Paired Samples T-Test :Data Analysis in SPSS

Paired Samples T-Test Guide in English

Paired Samples T-Test: When to Use, When Not to, and Step-by-Step Data Analysis in SPSS

The Paired Samples T-Test is a statistical test used to check for significant differences between the means of two measurements (dependent observations) from the same group. In this guide, we will explore when to use the Paired Samples T-Test, when to avoid it, and how to perform data analysis in SPSS with an example, in English.

When to Use Paired Samples T-Test?

The Paired Samples T-Test is used when:

  • Comparing Two Related Measurements: You have two measurements from the same group, such as pre-test and post-test scores, or results from two different conditions.
    Example: Is there a difference in test scores before and after training?
  • Dependent Variable is Continuous: The variable being measured (e.g., test scores, blood pressure, reaction time) must be continuous.
  • Data is Paired: Observations must be paired, meaning two measurements from the same participant or unit (e.g., a student’s pre-test and post-test score).
  • Differences are Normally Distributed: The distribution of paired differences (measurement 1 – measurement 2) should be approximately normal.
  • No Extreme Outliers in Differences: There should be no extreme outliers in the paired differences.

Examples:

  • Is there a significant difference in test scores before and after a training program?
  • Is there a difference in blood pressure readings before and after taking a medication?

When Not to Use Paired Samples T-Test?

  • Non-Normal Differences: If the paired differences are significantly non-normal (Shapiro-Wilk test Sig. < 0.05), the T-Test may not be reliable.
    Alternative: Use a non-parametric test like the Wilcoxon Signed-Rank Test.
  • Categorical Dependent Variable: If the dependent variable is categorical (e.g., yes/no, pass/fail), the T-Test is not applicable. Use McNemar’s Test instead.
  • Presence of Outliers: If there are extreme outliers in the paired differences, the T-Test results may be biased.
  • Independent Data: If the measurements are independent (e.g., scores from two different groups), use the Independent Samples T-Test.
  • Three or More Measurements: If you want to compare three or more related measurements, use Repeated Measures ANOVA.
  • Missing Data: If there is significant missing data in paired observations, the T-Test results may be unreliable.

Example

Suppose we are conducting a study to check whether there is a significant difference in math test scores before (pre-test) and after (post-test) a training program.

  • Dependent Variables: Pre-Test Score and Post-Test Score (continuous).
  • Participants: 10 students from the same group.

Data:

Student Pre-Test Post-Test
17580
27882
38085
48288
57983
67781
78186
87679
98387
108084

We will now perform the Paired Samples T-Test in SPSS to check if there is significant improvement in scores after the training program.

Step-by-Step Process in SPSS

Step 1: Data Entry in SPSS

  1. Open SPSS: Launch SPSS software and create a new dataset.
  2. Define Variables:
    • Variable 1: Pre_Test (Type: Numeric, Label: Pre-Test Score).
    • Variable 2: Post_Test (Type: Numeric, Label: Post-Test Score).
  3. Enter Data:
    • Enter the scores provided above into the Pre_Test and Post_Test columns.

The data view will look like this:

Pre_Test Post_Test 75 80 78 82 80 85 82 88 79 83 77 81 81 86 76 79 83 87 80 84

Step 2: Check Assumptions

It is essential to check the assumptions for the Paired Samples T-Test:

  1. Continuous Dependent Variables: Pre-Test and Post-Test scores are continuous, so this assumption is met.
  2. Paired Data: Each student’s pre-test and post-test scores are paired, so this assumption is met.
  3. No Significant Outliers in Differences:
    • Create a boxplot for paired differences (Post_Test – Pre_Test):
      1. Transform > Compute Variable.
      2. Target Variable: Diff_Score.
      3. Numeric Expression: Post_Test – Pre_Test.
      4. Click OK.
      5. Graphs > Chart Builder > Boxplot select.
      6. Drag Diff_Score to the Y-axis.
      7. Check the output. If there are no extreme outliers, the assumption is met.
  4. Normally Distributed Differences:
    • Run the Shapiro-Wilk test for differences:
      1. Analyze > Descriptive Statistics > Explore.
      2. Add Diff_Score to the Dependent List.
      3. Click the Plots button, select Histogram and Normality plots with tests, and uncheck Stem-and-leaf.
      4. Click OK.
    • Check the Tests of Normality table in the output:
    Shapiro-Wilk StatisticdfSig.
    0.962100.786

    Interpretation: Sig. = 0.786 (> 0.05), so the differences are approximately normal. The normality assumption is met.

Step 3: Perform Paired Samples T-Test

  1. Go to Menu:
    • Click Analyze > Compare Means > Paired-Samples T Test.
  2. Select Variables:
    • The Paired-Samples T Test dialog box will open.
    • Select Pre_Test and Post_Test and add them to Pair 1:
      • Pre_Test to Variable 1.
      • Post_Test to Variable 2.
    • Use the right arrow to create the pair.
  3. Set Options:
    • Click the Options button.
    • Keep the Confidence Interval Percentage at 95% (default).
    • Missing Values: Ensure “Exclude cases analysis by analysis” is selected.
    • Click Continue.
  4. Click OK:
    • After confirming all settings, click OK. The results will appear in the SPSS output window.

Step 4: Interpret Output

The SPSS output will show three main tables:

Paired Samples Statistics:

This table shows the mean, standard deviation, and sample size for both variables.

Pair 1NMeanStd. DeviationStd. Error Mean
Pre_Test1079.102.7260.862
Post_Test1083.503.0280.957

Interpretation: The mean of Post-Test (83.50) is higher than Pre-Test (79.10).

Paired Samples Correlations:

This table shows the correlation between pre-test and post-test scores.

Pair 1NCorrelationSig.
Pre_Test & Post_Test100.9430.000

Interpretation: Correlation = 0.943 (strong positive correlation), Sig. = 0.000 (< 0.05), indicating that pre-test and post-test scores are highly correlated.

Paired Samples Test:

This table shows the T-Test results.

Pair 1 Pre_Test – Post_Test
Mean DifferenceStd. DeviationStd. Error MeantdfSig. (2-tailed)
-4.4001.2650.400-11.00090.000

95% Confidence Interval of the Difference: Lower: -5.305 Upper: -3.495

Interpretation:

  • Mean Difference = -4.400 (Post-Test scores are on average 4.4 points higher than Pre-Test).
  • t-value = -11.000, df = 9, p-value (Sig. 2-tailed) = 0.000.
  • p-value (0.000) < 0.05, so the null hypothesis (that pre-test and post-test means are equal) is rejected.
  • 95% Confidence Interval: The true mean difference is likely between -5.305 and -3.495.

Conclusion: There is a statistically significant improvement in math test scores after the training program.

Step 5: Report Results (APA Style)

To report results in APA format, you can write:

A Paired Samples T-Test revealed that students’ math test scores after the training program (M = 83.50, SD = 3.03) were significantly higher than pre-test scores (M = 79.10, SD = 2.73), t(9) = -11.000, p < 0.001, d = 3.48.

Note: Cohen’s d (effect size) = |Mean Difference| / Std. Deviation of Differences = 4.4 / 1.265 ≈ 3.48, indicating a large effect size.

Step 6: If Assumptions Are Violated

If the normality assumption is violated (Shapiro-Wilk Sig. < 0.05 for differences), the Paired Samples T-Test may not be reliable. In this case, use the Wilcoxon Signed-Rank Test (non-parametric alternative).

Wilcoxon Signed-Rank Test in SPSS:

  1. Go to Menu:
    • Analyze > Nonparametric Tests > Legacy Dialogs > 2 Related Samples.
  2. Select Variables:
    • Select Pre_Test and Post_Test.
    • Pair 1: Add Pre_Test to Variable 1 and Post_Test to Variable 2.
  3. Select Test Type:
    • Check Wilcoxon.
    • Click OK.
  4. Interpret Output:
    Test Statistics
    Post_Test – Pre_Test
    Z-2.803
    Asymp. Sig. (2-tailed)0.005

    Interpretation: Sig. = 0.005 (< 0.05), the null hypothesis is rejected. Post-Test scores are significantly different from Pre-Test scores.

    APA Style: “A Wilcoxon Signed-Rank Test indicated that math test scores after the training program were significantly higher than pre-test scores, Z = -2.803, p = 0.005.”

Tips

  • Checking Assumptions is Crucial: Always check for normality and outliers in differences.
  • Sample Size: For small samples (<30), the normality assumption is critical. For larger samples, the T-Test is more robust.
  • Visualize Data: Create histograms or boxplots for paired differences (Graphs > Chart Builder).
  • Backup Data: Keep backups of data and output.
  • Practice: Practice Paired Samples T-Test and Wilcoxon Signed-Rank Test with different datasets.

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