Please refer to Table 73, Table 74, Table 75 and Table 77 for the results of Gosset’s t-test, the confidence interval for the mean, the confidence interval for the mean difference and Cohen’s d effect size for the UWES scale and its sub-scales, respectively.
The results obtained by applying visual and numerical methods for testing the normality of the data indicates that the data for the UWES scale, absorption sub-scale and vigor sub-scale appears to be approximately normally distributed for both generations except for the dedication sub-scale. The Shapiro-Wilk test of normality indicated the departure from normality for the dedication sub-scale (particularly for Generation Y) though the visual inspection of the histograms, box plots and z-values for the skewness and kurtosis indicated approximately normal distribution. Therefore, for the dedication sub-scale both parametric (Gosset’s t-test) and non-parametric (Mann-Whitney U Test) tests are used. As stated previously, the t-test is robust to the data which has some departure from normality.
Hypothesis testing is conducted by considering the two-tailed test. p-value method is used for statistically testing the null hypothesis. The level of significance is set at α = .05 for all the hypotheses. It is considered that if the p-value is less than the level of significance, the null hypothesis will be rejected.
4.21.1 Parametric test (Gosset’s t-test)
Based on the results of the F-ratio test and Levene’s test for the equality of variances, which indicated that the variances are equal across both generation groups, Gosset’s t-test or the student’s t-test is used to compare the means of Generation Z and Generation Y sample population for the work engagement (UWES) scale and its sub-scales (vigor, dedication and absorption). The level of significance considered for the t-test is set at α = .05. The mean values for Generation Z’s work engagement (UWES) scale and its sub-scales (vigor, absorption and dedication) are less in comparison to the mean values for Generation Y’s work engagement, vigor, dedication and absorption respectively. Both generations have a lower mean value for
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the absorption sub-scale as compared to the remaining two sub-scales and the higher mean value for the dedication sub-scale when compared with the other two remaining sub-scales. As the assumption of normality seems to be violated for the Generation Y dedication sub-scale and is very close to that violation based on the Shapiro-Wilk result for Generation Z dedication sub-scale, additional help is taken from the non-parametric test (Mann-Whitney U test) for the dedication sub-scale and the results of this test are published in Table 76.
Table 73
Results of Gosset’s T-Test: Two-Sample Assuming Equal Variances for the UWES Scale and its Sub-Scales for Generation Z and Generation Y
4.21.2 Confidence intervals for the mean and the mean difference
Table 74 contains information about the confidence intervals for the mean for work engagement, vigor, dedication and absorption variables for both generations and Table 75 contains the information about the confidence intervals for the mean difference for the UWES scale and its sub-scales.
How well the sample statistic (e.g. mean) estimates the underlying population value is always an issue and this issue is addressed by the computation of confidence interval (CI) as it provides a range of values that is likely to contain the population parameter of interest (NIST Sematech, n.d., para. 1). The CI is formed at a confidence level and it means that if the sample population is sampled many times and if the interval estimates are made each time, the resulting intervals would bracket the true population parameter in approximately 95% of the cases (NIST Sematech, n.d., para. 2).
Generation Z Generation Y Generation Z Generation Y Generation Z Generation Y Generation Z Generation Y Mean 3.64 3.78 3.70 3.81 3.53 3.66 3.71 3.88 Variance 1.11 0.94 1.14 0.95 1.20 1.07 1.78 1.36 Observations 97 92 97 92 97 92 97 92 Pooled Variance 1.03 - 1.05 - 1.13 - 1.58 - Hypothesized Mean Difference 0 - 0 - 0 - 0 -
df 187 - 187 - 187 - 187 - t Stat -0.92 - -0.73 - -0.86 - -0.94 - P(T<=t) one-tail 0.18 - 0.23 - 0.19 - 0.17 - t Critical one-tail 1.65 - 1.65 - 1.65 - 1.65 - P(T<=t) two-tail 0.36 - 0.47 - 0.39 - 0.35 - t Critical two-tail 1.97 - 1.97 - 1.97 - 1.97 - Note. Gosset's t-test is based on the mean values of the UWES scale and its sub scales. Gosset's t-test is used after conducting the F-ratio test and Levene's test for the equality of variance.
Vigor Sub-Scale Absorption Sub-Scale Dedication Sub-Scale UWES Scale
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Table 74
Generation-Wise Mean and 95% Confidence Interval for Mean for Work Engagement, Vigor, Dedication and Absorption
Table 75
95% Confidence Interval for the Mean Difference for Work Engagement, Vigor, Dedication and Absorption
4.21.3 Hypothesis testing: Gosset’s t-test results
4.21.3.1 Overall hypothesis for the UWES scale
The result of the two independent samples t-test indicates that there is not a significant statistical difference between work engagement of Generation Z (n = 97, M = 3.64, SD = 1.05, 95% CI [3.43, 3.86]) and work engagement of Generation Y (n = 92, M = 3.78, SD = 0.97, 95% CI [3.58, 3.98]), t(187) = -0.92, p = .36, d = .13, 95% CI [-0.43, 0.15] in Auckland. As it is a statistically non-significant result (p = .36) at 5% level of significance (α = .05), we fail to reject the null hypothesis.
4.21.3.2 Hypothesis testing for vigor
The result of the two independent samples t-test indicates that there is not a significant statistical difference between vigor of Generation Z (n = 97, M = 3.70, SD = 1.07, 95% CI
Mean Lower Bound Upper Bound Mean Lower Bound Upper Bound
Work Engagement 3.78 3.58 3.98 3.64 3.43 3.86
Vigor 3.81 3.61 4.01 3.70 3.49 3.92
Absorption 3.66 3.45 3.88 3.53 3.31 3.75
Dedication 3.88 3.64 4.13 3.71 3.44 3.98
Generation Y Generation Z
95% Confidence Interval for Mean 95% Confidence Interval for Mean
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[3.49, 3.92]) and vigor of Generation Y (n = 92, M = 3.81, SD = 0.97, 95% CI [3.61, 4.01]), t(187) = -0.73, p = .47, d = 0.11, 95% CI [-0.40, 0.19] in Auckland. As it is a statistically non- significant result (p = .47) at 5% level of significance, we fail to reject the null hypothesis. 4.21.3.3 Hypothesis testing for absorption
The result of the two independent samples t-test indicates that there is not a significant statistical difference between absorption of Generation Z (n = 97, M = 3.53, SD = 1.09, 95% CI [3.31, 3.75]) and absorption of Generation Y (n = 92, M = 3.66, SD = 1.03, 95% CI [3.45, 3.88]), t(187) = -0.86, p = .39, d = 0.13, 95% CI [-0.44, 0.17] in Auckland. As it is a statistically non-significant result (p = .39) at 5% level of significance, we fail to reject the null hypothesis. 4.21.3.4 Hypothesis testing for dedication
The result of the two independent samples t-test indicates that there is not a significant statistical difference between dedication of Generation Z (n = 97, M = 3.71, SD = 1.33, 95% CI [3.44, 3.98]) and dedication of Generation Y (n = 92, M = 3.88, SD = 1.17, 95% CI [3.64, 4.13]), t(187) = -0.94, p = .35, d = 0.14, 95% CI [-0.53, 0.19] in Auckland. As it is a statistically non-significant result (p = .35) at 5% level of significance, we fail to reject the null hypothesis.
4.21.4 Non-parametric test (Mann-Whitney U test)
In addition to the parametric test (Gosset’s t-test) for the dedication sub-scale, the non- parametric (Mann-Whitney U test) is performed for the dedication sub-scale as the Shapiro- Wilk test of normality indicated a departure from normality for Generation Y dedication sub- scale, W(92) = .97, p = .040 and is very close to the level of significance (α = .05) for the Generation Z dedication sub-scale, W(97) = .97, p = .055.
The Mann-Whitney U test is a non-parametric alternative to the independent t-test. The null hypothesis under this test requires that the two groups come from the same population (homogeneous having the same distribution) (Grande, 2017; Nachar, 2008). For the non- normal and non-identical distributions, the null hypothesis is that there is not a significant statistical difference between the mean ranks of two groups and the alternate hypothesis is that there is a significant statistical difference between the mean ranks of two groups. For the non- normal but identical distributions, the null hypothesis is that there is not a significant statistical difference between the medians of the two groups and the alternative hypothesis is that there
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is a significant statistical difference between the medians of the two groups (Grande, 2017; Lambert, 2017a; Lambert, 2017b; O’Loughlin, 2016). The assumption of the Mann-Whitney U test is that the distribution of two groups though not normally distributed should be the same to infer it in terms of the medians and this assumption can be checked by referring to the histogram and box plots (Grande, 2017; Lambert, 2017a; Lambert, 2017b). The histogram and the box plots are already reported under the normality section. It is indicated by the histogram and box plot that the distribution of both Generation Y’s dedication sub-scale and Generation Z’s dedication sub-scale appears to be same as most of the observations are concentrated towards the middle and the right side of the histogram and very few observations are appearing towards the left side of the histogram. The histogram for both groups looks approximately identical. The box plot for both generations indicates the similar shape of the distribution. The test of homogeneity of variance (Levene’s test) also confirms that the distribution of both groups is approximately similar. The result of the Levene’s test for the equality of variance has already been reported. As the assumption of the Mann-Whitney U test for having a non-normal but identical distribution has been met, the inference is based on the medians of these two generations. Please refer to Table 76.
The null hypothesis for the Mann-Whitney U test for the dedication sub-scale is that there is no difference between the medians of Generation Z and Generation Y for the dedication sub- scale. It is a two-tailed test with a level of significance set at 5% (α = .05).
Table 76
Result of Mann-Whitney U Test for the Dedication Variable of Generation Z and Y
The result of the Mann-Whitney U test for the dedication sub-scale shows that the Mdn = 3.90 for the Generation Y dedication sub-scale is higher as compared to the Mdn = 3.80 for the
Generation Z dedication sub-scale, U = 4174.50, n1 = 97, n2 = 92, p = .44, η2 = .00, two-tailed,
where n1 means Generation Z sample size and n2 means Generation Y sample size but it is a
Measures n Mean Rank Sum of Ranks Statistics Median Effect Size
Generation Z 97 92.04 8927.50 - 3.80 -
Generation Y 92 98.13 9027.50 - 3.90 -
Mann-Whitney U Statistics - - - 4174.50 - -
Z - - - -0.77 - -
Z2 - - - 0.59 - -
Asymp. Sig. (2-tailed) - - - 0.44 - -
Eta- Squared (η2) - - - 0.00 - No effect
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statistically non-significant result, therefore we fail to reject the null hypothesis. The computed
eta-squared (η2 = .00) effect size is indicating no-effect.
4.21.5 Cohen’s d effect size for the UWES and its sub-scales
Effect size is the quantification of the difference between two groups and has an emphasis on the size of the difference rather than confounding it with the sample size. It is measured in the standard deviation units (Coe, 2002).
The computed Cohen’s d effect size is in the range of d = .11 to d = .14 for the UWES scale and its sub-scales, which means a very small effect for the UWES scale and its sub-scales. The negative or positive value of the Cohen’s d depends upon which group’s mean is subtracted first from the other group’s mean. Please refer to Table 77 for the results.
Table 77
Results of Cohen’s d Effect Size for the UWES Scale and its Sub-Scales for Both Generations