Analysing a Likert Scale

Carlos Rodriguez, PhD
December 26, 2015

Introduction

The app in shinyapps is intended to analyse each one of the 40 Likert items which compose a Likert scale answered by 39 participants in an experiment to prove whether the Balanced Scorecard is better in developing Business Plans than the traditional method.

The app allows you to choose a Likert item, one a time, and executes a CHI Squared test.

As shinyapps.io does not support HH package, I installed an alternative shiny server running in my computer, this can generate graphics with such package, please visit it here.

Downloading and reading the dataset

Column PART represents each individual participant. Column TRAT contains the method used: BSC for the Balanced Scorecard, HO for the traditional method. Following columns contains each individual response for each Likert item, for example column c1i1 contains the individual responses for the item Time devoted to exercise was definitively well seized. Each response is a value between 1 and 5, being 1 = Strongly Disagree; 2 = Disagree; 3 = Neutral; 4 = Agree; and 5 = Strongly Agree.

We first download the dataset from dropbox.

Below appears the output of the names command over the dataset:

 [1] "PART"  "TRAT"  "c1i1"  "c1i2"  "c1i3"  "c1i4"  "c1i5"  "c1i6" 
 [9] "c2i1"  "c2i2"  "c2i3"  "c2i4"  "c2i5"  "c2i6"  "c2i7"  "c2i8" 
[17] "c2i9"  "c2i10" "c2i11" "c3i1"  "c3i2"  "c3i3"  "c3i4"  "c3i5" 
[25] "c4i1"  "c4i2"  "c4i3"  "c5i1"  "c5i2"  "c5i3"  "c5i4"  "c5i5" 
[33] "c5i6"  "c6i1"  "c6i2"  "c6i3"  "c6i4"  "c6i5"  "c6i6"  "c6i7" 
[41] "c6i8"  "c6i9"

Crosstab of a Likert item

Variable by rows is the Treatment which is a dichotomic variable where BSC contains the responses of the participants that used the Balanced Scorecard, HO contains the responses of the participants that used the traditional method. Variable by columns contains the responses for each level of agreement: Each column accumulates individual responses, giving 1 point for each case where a individual selected one of the options which are: Strongly Disagree; Disagree; Neutral; Agree; and Strongly Agree.

For each Likert item, a crosstab is built to view the level of responses for each treatment:

xt <- xtabs(~ TRAT + c1i1, data = likert)
        dimnames(xt) = list("Treatment"=c("BSC","HO"),"Responses"=c("Strongly Disagree", "Disagree","Neutral","Agree","Strongly Agree"))
        xt

         Responses
Treatment Strongly Disagree Disagree Neutral Agree Strongly Agree
      BSC                 1        0       1     6             12
      HO                  0        1       0     2             16

CHI Squared test for a Likert item

If p-value is less than 0.05, there is a statistically significant difference between the method BSC and HO. The graphic shows the levels of response for each method.
chisq.test(xt)


    Pearson's Chi-squared test

data:  xt
X-squared = 5.5494, df = 4, p-value = 0.2354

plot of chunk unnamed-chunk-4