Statisics for social science

Statistics for social science

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Statistics for social science

Each variable in a data set has its own levels of measurement: nominal, ordinal, interval, or ratio. This paper advances the idea that the measure of association is mainly used to evaluate directions and strength of association between two variables. Test of significance, however, quantify the probability that statistical results of the data set could have happened due to random chances. The following two variables from GSS 2016 will be analyzed to investigate strength of association between the two variable: Stress (independent variable) and job satisfaction (dependent variable).

Measures of association

Since both the variables (IV and DV) are ordinal, Gamma and Proportional Reduction in Error (PRE) are the appropriate measures to evaluate the strength of association and direction. Gamma provides a continuous number that ranges from -1 to 1. In this case, -1 indicates a perfect negative association, while +1 indicates a perfect positive association and 0 represent no relationship. In other words, the strength of association enhances as the number increases or decreases from zero. The test from the table below measures the relationships between work satisfaction and work stressful.

The Gamma value of -.246 means that, knowing the level of work stress reduces the error in predicting work satisfaction by 24.6%. Moreover, the value indicates moderate relationships between the variables; and they are negatively associated.

Test of Significance

In the test of significance, the p-value is examined to determine whether the results of the data set are statistically significant. The lower p-value suggests strong evidence. The test of significance for the below are the five steps of hypothesis testing:

Step 1

The research question is “is there a relationship between work satisfaction and work stress?” Additionally, the null and research hypotheses are as follows:

H0: There is no correlation between work satisfaction and stress at work.

H1: correlation exists between work satisfaction and stress at work.

Step 2

In statistical research, the data set is deemed to be statistically significant if the probability of the phenomenon being random is less than 1/20.Therefore the appropriate level of significance for this study is .05. By setting = .05 we mean that the probability of rejecting the null hypothesis when it is true is .05. Furthermore, the study involves a two-tailed hypothesis because we are interested in testing the possibility of a relationship in all the direction (Chen& Nadarajah, 2014).

Step 3

A lower p-value suggests strong evidence to support the claim of the research hypothesis. In this case, if the p-value is less than 0.05 (5%), then the null hypothesis is rejected. If the p-value is greater than 0.05 (5%), however, the null hypothesis is accepted (fail to reject) (Gonçalves, Carvalho & Alcaniz, 2015).

Step 4

The table below demonstrates the chi-square test:

Chi-square assumption has been violated because four cells (20%) have expected count of less than 5. Therefore, it is imperative to recode the stress variable to resolve the problem. The code below performs the process:

RECODE STRESS (2.1 thru 3.9=2) (Lowest thru 2=1) (4 thru Highest=3) INTO StressRecoded.

VARIABLE LABELS StressRecoded 'StressRecoded'.

EXECUTE.

CROSSTABS

/TABLES=SATJOB BY StressRecoded

/FORMAT=AVALUE TABLES

/STATISTICS=CHISQ

/CELLS=COUNT EXPECTED

/COUNT ROUND CELL.

The table above demonstrates the chi-square test of the recoded data. It shows that 0 cells have an expected count of less than 5, therefore the assumption of chi-square test have been resolved. The sig value (p-value) is .000.

Step 5

Since the p-value < .05, we accept the research hypothesis. There is enough significance evidence at 5% level of confidence to support the claim that correlation exists between work satisfaction and stress at work. Therefore we conclude that work stress has a negative impact on job satisfaction.

References

Chen, Z., & Nadarajah, S. (2014). On the optimally weighted z-test for combining probabilities from independent studies. Computational statistics & data analysis, 70, 387-394.

Gonçalves, R. S., Carvalho, G. C., & Alcaniz, J. S. (2015). Low-z test for interacting dark energy. Physical Review D, 92(12), 123504.