# Transformations for independent samples t-test

## Logarithmic transformations are used with non-normal distributions when comparing two independent groups

The statistical assumption of normality is one of the central tenets of statistics as a mathematical science, but also one of its most weakest components. Parametric statistics require a normal distribution to be properly interpreted and generalized to populations. If a variable's distribution is non-normal, there are several options that researchers can choose from to answer the research question.

1. Researchers can conduct a

2. Researchers can identify any

3. Researchers can run a

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

1. Click

2. Click

3. In the

4. Click on the continuous outcome variable to highlight it.

5. Click on the

6. Type "

7. Click

8. In the

**.**__T__ransform2. Click

**.**__C__ompute Variable3. In the

**box, give the outcome a new name that reflects it has been transformed.**__T__arget Variable:4. Click on the continuous outcome variable to highlight it.

5. Click on the

**arrow**button to bring the variable over into**Num**box.__e__ric Expression: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

1. When researchers click on the

2. Click

3. Click

4. Click on the outcome variable that has a "

5. Click on the

6. Click

7. In the

8. Look at the original outcome variable and identify the observations that

9. Make a decision on whether to

**Save standardi**box when checking for the assumption of normality, a new variable was created with a "Z" at the front and the name of the outcome after it. Example:__z__ed values as variables**Zoutcome**2. Click

**.**__D__ata3. Click

**S**.__o__rt Cases4. 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**box.**__S__ort by: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

1. The data is entered in a between-subjects fashion.

2. Click

3. Drag the cursor over the

4. Drag the cursor over the

5. Click

6. Click on the continuous outcome variable to highlight it.

7. Click on the

8. Click on the "grouping" variable to highlight it and click on the arrow to move it into the

9. Click on the

10. Enter the

11. Enter the

12. Click

13. Click

2. Click

**.**__A__nalyze3. Drag the cursor over the

**drop-down menu.**__N__onparametric Tests4. Drag the cursor over the

**drop-down menu.**__L__egacy Dialogs5. Click

**.**__2__Independent Samples6. Click on the continuous outcome variable to highlight it.

7. Click on the

**arrow**button to move the outcome variable into the**box.**__T__est Variable List:8. Click on the "grouping" variable to highlight it and click on the arrow to move it into the

**box.**__G__rouping Variable:9. Click on the

**button.**__D__efine Groups10. Enter the

**categorical value for the first independent group**into the**Group**box. Example:__1__:**"****0"**11. Enter the

**categorical value for the second independent group**into the**Group**box. Example :__2__:**"****1"**12. Click

**Continue**.13. Click

**OK**.### The steps for interpreting the SPSS output for a Mann-Whitney U test

1. In the

If it is

If the

2.

**Test Statistics**table, look at the*p*-value associated with**Asymp. Sig. (2-tailed)**row. This is the*p*-value that will be interpreted.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.Click on the

**Download Database**and**Download Data Dictionary**buttons for a pre-configured database and data dictionary for transformations for independent-samples t-test.## Hire A Statistician - Statistical Consulting for Professionals

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