Not defined

Test Type:

Not determined

Significance Level:

α = 0.05 (default)

Quick Checklist - Verify each item:
  • ✓ Clear parameter: I've identified whether I'm testing μ (mean) or p (proportion)
  • ✓ Null uses equals: My null hypothesis uses = (not ≠, <, or >)
  • ✓ Alternative is appropriate: My alternative uses ≠, <, or > as appropriate
  • ✓ Single group: I'm describing ONE group, not comparing multiple groups
  • ✓ No causation language: I'm not using words like "causes," "affects," or "influences"
  • ✓ No relationship language: I'm not using words like "related to," "associated with," or "correlation"
  • ✓ Obtainable data: I can realistically collect the data I need
  • ✓ Correct test selected: I know whether to use a t-test (for means) or proportion test (for proportions)
  • ✓ Proper notation: I'm using Greek letters (μ, p) not sample statistics (x̄, p̂)
  • ✓ Specific values: I have exact numbers in my hypotheses, not vague terms
  • ✓ Significance level chosen: I've selected α before collecting data
Critical Rules to Remember:
  • Avoid Implying Causation: Hypothesis testing describes what exists in a population but does NOT establish what causes it.
  • Avoid Implying Relationships: Basic hypothesis testing examines one variable at a time, not how two variables relate to each other.
  • Use Proper Notation: Hypotheses are always about populations (μ, p), not samples (x̄, p̂).
  • Be Specific and Testable: Use exact numbers, not words like "high," "low," "most," or "few."
Next Steps: Conducting Your Hypothesis Test
After formulating your hypotheses, you will:
  1. Collect your sample data
  2. Calculate the appropriate test statistic
  3. Find the p-value
  4. Compare the p-value to your chosen α
  5. Make your decision: reject H₀ or fail to reject H₀
  6. State your conclusion in context