# Transformations for ANOVA

## Account for non-normal distributions when comparing three independent groups

The statistical assumption of normality is one of the foundational tenets of statistics. Parametric statistics require a normal distribution to be correctly interpreted. If a variable's distribution is non-normal, there are several options that one can choose to still answer a research question.

1. Conduct a

2. Identify any

3. Run a

1. Conduct a

**logarithmic transformation**for the variable's distribution which will "normalize" the distribution. The interpretability of the means and standard deviations of the analysis is lost, but the*p*-value and the effect size is still interpretable.2. Identify any

**outliers**(values that are more than 3.29 standard deviations away from the mean) and check for data entry errors. If any observations meet this criterion and the proportion 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 they completely delete the observations.3. Run a

**non-parametric**Kruskal-Wallis test. Non-parametric tests are robust enough to handle violations of normality.### The steps for conducting logarithmic transformations for ANOVA 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

**Transform**.2. Click

**Compute Variable**.3. 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**to move the variable 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 transformed outcome variable.### The steps for interpreting the transformed variable for ANOVA

1. When researchers clicked on the

2. Click

3. Click

4. Click on the outcome variable that has a "

5. Click on the arrow 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 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**Kruskal-Wallis**test.### The steps for conducting a Kruskal-Wallis test when violating assumptions of ANOVA in SPSS

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 then click on the arrow to move the "grouping" variable 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

**.**__K__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 then click on the arrow to move the "grouping" variable into the

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

**button.**__D__efine Range10. Enter the

**categorical value for the independent group that has the smallest value**into the**Mi**box. Example:__n__imum:**"****0"**11. Enter the

**categorical value for the independent group that has the largest value**into the**Ma**box. Example:__x__imum:**"****2"**12. Click

**Continue**.13. Click

**OK**.### The steps for interpreting the SPSS output for a Kruskal-Wallis test

1. In the

If it is

If the

2.

**Test Statistics**table, look at the*p*-value associated with**Asymp. Sig.**row. This is the*p*-value that is 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 Kruskal-Wallis test.Click on the

**Download Database**and**Download Data Dictionary**buttons for a configured database and data dictionary for transformations for ANOVA.## Hire A Statistician - Statistical Consulting for Professionals

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