Chapter 10, Problem 32PR

(a)

To determine

State the decision for each of the measure.

Answer to Problem 32PR

For the measure opportunity to promote the null hypothesis is rejected.

For the measure high pay the null hypothesis is rejected.

For the measure pay according the null hypothesis is rejected.

Explanation of Solution

The given results reported that the study of psychological contract.

Decision rule based on the P-value:

• If the p-value $\le \left(\alpha =0.05\right)$, the null hypothesis is rejected and the test is significant.
• If the p-value $>\left(\alpha =0.05\right)$, the null hypothesis is retained and the test is not significant.

Conclusion for measure opportunity to promote:

The p-value for measure opportunity to promote is less than 0.001.

The level of significance is 0.05.

The $p\text{-value}\left(<0.001\right)<\alpha \left(=0.05\right)$

The null hypothesis is rejected and the test is significant.

Conclusion for measure high pays:

The p-value for measure high pays is less than 0.001.

The level of significance is 0.05.

The $p\text{-value}\left(<0.001\right)<\alpha \left(=0.05\right)$

The null hypothesis is rejected and the test is significant.

Conclusion for measure pays according to performance:

The p-value for measure pay according to performance is less than 0.001.

The level of significance is 0.05.

The $p\text{-value}\left(<0.001\right)<\alpha \left(=0.05\right)$

The null hypothesis is rejected and the test is significant.

Hence, for all the three measures the null hypothesis is rejected.

(b)

To determine

Find the values of omega-squared for each of the measures.

Answer to Problem 32PR

The proportion of variance for measure opportunity to promote is 0.05 and effect size is small.

The proportion of variance for measure high pay is 0.10 and effect size is medium.

The proportion of variance for measure pay according to performance is 0.11 and effect size is medium.

Explanation of Solution

Calculation:

Omega-square:

The proportion of variance is also measured using omega-square. The bias that is caused by eta-square is corrected by omega-squared. The value of omega-square is conservation and give small estimate of proportion of variance. It is denoted by $\left({\omega }^2\right)$.

${\omega }^2=\frac{t^2-1}{t^2+df}$

In the formula, t is the value of test statistic and df is the corresponding degrees of freedom. Subtracting 1 in the numerator reduces the effect size.

The description of effect size using Omega-square:

• If value of omega-squared is less than 0.01, then effect size is trivial.
• If value of omega-squared is in between 0.01 and 0.09, then effect size is small.
• If value of omega-squared is in between 0.10 and 0.25, then effect size is medium.
• If value of omega-squared is greater than 0.25, then effect size is large.

The degrees of freedom for related samples design is, $n_D-1$, $n_D$ denotes number of the difference in the scores.

There are 255 employees in the sample. The degrees of the freedom is,

$\begin{array}{c}df=n_D-1\\ =255-1\\ =254\end{array}$

Omega-square for opportunity to promote:

The value of test statistic for related t samples test is 3.65 and degrees of freedom is 254. The value of omega-square is,

$\begin{array}{c}{\omega }^2=\frac{t^2-1}{t^2+df}\\ =\frac{{3.65}^2-1}{{3.65}^2+254}\\ =\frac{13.3225-1}{13.3225+254}\end{array}$

$\begin{array}{c}=\frac{12.3225}{267.3225}\\ =0.05\end{array}$

The value of omega square is 0.05. This value is lies between 0.01 and 0.09 and hence the effect size is small.

Omega-square for high pay:

The value of test statistic for related t samples test is 5.50 and degrees of freedom is 254. The value of omega -square is,

$\begin{array}{c}{\omega }^2=\frac{t^2-1}{t^2+df}\\ =\frac{{5.50}^2-1}{{5.50}^2+254}\\ =\frac{30.25-1}{30.25+254}\end{array}$

$\begin{array}{c}=\frac{29.25}{284.25}\\ =0.10\end{array}$

The value of omega square is 0.10. This value is lies between 0.10 and 0.25 and hence the effect size is medium.

Omega-square for pay according to performance:

The value of test statistic for related t samples test is 5.61 and degrees of freedom is 254. The value of omega -square is,

$\begin{array}{c}{\omega }^2=\frac{t^2-1}{t^2+df}\\ =\frac{{5.61}^2-1}{{5.61}^2+254}\\ =\frac{31.4721-1}{31.4721+254}\end{array}$

$\begin{array}{c}=\frac{30.4721}{285.4721}\\ =0.11\end{array}$

The value of omega square is 0.11. This value is lies between 0.10 and 0.25 and hence the effect size is medium.