How do you analyze Likert scale data? Likert scales are the most broadly used method for scaling responses in survey studies. Survey questions that ask you to indicate your level of agreement, from strongly agree to strongly disagree, use the Likert scale. The data in the worksheet are five-point Likert scale data for two groups.

Likert data seem ideal for survey items, but there is a huge debate over how to analyze these data. The general question centers on whether you should use a parametric or nonparametric test to analyze Likert data.

Read my post that compares parametric and nonparametric hypothesis tests.

Most people are more familiar with using parametric tests. Unfortunately, Likert data are ordinal, discrete, and have a limited range. These properties violate the assumptions of most parametric tests. The highlights of the debate over using each type of test with Likert data are as follows:

- Parametric tests assume that the data are continuous and follow a normal distribution. Although, with a large enough sample, parametric tests are valid with nonnormal data. The 2-sample t-test is a parametric test.
- Nonparametric tests are accurate with ordinal data and do not assume a normal distribution. However, there is a concern that nonparametric tests have a lower probability of detecting an effect that actually exists. The Mann-Whitney test is an example of a nonparametric test.

What is the best way to analyze Likert scale data? This choice can be a tough one for survey researchers to make.

## Which Test is Better for Analyzing Likert Scale Data

Studies have attempted to resolve this debate once and for all. Unfortunately, many of these studies assessed a small number of Likert distributions, which limits the generalizability of the results. Recently, more powerful computers have allowed simulation studies to meticulously analyze a broad spectrum of distributions.

In this post, I highlight a study by de Winter and Dodou*. Their study is a simulation study that assesses the capabilities of the Mann-Whitney test and the 2-sample t-test to analyze five-point Likert scale data for two groups. Let’s find out if one of these statistical tests is better to use!

The investigators assessed a group of 14 distributions of Likert data that cover the gamut. The computer simulation generated independent pairs of random samples that contained all possible combinations of the 14 distributions. The study produced 10,000 random samples for each of the 98 combinations of distributions. Whew! That’s a lot of data!

The study statistically analyzed each pair of samples with both the 2-sample t-test and the Mann-Whitney test. Their goal is to calculate the error rates and statistical power of both tests to determine whether one of the analyses is better for Likert data. The project also looked at different sample sizes to see if that made a difference.

## Comparing Error Rates and Power When Analyzing Likert Scale Data

After analyzing all pairs of distributions, the results indicate that both types of analyses produce type I error rates that are nearly equal to the target value. A type I error rate is essentially a false positive. The test results are statistically significant but, unbeknownst to the investigator, the null hypothesis is actually true. This error rate should equal the significance level.

The 2-sample t-test and Mann-Whitney test produce nearly equal false positive rates for Likert scale data. Further, the error rates for both analyses are close to the significance level target. Excessive false positives are not a concern for either hypothesis test.

Regarding statistical power, the simulation study shows that there is a minute difference between these two tests. Apprehensions about the Mann-Whitney test being underpowered were unsubstantiated. In most cases, if there is an actual difference between populations, the two tests have an equal probability of detecting it.

There is one qualification. A power difference between the two tests exists for several specific combinations of distribution pairs. The difference in power affects only a small portion of the possible combinations of distributions. My suggestion is to perform both tests on your Likert data. If the test results disagree, look at the article to determine whether a difference in power might be the cause.

In most cases, it doesn’t matter which of the two statistical analyses you use to analyze your Likert data. If you have two groups and you’re analyzing five-point Likert data, both the 2-sample t-test and Mann-Whitney test have nearly equivalent type I error rates and power. These results are consistent across group sizes of 10, 30, and 200.

Sometimes it’s just nice to know when you don’t have to stress over something!

## Reference

*de Winter, J.C.F. and D. Dodou (2010), Five-Point Likert Items: t test versus Mann-Whitney-Wilcoxon, *Practical Assessment, Research and Evaluation*, 15(11).

Deidre Whitfield says

How do you analyze NA data when computing the average using the Likert? Should you use zero as the value or can you assign it a value? If so, is there a best value to give NA responses?

Jim Frost says

Hi Deidre,

NA responses can be difficult to include in your analysis. There’s no one size fits all answer. You’ll need to determine if NA fits in logically with your scale, and what value it represents. That’ll vary based on the subject area and the scale.

In some cases, NA values may need to be excluded. For example, in a strongly agree to strongly disagree scale, if NA truly means not applicable, the respondent is indicating that the item does not apply to them. In those cases, you should consider excluding their response from the dataset for that item. You’ll have to think about whether NA is different than say Neither agree or disagree, or whatever the middle value is.

However, if you can take NA to represent some sort of middle value, or something else, you can use it for that. However, you have to be very careful. And, in fact, I’d say that if you can use NA to represent some other value for that question, it represents bad survey design because you have two different options for item that are equivalent. If NA maps to another option, it’s probably best to not even include NA as option for that item in the first place. For example, if the question is, how strongly does an issue affect you? And the scale ranges from very strongly affects me to does not affect me at all, an NA response probably corresponds to does not affect me at all. But, why include both because they’re redundant?

For that reason, my guess is that NA does not map directly to another option most of the time. But, you’ll have to consider the scale and whether a value on it maps to NA. I can see cases where NA might equal no opinion.

Traci says

Jim,

Love you website, it is easy to understand and has helped me a lot. I have a question. I have 2 sets of survey data. One from patients (n=42) and one from staff (n=12). There are two sub-scales that I want to compare the two groups on but am concerned about the difference in sample sizes. Would I use a Mann-Whitney just on the two sub-scales?? The sub-scales were measured on a 5-point Likert scale. Your help is appreciated.

Jim Frost says

Hi Traci, thanks for the kind words. I really appreciate them!

I wouldn’t worry about the unequal sample sizes as long as your smallest group has more than 10, which it does.

The benefit of equal sized group comes in the form of statistical power, which the ability to detect a difference. It appears like you have 54 observations. Now, if you had two groups each with 27 observations to produce that total of 54, your test would have more power than what you’ve actually got. However, reality isn’t always nice and neat, and you have to work with what you’ve got. So, it’s fine to test those two groups. The statistical power is somewhat less than what it would’ve been with equal sized groups, but it’s not inherently problematic.

Shuchi says

Hi Jim,

I m a learner and doing a correlational research on job satisfaction and attitude of teachers,for job satisfaction I have used a likert scale.In this scale there are 8 factors of job satisfaction and there are fixed number of statements for each factor like factor A has 7 statements.Also the scale has 52 statements.Before data analysis can I use mean score of each participant i.e. raw score /52.And same approach for factor analysis too i.e. raw score of factor A /7

Jim Frost says

Hi Shuchi,

There’s general rule of thumb that if you have a discrete variable that has 10 equally spaced values or more, and the data are spread across those values, you can treat it as a continuous variable. If you satisfy that, I think you’re safe. And, it sounds like if you’re summing the scores for those statements you’ll be ok. Using the average is

probablyok too because you are effectively using the same amount of information.Joseph says

My is not a response to the question asked but a more clarification on this issue. Assuming one uses a four point scale can we still use t-test? Also can we call a four point scale likert?

Jim Frost says

Hi Joseph,

Unfortunately, I don’t know for sure. I haven’t read research about it that says one way or another. The research that is the basis for this post only assessed 5-point scales. Honestly, I was surprised that t-tests worked as well as they did for 5 point scales! Four points scales satisfy the t-test assumptions even less than 5 point scales. So, I think that would be risky–but I can’t say that I know for sure.

As for the terminology, I’ve seen it argued both ways. Some say that a Likert scale specifically refers to a 5-point ordinal scale. While I’ve seen others say that it doesn’t have to be 5-points. My own take is that there are probably other more important considerations for what constitutes a Likert scale. Namely, that the values need to be balanced between positive and negative relative to a neutral value. Additionally, the distance between values are equal.

In other words, a Likert scale is a special type of ordinal data scale. Ordinal data don’t require those properties (balance, neutral value, and equal spacing), but in my mind, Likert scales do require those properties, but don’t require specifically 5-points. With four points, I’m not sure that your data can satisfy all of those requirements.

I hope this helps!

Haris says

Hi Jim, I know this is a long time since your post. I had a query.

I am involved with analysing some days where an educational intervention was performed for students. Likert scale was used to assess pre- and post- intervention changes in knowledge, confidence level etc.

I do not think one can use the scale data like Likert as they are, to assess significance with t-test or the Mann-Whitney test.

Do you think we should assign numerical values to the scale data before using the tests of statistical significance?

For example 0.2 for a Likert reading of 1 on a scale of 5, 0.8 for 4/5 etc. ?

Bokossa Sidoine says

in my comprehension we can you use 2-sample t-test or Mann-Whitney If we have two groups and analyzing five-point Likert.i have one question.

what about if we have more than two groups and more than five-point Likert?

very intersting thanks you so much..

Jim Frost says

That’s correct. As for the other cases you mention, it looks promising but we can’t say definitively from this research. However, as you increase the number of values (e.g., a 7-point scale), the data are becoming more like a continuous variable, which is good. And the F-test in ANOVA is a generalization of the t-test. So, the results should be applicable to these other cases. The question in my mind is that as you increase the number of groups with ANOVA, you’d need to be sure to keep the number of observations per group at a good number. So, it looks promising for these other cases that you mention, but I can’t state definitively that it’s true based on the specific research that I’ve read.

niaz hussain ghumro says

Good and very informative

Jim Frost says

Thank you!

Naveen Kumar S says

Hi sir,

am Naveen Kumar S, from india. recently on 1st july 2017 GST was implemented across India and am writing a research paper on GST and the issues faced by the respondents (both CAs and tax payers) after GST implementation. for this i had received the responses through likert scale based questions and now stuck in analyzing the data. dont know in which perspective i have to initiate (the main theme is-issues faced by them in post GST implementation) and also as a learner cant able to frame the null and altenate hypothesis…

pls help me in this regard and give some hint/ solution for the same as early as possible…

thanks in advance

with regards

Naveen S

[email protected]