Statistical Reasoning in Psychology (Coursework Sample)

Statistical Reasoning in Psychology
The Summary of the Analysis
This section contains the summary of the result of the analysis of the two independent departments. Below is the statement of the null hypothesis and the alternate hypothesis. The aim of this analysis is to carefully inspect the effect of reduced work hours (RWH) on the performance of the employees in the company. In view of this, a sample size of 30 was taken from two independent departments of the company (Group 1 and group 2).
Statement of Hypothesis:
H0: µ1 - µ2 = 0
Ha: µ1 - µ2 < 0
The null hypothesis states that there is no difference in employee performance while the alternate hypothesis states that the performance of group 1 is less than the performance of group 2 (1-tail test). The choice of 1-tail test is due to the presence of direction in the alternate hypothesis.
Table 1: Summary of Result
t-Test: Two-Sample Assuming Equal Variances

 

 

 


 

 

GROUP 1

GROUP 2

Mean

5.61

7.326667

Variance

4.798172414

1.855816

Observations

30

30

Pooled Variance

3.326994253

 

Hypothesized Mean Difference

0

 

df

58

 

t Stat

-3.645067529

 

P(T<=t) one-tail

0.000286392

 

t Critical one-tail

1.671552762

 

P(T<=t) two-tail

0.000572783

 

t Critical two-tail

2.001717484

 

Source: Author’s computation, 2022
The table above contains the summary of the result of the analysis. This data was computed using Microsoft Excel’s data analysis tool pack. The choice of t-test’s two samples assuming equal variances is because of the need to compare two independent department groups in the analysis. The pooled variance is a statistic calculated using the values of the individual variances (This value was calculated because of the choice of t-test: two samples assuming equal variance).
The significance level of the comparison is 5%, hence we have 95% confidence that the result of the hypothesis test is valid. From part 1 of this assignment, the alpha level is 0.05. The alpha level is the probability of making the wrong decision when the null hypothesis is true (i.e the probability of committing Type 1 error) This implies that when the probability of obtaining a sample mean is less than 5% if the null hypothesis were true, then we reject the value stated in the null hypothesis. From table 1, the mean and variance of group 1 are approximately 5.610 and 4.798 respectively (to 3 decimal places). Similarly, the mean and variance of group 2 are approximately 7.327 and 1.856 respectively (to 3 decimal places).
The value of the test statistic is -3.645. The Critical value for a one-tailed test is approximately 1.672 while the critical value for a 2-tailed test is approximately 2.002. The test is a one-tailed test due to the existence of a stated direction in the alternative hypothesis, which is more effective. It can also be seen from the table that the value of the p-value for one-tail and two-tail is approximately 0.0003 and 0.0006 respectively.
Decision: Reject the null hypothesis, as the p-value is less than the alpha level. There is enough evidence to support the claim that the performance of group 1 is less than the performance of group 2. From the table above, the value of the p-value is less than 0.05, hence the rejection of the null hypothesis. We can also make this decision using the value of the test statistic; reject the null hypothesis, as the absolute value of the test statistic (3.645) is greater than the absolute value of the critical value (1.672). Hence, there is a significant difference in the comparison of the groups.
Conclusion: There is a significant difference in the co