Statistical Analysis of Group Differences: Independent and Paired t-tests with Non-parametric Alternatives
Overview
This lab report presents statistical analyses comparing differences between two groups or conditions using multiple testing approaches. The paper demonstrates the application of independent t-tests for memory measures, paired t-tests for verbal and performance IQ scores, and non-parametric Mann-Whitney U tests for fatigue levels, interpreting significance at the 0.05 alpha level.
What this lab report covers
- Independent t-test analysis of memory measures between treatment and control groups
- Paired t-test comparison of WASI verbal IQ and performance IQ scores
- Mann-Whitney U non-parametric test examining fatigue levels across groups
Preview
Finding Differences Between Two Groups or Conditions
- Independent t-test for memory study
Group Statistics | |||||
group | N | Mean | Std. Deviation | Std. Error Mean | |
memory measure | treatment group | 10 | 13.10 | 2.470 | .781 |
control group | 20 | 7.85 | 2.889 | .646 | |
Independent Samples Test | ||||||||||
Levene's Test for Equality of Variances | t-test for Equality of Means | |||||||||
F | Sig. | t | df | Sig. (2-tailed) | Mean Difference | Std. Error Difference | 95% Confidence Interval of the Difference | |||
Lower | Upper | |||||||||
memory measure | Equal variances assumed | .927 | .344 | 4.910 | 28 | .000 | 5.250 | 1.069 | 3.060 | 7.440 |
Equal variances not assumed | 5.180 | 20.893 | .000 | 5.250 | 1.014 | 3.142 | 7.358 | |||
At 95% confidence, the sig. value for the independent sample t-test of memory measure is 0.344. the value is greater than the 0.05 alpha value indicating that the variable is not statistically significant.
- Paired t test for VIQ and PIQ Variables
Paired Samples Statistics | |||||
Mean | N | Std. Deviation | Std. Error Mean | ||
Pair 1 | WASI verbal IQ score. | 110.52 | 23 | 12.587 | 2.625 |
WASI performance IQ. | 112.00 | 23 | 9.968 | 2.078 | |
Paired Samples Correlations | ||||
N | Correlation | Sig. | ||
Pair 1 | WASI verbal IQ score. & WASI performance IQ. | 23 | .409 | .053 |
Paired Samples Test | |||||||||
Paired Differences | t | df | Sig. (2-tailed) | ||||||
Mean | Std. Deviation | Std. Error Mean | 95% Confidence Interval of the Difference | ||||||
Lower | Upper | ||||||||
Pair 1 | WASI verbal IQ score. - WASI performance IQ. | -1.478 | 12.457 | 2.597 | -6.865 | 3.908 | -.569 | 22 | .575 |
at 95% confidence interval, the sig. value for the paired sample t-test of both VIQ and PIQ is 0.575. The value is greater than the 0.05 alpha values and therefore, the relationship between the two variables is not statistically significant.
- Mann Whitney Non-Parametric Test for Fatigue
Ranks | ||||
group | N | Mean Rank | Sum of Ranks | |
memory measure | treatment group | 8 | 5.75 | 46.00 |
control group | 7 | 10.57 | 74.00 | |
Total | 15 | |||
Test Statisticsa | |
memory measure | |
Mann-Whitney U | 10.000 |
Wilcoxon W | 46.000 |
Z | -2.133 |
Asymp. Sig. (2-tailed) | .033 |
Exact Sig. [2*(1-tailed Sig.)] | .040b |
a. Grouping Variable: group | |
b. Not corrected for ties. | |
The Mann Whitney parametric test shows the group with the highest fatigue level. Using the mean rank.