how to analyse likert scale questionnaire data

Statistical Methods for Ordinal Survey Responses

Ordinal scales, like those frequently employed in surveys, present unique considerations for statistical treatment due to the ordered nature of response categories. While categories are ranked, the intervals between them are not necessarily equal. Consequently, methods appropriate for interval or ratio data may be unsuitable.

Descriptive Statistics

  • Frequencies and Percentages: Calculating the distribution of responses across categories provides a basic understanding of central tendencies. Visualizations like bar charts effectively illustrate these distributions.
  • Median: The median, representing the middle value, is often a more robust measure of central tendency than the mean, especially when data is skewed.
  • Mode: The most frequently occurring response category.
  • Interquartile Range (IQR): This measures the spread of the middle 50% of the data and is less sensitive to outliers than the standard deviation.

Inferential Statistics: Non-Parametric Approaches

Due to the ordinal nature of the data and potential violations of normality assumptions, non-parametric tests are frequently preferred. These tests make fewer assumptions about the underlying distribution of the data.

Comparison of Two Groups

  • Mann-Whitney U Test (Wilcoxon Rank-Sum Test): Compares the distributions of two independent groups. Determines if one group tends to have larger values than the other.
  • Wilcoxon Signed-Rank Test: Used for comparing two related samples or paired observations. Assesses whether there's a significant difference between the matched pairs.

Comparison of Three or More Groups

  • Kruskal-Wallis Test: An extension of the Mann-Whitney U test to compare three or more independent groups. Determines if at least one group stochastically dominates the others.
  • Friedman Test: A non-parametric alternative to the repeated measures ANOVA, suitable for comparing three or more related samples.

Correlation

  • Spearman's Rank Correlation (ρ): Measures the monotonic relationship between two variables. It assesses the strength and direction of association based on the ranks of the data, rather than the actual values.
  • Kendall's Tau (τ): Another non-parametric correlation coefficient, also measuring monotonic association. Often preferred over Spearman's when there are many tied ranks.

Inferential Statistics: Parametric Considerations and Cautions

While generally discouraged due to the ordinal nature of data, some researchers treat ordinal data as interval data and employ parametric tests. This practice is highly debated and requires careful justification, demonstrating that the assumptions of equal intervals and approximate normality are reasonably met. Common parametric tests include:

  • T-tests: For comparison of means between two groups. However, the underlying assumption of interval data must be carefully considered.
  • ANOVA (Analysis of Variance): For comparison of means across three or more groups. Similarly, caution is warranted due to data characteristics.

If parametric tests are used, thorough justification and robustness checks (e.g., examining residuals for normality) are essential. The implications of potential assumption violations should be acknowledged in the interpretation of results.

Software and Implementation

Most statistical software packages (e.g., R, SPSS, SAS, Stata) provide functionalities for performing the methods described above. Appropriate function calls and syntax will vary depending on the specific software being used.