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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