Statistical test - which method?

[Tina Bader]

Hey!

For the hypothesis testing, I have a dependent variable which is job satisfaction (on a Likert-type-scale from 1-10) and an independent variable which is education and training in years.
To my knowledge, job satisfaction is ordinally scaled and education in years is measured on a ratio scale.
Which statistical method can I use? Am I right with correlation method of Spearman? Do you have other suggestions?

Thank you very much.

Kind regards,
Tina

[Clyde Schechter]

The Spearman correlation would be one satisfactory approach. I should also point out that in many populations, the education and training variable will have a reasonably close to normal distribution, so that inferences from Pearson correlation would be valid even in small samples. So Pearson r could be another way to go, or, equivalently, linear regression. Of course, you have to be comfortable with treating your job satisfaction variable as if it were a quantitative variable with interval properties. The idea behind Likert scales is that the response options correspond to equally spaced levels of the underlying construct, so that the score from the scale is, in fact, effectively an interval-level variable. But then again, Likert scales don't usually have 10 options, and I would defer to the opinion of somebody who is familiar with this scale and its psychometric properties.

But before doing any of that, I would examine it graphically. You might find a highly non-linear relationship that would not be properly captured by any of those techniques.

[Carlo Lazzaro]

Tina:
as an aside to Clyde's excellent advice, if you decide to take the matter further and go -regress- you should exclude a possibe endogeneity problem; person's ability can affect both education level and job satisfaction.

[Marcos Almeida]

If I understood right, this was underlined in both previous posts. I mean, with a dep var ranging from 1 to 10, depending on its pattern, oftentimes there may be room to put a standard OLS to a test.

[Tina Bader]

Thank you very much for your quick answers. As I am not very familiar with the statistical methods, I am a bit confused and have some more questions. Could you please help me!

Dependent variable= Job satisfaction (ordinal scale, treated as interval scaled); Independent variable= Education and training in years (ratio scaled)
Number of observations= 2871

Summary statistics: MEAN / STANDARD DEVIATION
Job satisfaction= 6.469871 / 2.278451; Education in years= 11.68599 / 2.308687

First, I checked the variances by means of the sdtest. The result is that the variances are quite equal (also regarding the summary statistics - standard deviations).
Then, I tried to check if they are normally distributed. I used the Shapiro-Francia test because n > 2000. The results are:


Shapiro-Francia W' test for normal data

Variable	Obs	W'	V'	z	Prob>z
education	2,812	0.89342	182.914	12.737	0.00001
job satisfaction	2,871	0.98026	34.538	8.672	0.00001

According to my research, the Shapiro-Francia test says that the variances are not equal, because prob>z is smaller than 0.05 (5% significance level). How do I interpret the results concerning the variances now? Are they equal or not?

I also used the sktest and got following results:
Skewness/Kurtosis tests for Normality
------ joint ------

Variable	Obs	Pr(Skewness)	Pr(Kurtosis)	adj chi2 (2)	Prob>chi2
education	2,812	0.0000	0.0000	.	0.0000
jobsatisfaction	2,871	0.0000	0.5551	.	0.0000

And then I tried to examine the relationship between education in years and job satisfaction graphically; command: graph twoway (lfit education jobsatisfaction) (scatter education jobsatisfaction).



How can I interpret this scatterplot and the relationship between education in years and job satisfaction? And what are my concluding findings / which statistical methods are appropriate?

correlate education jobsatisfaction)
(obs=2,714)

	education	jobsatisfaction
education	1.0000
jobsatisfaction	0.0251	1.0000

pwcorr education jobsatisfaction, sig

	education	jobsatisfaction
education	1.0000
jobsatisfaction	0.0251	1.0000
	0.1919

Could you please help me, so that I can apply the statistical tests? THANK YOU VERY MUCH!

Kind regards,
Tina Bader

[Carlo Lazzaro]

Tina:
with large samples, even a minimal departure from normality makes the tests you ran significant.
You should not worried about that, but I'm still not clear with your research goals.
Are you sure that you want correlation instead of going -regress-?

[Tina Bader]

Thanks for your answer Carlo.
Normality is not the problem, but can I assume a linear relationship between job satisfaction and education in years?
Is it wrong to first look at the correlations? Of course I used -regress- and got the following results.

First, I used job satisfaction with its 0-10 Likert-type scale as the dependent variable (ordinal scale, treated as interval scaled); Independent variable= Education and training in years (ratio scaled).



To compare, I generate a new variable for job satisfaction which summarizes 0-6 to a low level, 7-8 to a moderate level, 9-10 to a high level of job satisfaction.
I generated a new variable for education and training which summarizes three types of school-leaving qualifications. Both new created variables are now ordinal scaled - right?




Does it make sense to use the new generated variables or better analyse it with the old variables?

Thank you very much for your help.

[Marcos Almeida]

Just a side note, after Carlo's reply.

The correlation shows a tiny r, which is non-significant. What is more, the fit line points to a non-significant coefficient as well.

This seems to be "the" result. Maybe trying to get a different result, I mean, a significant p-value , if it was no programmed at all, will eventually be taken as a fishing expedition. By the way, should there be a rationale for happiness according to the level of education? If the answer is positive, the pattern of distribution shows the opposite way...

[Tina Bader]

Marcos, thank you for your notes. The expectation of this hypothesis is that higher-educated temporary agency workers (more years of education and training) have higher job satisfaction levels.

[Carlo Lazzaro]

Tina:
- I would definitely go -regress- instead of -pwcorr- (or other rank-based correlation approaches);
- -regress- allows you to investigate a possible turning point in education: that is, a maximum in the number of years of education after that job satisfaction actually decreases. Put differently, you might find out that the relationship between years of education and job satisfaction is not linear, but quadratic. Please note that this situation is perfectly legal under -regress-, as the linearity should be in coefficients, not in predictors;
- again, I suspect that you might have an endogeneity issue to cope with: personal ability (which, in your case in currently embedded in residuals) can well influence both education attainment (ie, one of your predictors) and job satisfaction (ie, your dependent variable).