Two-Way Contingency Table Analysis

Green and Salkind (2017) described a two-way contingency table analysis as a way to find if a statistical relationship between two variables exists. Bougie and Sekaran (2019) stated that a contingency table analysis only measures nominal or ordinal relationships. In this case, we analyzed the relationship between nominal and ordinal variables, one with two levels and the other with three.

Research Question

Is there a statistically significant relationship between work shift and morale?

Hypotheses

H0: There is not a statistically significant relationship between work shifts and morale.

H1: There is a statistically significant relationship between work shift and morale.

Results

In this subheading, I will present descriptive statistics, discuss testing of the assumptions, present inferential statistic results, and conclude with a concise summary. 

Descriptive Statistics

A total of 19 employees participated in the study. The assumptions of normality, linearity and homoscedasticity were evaluated with no significant violations noted. Table 1 depicts descriptive statistics for the study variables. Figure 1 depicts a bar chart of the crosstabulation, indicative of the relationship between work shift and morale.

    Morale  
Work Shift Preference   High Low Total
Day Shift Count 1 7 8
  Expected Count 2.9 5.1 8
  % within Work Shift Preference 12.5% 87.5% 100%
Night Shift Count 4 0 4
  Expected Count 1.5 2.5 4
  % within Work Shift Preference 100% 0% 100%
Swing Shift Count 2 5 7
  Expected Count 2.6 4.4 7
  % within Work Shift Preference 28.6% 71.4% 100%
Total Count 7 12 19
  Expected Count 7 12 19
  % within Work Shift Preference 36.8% 63.2% 100%

Figure 1. Bar Chart of Work Shift and Morale. The statistics indicate that the day shift is associated with high morale.

Inferential Results

A two-way contingency table analysis was conducted to evaluate how morale was affected by the day shift, night shift, and swing shift. The two variables were work shift with three levels (day shift, night shift, and swing shift) and morale with two levels (low and high). Invalidating the null hypothesis, work shift and morale were found to be significantly related, Pearson χ2(2,N=19)=9.1,p=.0112(2,N=19)=9.1, p=.011, Cramér’s V=.69V=.69. The percentages of high morale based on work shift for day shift, night shift, and swing shift were 87.5%, 0%, and 71.4%, respectively.

References

Bougie, R. & Sekaran, U. (2019). Research methods for business: A skill-building approach (8th ed.). John Wiley & Sons.

Green, S. B., & Salkind, N. J. (2017). Using SPSS for Windows and Macintosh: Analyzing and understanding data (8th ed.). Pearson.

Appendix – Two-Way Contingency Table Analysis

 SPSS Output

Case Processing Summary
  Cases
Valid Missing Total
N Percent N Percent N Percent
Work_Shift_Preference * Morale 19 100.0% 0 0.0% 19 100.0%
Work_Shift_Preference * Morale Crosstabulation
  Morale Total
Low High
Work_Shift_Preference Day Shift Count 1 7 8
Expected Count 2.9 5.1 8.0
% within Work_Shift_Preference 12.5% 87.5% 100.0%
Night Shift Count 4 0 4
Expected Count 1.5 2.5 4.0
% within Work_Shift_Preference 100.0% 0.0% 100.0%
Swing Shift Count 2 5 7
Expected Count 2.6 4.4 7.0
% within Work_Shift_Preference 28.6% 71.4% 100.0%
Total Count 7 12 19
Expected Count 7.0 12.0 19.0
% within Work_Shift_Preference 36.8% 63.2% 100.0%
Chi-Square Tests
  Value df Asymptotic Significance (2-sided)
Pearson Chi-Square 9.100a 2 .011
Likelihood Ratio 10.604 2 .005
Linear-by-Linear Association .510 1 .475
N of Valid Cases 19    
a. 5 cells (83.3%) have expected count less than 5. The minimum expected count is 1.47.
Symmetric Measures
  Value Approximate Significance
Nominal by Nominal Phi .692 .011
Cramer’s V .692 .011
N of Valid Cases 19  

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