How To Do Regression Analysis Of Likert Scale Data In R

Likert information—properly pronounced like "LICK-ert"—are ordered responses to questions or ratings. Responses could be descriptive words, such as "agree", "neutral", or "disagree," or numerical, such every bit "On a scale of 1 to 5, where 1 is 'non interested' and 5 is 'very interested'…" Likert data is commonly collected from surveys evaluating pedagogy programs, as well in a variety of stance surveys and social science surveys.

Likert data

Numbers of responses

Almost ordinarily, a 5- or 7- point scale is used for Likert items. It is believed that most people can think about or visualize 5 or 7 ordered options hands. Younger children, however, may practice better with a 3-betoken scale or a simple dichotomous question. On the other manus, if the audience is educated about a subject and trained in the evaluation, a ten-bespeak scale could be used.

Symmetry

Responses to Likert items are normally symmetrical. That is, if there are options for "hold" and "strongly agree", there should be options for "disagree" and "strongly disagree".

Neutral responses

Responses to Likert items also tend to accept a neutral option, such as "neutral", "neither agree nor disagree". Neutral responses may likewise be terms like "sometimes" or "occasionally" if "never" and "rarely" on ane side are balanced with "often" and "always".

Grade of responses

Numbered responses are typically described with descriptive terms, either for every number, for just the end points, or for the end points and the centre points, for example:

Strongly Concur Neutral Disagree Strongly
agree disagree

i two 3 iv 5

———————————————————————————————

Strongly Strongly
concord disagree

one 2 3 4 5

———————————————————————————————

Strongly Neutral Strongly
agree disagree

1 2 iii iv 5

Other options for Likert responses include faces (smiley face, neutral face, frowny face), and a line on which respondents mark their response.

Opt-out answers

Questions may also include opt-out responses, like "Don't know" or "Non applicable". These are included outside the Likert responses.

Strongly Neutral Strongly
agree disagree

ane 2 3 4 5 Not applicative

I am in favor of including opt-out responses as it tends to encourage more honest responses. It seems to me it is better to allow a respondent to opt out of answering a question rather than force an inauthentic response. It is possible that a respondent has no stance or doesn't understand a question, or that a question is non applicable for them.

That being said, the opt-out respond "Don't know" may not be a cracking pick, simply considering respondents and researchers may interpret "Don't know" as a "Neutral" answer. It may be amend to choose less ambiguous opt-out answers like "Not applicable".

Examples of Likert detail responses

See:

Vagias, W.M. (2006). Likert-type scale response anchors. Clemson International Constitute for Tourism & Inquiry Development, Department of Parks, Recreation and Tourism Management. Clemson University. world wide web.clemson.edu/centers-institutes/tourism/documents/sample-scales.pdf.

Brownish, S. Likert Scale Examples for Surveys. Iowa State University Extension. www.extension.iastate.edu/ag/staff/info/likertscaleexamples.pdf.

Likert items and Likert scales

Technically, a Likert particular is a single question with Likert responses, whereas a Likert calibration is a group of items viewed together as a single measure. For example, one could accept several Likert items with various questions about religious attitudes or behaviors, and then combine those items to a single Likert scale on religiosity.

When presenting methods and results, it is important to exist clear if information were handled as Likert item data or Likert scale data.

This book volition care for Likert information as individual Likert items, and will non create Likert scales.

Analysis of Likert item data

Likert information should be treated as ordinal data

There is some understanding that Likert particular data should generally be treated as ordinal and not treated as interval/ratio data.

One consideration is that values in interval/ratio information need to be equally spaced. That is, 2 is as between 1 and iii, and yous could average 1 and three and the response would be ii. Simply it is not clear that "agree" is as spaced between "strongly agree" and "neutral". Nor is it clear that "strongly agree" and "neutral" could be averaged for a outcome of "agree". Only numbering the response levels does non make the responses interval/ratio data.

This book will treat Likert information every bit ordinal data. It will avoid using parametric tests, such as t-test and ANOVA, with Likert information. Likert information typically exercise non meet the assumptions of those parametric tests.

Instead, we will use nonparametric tests, permutation tests, and ordinal regression.

A couple other properties propose that Likert data should non be treated as interval/ratio information. Likert information are not continuous; that is, there typically aren't any decimal points in Likert responses. Also, the responses in Likert data are constrained at their ends; that is, on a 5-point scale, the responses cannot exist below one or above 5.

Where it is useful, this book volition treat Likert information equally nominal data for certain types of summaries. In general information technology is amend to not treat ordinal data equally nominal data in statistical analyses. One reason is that when treating the data as nominal information, the information about the ordered nature of the response categories is lost. Still, sometimes it is useful to plummet Likert responses into categories; for case, group "strongly agree" and "agree" together as ane category and reporting its frequency as a per centum of responses.

Some people treat Likert data as interval/ratio data

Not anybody agrees that Likert item information should not be treated as interval/ratio information. A quick search of the internet will produce enough of examples of people defending treating Likert information equally interval/ratio data.

Cases in which treating Likert responses as interval/ratio data may exist reasonable include:

• When there are a high number of response options per question (say 10)

• When only the endpoints of the responses are indicated with text descriptors

• When response options are causeless to be equally spaced

• When respondents marker their answer on a line and then that the precise location of the mark tin can be measured

Analysis of Likert scale information

When several Likert items are combined into a scale, so that there are many possible numeric outcomes, the results are often treated as interval/ratio data.

This is non entirely permissible from a theoretical betoken of view since Likert scales are fabricated up of Likert items, and and so have the same backdrop. But information technology is oft a reasonable approach if the information meet the assumptions of the analysis. This is particularly the case if the calibration data take on many values.

Analysis of Likert data

Ordinal regression

Probably the best tool for the assay of experiments with Likert particular data equally the dependent variable is ordinal regression. The ordinal packet in R provides a powerful and flexible framework for ordinal regression. Information technology tin can handle a wide variety of experimental designs, including those with paired or repeated observations. Ordinal regression is relatively piece of cake to perform in R, but might be somewhat challenging for the novice in statistical analyses. Occasionally there are problems with fitting models or checking model assumptions. These cases may exist frustrating for the novice user.

Tests for ordinal tables

Another advisable tool for the analysis of Likert particular data are tests for ordinal information arranged in contingency table form. These include the linear-by-linear test, which is a test of association betwixt two ordinal variables, and the Cochran-Armitage test, which is a test of clan between an ordinal variable and a nominal variable. The major limitation to these tests is that they are limited to data bundled in a two-dimensional table. Likewise, these tests require the spacing between ordinal categories to be indicated. By default the tests presume that the categories are equally spaced, but the functions in R permit other spacing patterns to be used.

Permutation tests

Some other tool appropriate for the assay of Likert item data are permutation tests. The money package in R provides a relatively powerful and flexible framework for permutation tests with ordinal dependent variables. It tin can handle models analogous to a one-way analysis of variance with stratification blocks, including paired or repeated observations. This covers more than than all the designs that can be handled with the common traditional nonparametric tests.

Traditional nonparametric tests

Traditional nonparametric tests are by and large considered appropriate for analyses with ordinal dependent variables. They have the advantages of beingness widely used and probable to be familiar for readers. One disadvantage of these tests is that the variety of designs they can handle is express. The Kruskal–Wallis test can analyze a model analogous to a one-manner analysis of variance. The Friedman and Quade tests can clarify data in an unreplicated complete block pattern with paired or repeated observations.

Every bit a technical note, some authors take questioned using traditional nonparametric tests with Likert item data. One consideration is that the underlying statistics for some tests are based on the dependent variable being continuous in nature. Another consideration is that, while these tests accept provisions to handle tied values, some authors worry that they may not behave well when at that place are many ties, every bit is likely for Likert data.

Still, the results of the simulation studies below show that traditional nonparametric tests are expert approximations for ordinal regression in most cases.

Optional: Simulated comparisons of traditional nonparametric tests and ordinal regression

These simulations used results from a five-point Likert particular as the dependent variable. Here, the results from the ordinal regression are used as the preferred standard.

Mann–Whitney test

When sample sizes were reasonably large and equal between groups (northward per group = 25), p-values from Mann–Whitney were closely related to those from ordinal regression, with the Mann–Whitney test being underpowered only slightly.

p-values from Mann–Whitney exam compared to those from ordinal regression (cumulative link model) with imitation data. Dependent variable is 5-point Likert data. Both groups have equal sample sizes (north per group = 25). The blue line is the 1:one line. The cherry-red lines indicate a p-value of 0.05 on each axis.

Pocket-sized sample size

When sample sizes were small (n per group = 8), p-values from Mann–Whitney were still closely related to those from ordinal regression, merely the Isle of man–Whitney test was underpowered compared with ordinal regression.

p-values from Isle of man–Whitney test compared to those from ordinal regression (cumulative link model) with simulated data. Dependent variable is 5-point Likert data. Both groups take equal sample sizes (n per grouping = eight). The blue line is the 1:1 line. The blood-red lines signal a p-value of 0.05 on each axis.

Kruskal–Wallis test

When there were more 2 groups (hither 1000 = five, with north per grouping = 25), p-values from Kruskal–Wallis were more dispersed relative to ordinal regression than were those from Mann–Whitney. Results from Kruskal–Wallis approximated those from ordinal regression relatively well for most cases in the region around p = 0.05 and below. In some cases, Kruskal–Wallis was underpowered in this region.

p-values from Kruskal–Wallis exam compared to those from ordinal regression (cumulative link model) with simulated data. Dependent variable is v-point Likert data. All groups have equal sample sizes (n per group = 25). The blue line is the one:1 line. The cherry-red lines bespeak a p-value of 0.05 on each axis.

Cochran–Armitage and permutation tests

Cochran–Armitage and permutation tests for ordinal data reasonably approximated results from ordinal regression for virtually cases in the region around p = 0.05 and below when the threshold = "equidistant" option was used for the cumulative link model. The Cochran–Armitage and permutation tests assume equal spacing of ordinal categories past default.

p-values for the methods matched less well when the threshold = "equidistant" selection was not used, or when at least 1 group had few observations (not shown).

Results from Cochran–Armitage and permutation tests were very similar in the region effectually p = 0.05 and below (not shown).

p-values from Cochran–Armitage test compared to those from ordinal regression (cumulative link model) assuming equally spaced categories in the ordinal variable. Dependent variable is 5-betoken Likert data. Ii groups with equal sample sizes (n per group = 25). The bluish line is the 1:one line. The ruddy lines indicate a p-value of 0.05 on each axis.

Optional: Simulated comparisons of traditional nonparametric tests and exact tests and Monte Carlo approaches

These simulations used results from a 5-point Likert item as the dependent variable. Here, the results from the exact test are assumed to be the preferred standard. The exact tests were conducted with the exactRankTests package. The results from this package appear to agree with those from the coin package for exact tests. Monte Carlo simulations used x,000 iterations.

Mann–Whitney test

When sample sizes were reasonably large and equal betwixt groups (due north per group = 25), p-values from Mann–Whitney were closely related to those from the verbal examination in the p = 0.05 region, with some variability .

p-values from Mann–Whitney test compared to those from verbal test with false data. Dependent variable is 5-betoken Likert information. Both groups accept equal sample sizes (n per group = 25). The blueish line is the one:1 line. The red lines indicate a p-value of 0.05 on each axis.

Modest sample size

When sample sizes were small (n per group = eight), p-values from Mann–Whitney were however related to those from verbal test but with more scattering of values.

p-values from Mann–Whitney test compared to those from exact test with simulated information. Dependent variable is 5-signal Likert data. Both groups accept equal sample sizes (n per group = eight). The blue line is the 1:ane line. The reddish lines indicate a p-value of 0.05 on each axis.

Mann–Whitney test and Monte Carlo

When sample sizes were reasonably big and equal betwixt groups (n per group = 25), p-values from Mann–Whitney were closely related to those from Monte Carlo simulations of the Isle of man–Whitney test, with some variability .

p-values from Kruskal–Wallis test compared to those from Monte Carlo simulated Kruskal–Wallis with simulated data. Dependent variable is v-bespeak Likert information. All groups have equal sample sizes (n per group = 25). The bluish line is the 1:1 line. The red lines indicate a p-value of 0.05 on each axis.

Kruskal–Wallis test and Monte Carlo

When there were more than than ii groups (hither k = 3, with n per group = 25), p-values from Kruskal–Wallis were sim

ilar to those from Monte Carlo simulated Kruskal–Wallis, with some variability.

p-values from Kruskal–Wallis test compared to those from Monte Carlo simulated Kruskal–Wallis with simulated information. Dependent variable is 5-point Likert information. All groups accept equal sample sizes (due north per grouping = 25). The blue line is the 1:1 line. The red lines indicate a p-value of 0.05 on each axis.

Optional reading

"Oh Ordinal data, what do nosotros practice with y'all?" from Dr. Nic. 2013. Acquire and Teach Statistics & Operations Research. learnandteachstatistics.wordpress.com/2013/07/08/ordinal/.

"Can Likert Scale Data ever exist Continuous?" from Grace-Martin, Grand. 2008. The Assay Gene. www.theanalysisfactor.com/can-likert-scale-information-ever-exist-continuous/.