Module 6 - t Tests - Applied Research Center - One Sample t-Test

Q: What is the purpose of a One Sample t-test?

A One Sample t-test checks whether the mean of a single variable differs from a specified constant.

Q: How are the null and alternate hypotheses defined in the example?

The null states the mean for Assignment 1 equals 23, and the alternate states it is not equal to 23.

Q: How do you decide whether to reject the null using SPSS results?

Use the significance level (typically .05). If p .05, fail to reject it. In the example, p < .001 leads to rejecting the null.

Sep 30, 2026

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Module 6 introduces t-tests as inferential methods for comparing one or two means, then focuses on the One Sample t-test. It explains how to test whether a single variable’s mean differs from a specified constant, including a full workflow: define null and alternate hypotheses, enter data into SPSS, run the analysis (Analyze > Compare Means > One-Sample T-test), interpret the output tables, and decide to reject or fail to reject the null using p-values. A worked example tests an Assignment 1 average against 23 and reports the resulting t, df, and 95% confidence interval before writing up conclusions.

LanguageEnglish

CategoryExam

FormatPDF

Pages39

Reading Time1 h 38 min

AccessFree to download

Module 6 Overview

Types of t Tests

One Sample t-Test

Step 1: State hypotheses

Step 2: Input data into SPSS

Step 3: Run the analysis

Step 4: Decide about the null

Step 5: Write up results

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Module 6: t Tests | | | --- | --- | | |
The Applied Research Center | Module 6 Overview 􀀡 Types of t Tests 􀀡 One Sample t Test 􀀡 Independent Samples t Test 􀀡 Paired Samples t Test 􀀡 Examples t-Tests 􀀡 Used for inferences concerning one or two means 􀀡 3 main types: 􀀡 One-sample t-test 􀀡 Independent samples t-test 􀀡 Paired samples t-test One Sample t-Test 􀀡 Used to test whether the mean of single variable differs from a specified constant. 􀀡 Example 􀀡 A researcher wants to test whether the average IQ score of a group of students differs from 100. 􀀡 A stats professor wants to determine whether the average grade on Assignment 1 differs significantly from 23 (anA average). One Sample t-Test 􀀡 Step 1: State the Null and Alternate Hypotheses 􀀡 Ho = The average grade on Assignment 1 is equal to 23. 􀀡 Ha = The average grade on Assignment 1 is not equal to 23. 􀀡 Is this a directional or nondirectional Ha? One Sample t-Test (cont ʼ d) 􀀡 Step 2: Input each student ʼ s grade into SPSS 􀀡 Step 3: Run the Analysis. 􀀡 Analyze 􀀡 Compare Means 􀀡 One Sample T-test 􀀡 Test variable = assign1 􀀡 Test value = 23 􀀡 Click OK One Sample t-Test (cont ʼ d) One-Sample Statistics | | N | Mean | Std. Deviation | Std. Error Mean | | --- | --- | --- | --- | --- | | assign1 | 15 | 21.0333 | 1.54072 | .39781 | One-Sample Test | | Test Value = 23 | | | | | | | --- | --- | --- | --- | --- | --- | --- | | | t | df | Sig. (2-tailed) | Mean Difference | 95% Confidence Interval of the Difference | | | | | | | | Lower | Upper | | assign1 | -4.944 | 14 | .000 | -1.96667 | -2.8199 | -1.1134 | One Sample t-Test (cont ʼ d) 􀀡 Step 4: Make a decision regarding the null 􀀡 M = 21.03, SD = 1.54 􀀡 t (14*) = -4.944 􀀡 p < .001 􀀡 What is the decision regarding the null? 􀀡 *14 = df = n-1 = 15-1 = 14 One Sample t-Test (cont ʼ d) 􀀡 Using the level of significance = .05, do we reject or fail to reject the null? 􀀡 If p < .05, we reject the null 􀀡 if p > .05, we fail to reject the null 􀀡 According to SPSS, p < .001 􀀡 .001 < .05, therefore, we reject the null! One Sample t-Test (cont ʼ d) 􀀡 Step 5:Write up your results. 􀀡 The null hypothesis stated that the average grade on Assignment 1 is equal to 23.A one sample t-test revealed that the average grade on Assignment 1 (M = 21.03, SD = 1.54) differed significantly from 23, t (14) = -4.944, p < . 001. Consequently, the null hypothesis was rejected.

FAQs

What is the purpose of a One Sample t-test?

A One Sample t-test checks whether the mean of a single variable differs from a specified constant.

How are the null and alternate hypotheses defined in the example?

The null states the mean for Assignment 1 equals 23, and the alternate states it is not equal to 23.

How do you decide whether to reject the null using SPSS results?

Use the significance level (typically .05). If p < .05, reject the null; if p > .05, fail to reject it. In the example, p < .001 leads to rejecting the null.

Sep 30, 2026

Upload by Damian