Transformations for independent samples t-test
Logarithmic transformations are used with non-normal distributions when comparing two independent groups
1. Researchers can conduct a logarithmic transformation for the variable's distribution which will "normalize" the distribution. They will lose the interpretability of the means and standard deviations within the analysis, but they will still be able to interpret the p-value and the effect size.
2. Researchers can identify any outliers (values that are more than 3.29 standard deviations away from the mean) and make sure that the values were entered correctly. If they were, and the amount of outliers do not make up more than 10% of all observations, then researchers can delete the outliers in a "listwise" fashion. This means that the observations are deleted outright from the analysis.
3. Researchers can run a non-parametric Mann-Whitney U test. Non-parametric tests are robust enough to handle violations of normality and still yield an interpretable p-value.
The steps for conducting a logarithmic transformation for an independent samples t-test in SPSS
2. Click Compute Variable.
3. In the Target Variable: box, give the outcome a new name that reflects it has been transformed.
4. Click on the continuous outcome variable to highlight it.
5. Click on the arrow button to bring the variable over into Numeric Expression: box.
6. Type "ln" and put parentheses around the variable. Example: ln(outcome)
7. Click OK.
8. In the Data View tab of SPSS, there is a logarithmically transformed outcome variable. Researchers can interpret the p-value yielded when using transformed variables, but they cannot interpret the mean and standard deviation of a transformed variable.
The steps for finding outliers in SPSS
2. Click Data.
3. Click Sort Cases.
4. Click on the outcome variable that has a "Z" in front of it.
5. Click on the arrow to move the "Z" outcome into the Sort by: box.
6. Click OK.
7. In the Data View, look at the "Z" outcome variable and identify any observations that are above an absolute value of 3.29.
8. Look at the original outcome variable and identify the observations that match the "Z" outcome observations above an absolute value of 3.29.
9. Make a decision on whether to delete the observation, transform the outcome variable using the steps above, or run a non-parametric Mann-Whitney U test.
The steps for conducting a Mann-Whitney U test when homogeneity of variance is violated
2. Click Analyze.
3. Drag the cursor over the Nonparametric Tests drop-down menu.
4. Drag the cursor over the Legacy Dialogs drop-down menu.
5. Click 2 Independent Samples.
6. Click on the continuous outcome variable to highlight it.
7. Click on the arrow button to move the outcome variable into the Test Variable List: box.
8. Click on the "grouping" variable to highlight it and click on the arrow to move it into the Grouping Variable: box.
9. Click on the Define Groups button.
10. Enter the categorical value for the first independent group into the Group 1: box. Example: "0"
11. Enter the categorical value for the second independent group into the Group 2: box. Example : "1"
12. Click Continue.
13. Click OK.
The steps for interpreting the SPSS output for a Mann-Whitney U test
If it is LESS THAN .05, then researchers have evidence of a statistically significant difference in the continuous outcome variable between the two independent groups.
If the p-value is MORE THAN .05, then researchers have evidence that there is NOT a statistically significant difference in the continuous outcome variable between the two independent groups.
2. Medians and interquartile ranges are reported for each independent group when using the Mann-Whitney U test.
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