When can parametric tests, which are generally more sensitive and more powerful, be used? Find out!

Likert scales are a common way to capture data about respondent’s opinion on surveys. These are items in which a respondent chooses an option from a range of values. For example: One to five or one to seven, ‘never’ to ‘always’ or ‘strongly disagree’ to ‘strongly agree’ with points in between.

Technically, Likert scale data are ordinal. This means that the response choices have a meaningful order, but the numbers themselves are not meaningful. For example, consider a scale from one to five with the following options: Strongly disagree, disagree, neutral, agree, and strongly agree. Someone who chooses ‘agree’ (score four) does not agree twice as much as someone who chooses ‘disagree’ (score two). So the numbers are not meaningful – only the order is.

To statistically analyze ordinal data, non-parametric tests should be used. Tests such as the Mann-Whitney U test or the Wicoxon signed ranks test can be used with ordinal data.

However, it is common to see ordinal data analyzed using parametric tests, such as the t-test or an ANOVA. Sometimes this is appropriate and sometimes it is not. So when can parametric tests, which are generally more sensitive and more powerful, be used? Only when the ordinal data meets all of the assumptions of the parametric test. These are:

1. The sampling distribution (not necessarily the data itself) is normally distributed. This will be true if:
   1. Sample size (n) is greater than 30; or
   2. n<30 and the data appears to be normally distributed on inspection.
2. There are at least 5 levels to the ordinal scale.
   There are no extreme scores – and it is essentially impossible to have extreme scores on a Likert scale since options are limited.
3. The variance of the two samples (or more) being compared is approximately equal. This is not an issue if n>30.