In fact, I would like to know specific rules and conditions for using parametric and non-parametric tests while analyzing data collected using a Likert Scale Survey (with five options: Strongly Agree to Strongly Disagree). The collected data are from about 400 participants and I am interested to make comparison for 4 groups within the sample.
Dear Agnes,
It is not a matter of whether T-test or ANOVA can be used or not. The principle here is to understand the nature of your dependent and independent variables. And for Likert scales, yes you can use both the tests. Computing each individual item score for the Likert scale gives you the total score, of which the nature of your dependent variable will be continuous. To find associations; if your independent variables have two categories, you may use T-test, but if they have three categories or more, you need to use ANOVA. However, these parametric tests are used if the continuous dependent variable is normally distributed. Otherwise, opt for the non-parametric ones!
Agreed with Kurubaran regarding the use of T-test and ANOVA. However, the notion that T-test and ANOVA cannot be used for non-normally distributed data are not well-supported with literature. You can use T-test and ANOVA for non-normally distributed data. Please read the paper by Geoff Norman.
Norman, G. (2010). Likert scales, levels of measurement and the “laws” of statistics. Advances in Health Sciences Education, 15(5), 625-632.
When you run a t-test (T-test is something different, but I assume you mean t-test), t^2 is F from the oneway anova. As far as what happens when the residuals are not normally distribution, long tails (large outliers) decrease the power, which is one reason why people sometimes opt for more robust measures (so the t-test and anova are generally viewed as non-robust measures since each squares the residuals, methods that are less influenced by outliers are more robust, see lots by Rand Wilcox including his textbooks). As far as "rules", there are not steadfast ones. Your decisions will be dependent on your particular context.
Dear Agnes, it is possible. As long as t-test and ANOVA both are for testing mean differences between the study groups. After you have collected data using Likert type questionnaire you can decide to use the exact values you have collected (e.g. from 1-7) with the highest indicating hi value from which mean scores differences can be achieved. Second, you can decide to have a cumulative values (adding together all the scale) from ordinal data to continuous ones. From such continuous data you can now decide to calculate the mean for each group and make comparisons between them using either t-test or ANOVA (if you have more than two groups). Agnes Mbonyiryivuze
If you enter your data in spss as agree, strongly agree etc the data is ordinal or nominal, use non parametric tests and not anova etc. If you enter your data in spss as scale ie ratio or interval use parametric tests like anova. According to your explanation, your data maybe ordinal,norminal consider using non parametric tests
Hello Agness. I have read very good and insightful answers/comments from all the contributors. My simple answer is "yes", you can use the t-test or ANOVA for a Likert scale survey. But ensure that your data meet all the requirements (assumptions) for a particular parametric test. If assumptions like normality and/or homogeneity of variances are violated, you may resort to non-parametric tests or some robust statistical tests. You can read a paper by @David M. Erceg-Hurn and Vikki M. Mirosevich (DOI:10.1037/0003-066X.63.7.591) on Modern Robust Statistical Methods if your data fail to meet those assumptions.
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