Background
The research question for this study was: Does age affect the number of hours worked in a week? Therefore, the dependent variable is hours worked in a week while the independent variable is age. The aim in this study is to therefore check whether age is a significant predictor of hours worked in a week.
From the previous works, we have checked the descriptive statistics of the two variables of interest. From the skewness, kurtosis and the histograms plotted using age and hours worked, we confirmed that indeed the two variables are normally distributed. The research hypotheses are as given below:
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H 0 : Age does not affect the number of hours worked in a week.
H 1 : Age affects the number of hours worked in a week.
Cross-tabulation
The tables below show the cross-tabulation results between age and hours worked in a week. The results will help us check whether there is a significant association between the two variables. Age has been reduced from a continuous level to an ordinal level of measurement with four levels (1 = 18-38 years; 2 = 39-58 years; 3 = 59-78 years and 4 = 79-98 years). Hours worked in a week was also reduced from a continuous level to an ordinal level of measurement with five levels (1 = 0-20 hours; 2 = 21-40 hours; 3 = 41-60 hours; 4 = 61-80 hours and 5 = 81-100 hours).
|
Hours in groups * Age in groups Crosstabulation |
||||||||
Age in groups |
Total |
|||||||
|
18-38 years |
39-58 years |
59-78 years |
79-98 years |
|||||
| Hours in groups | 0-20 hours | Count |
65 |
31 |
23 |
3 |
122 |
|
| % of Total |
5.8% |
2.8% |
2.0% |
.3% |
10.9% |
|||
| 21-40 hours | Count |
227 |
255 |
79 |
1 |
562 |
||
| % of Total |
20.2% |
22.7% |
7.0% |
.1% |
50.0% |
|||
| 41-60 hours | Count |
135 |
183 |
46 |
1 |
365 |
||
| % of Total |
12.0% |
16.3% |
4.1% |
.1% |
32.5% |
|||
| 61-80 hours | Count |
25 |
32 |
8 |
0 |
65 |
||
| % of Total |
2.2% |
2.8% |
.7% |
.0% |
5.8% |
|||
| 81-100 hours | Count |
5 |
4 |
1 |
0 |
10 |
||
| % of Total |
.4% |
.4% |
.1% |
.0% |
.9% |
|||
| Total | Count |
457 |
505 |
157 |
5 |
1124 |
||
| % of Total |
40.7% |
44.9% |
14.0% |
.4% |
100.0% |
|||
From the results in the above table, the age group that was most likely to work the highest percentage of hours per week (44.9%) was (39-58 years), followed by 18-38 years at 40.7%, then 59-78 years at 14.0% and lastly the 79-98 years age-group at 0.4%. This shows that age indeed has effects on working patterns. To confirm this, further analysis was performed as shown in the tables below:
|
Chi-Square Tests |
|||
|---|---|---|---|
|
Value |
df |
Asymp. Sig. (2-sided) |
|
| Pearson Chi-Square |
34.601 a |
12 |
.001 |
| Likelihood Ratio |
30.739 |
12 |
.002 |
| Linear-by-Linear Association |
.141 |
1 |
.707 |
| N of Valid Cases |
1124 |
||
| a. 8 cells (40.0%) have expected count less than 5. The minimum expected count is .04. | |||
A chi-square test was performed to check whether there was a significant association between age and number of hours worked in a week. From the results in the table above, it is evident that indeed age and number of hours worked are associated, χ2 = 34.601, p = 0.001.
An additional test to check on the strength between age and number of hours worked in a week was carried out. The results are as given below.
|
Symmetric Measures |
|||
|
Value |
Approx. Sig. |
||
| Nominal by Nominal | Phi |
.312 |
.001 |
| Cramer's V |
.309 |
.001 |
|
| N of Valid Cases |
1124 |
||
Findings in the table above show results from the Phi and Cramer’s V tests of association. In this case, we will use the Cramer’s V test since our variables have more than 2 levels. From the results, the strength of association between age and hours worked is strong, Cramer’s V value = 0.309, p = 0.001.
