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I'm working on my graduation research; one of the hypotheses I have is that there is a significant variation between male and female employees in their level of performance.

The t-test provided a p-value > 0.05 indicating no difference.

Out of curiosity, I ran the correlation test and again p-value > 0.05.

My question again is: is there a statistical rule I can rely on and cite in the research that states: we can predict no correlation if there is no significant difference?

additional info:

  • performance is measured by 5 point-scale (10 statements; each is given a value of 1 up to 5...the mean of performance is to sum all the statements values and divide them by 10)= continuous variable (dependent)

  • gender is an independent variable; male and female are not related to each other.

Nick Cox
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Ruba
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    I can see that if you are comparing two populations and look for significant differences than a test like the t test may be appropriate. When dealing with correlation you have a natural pairing as in your case perhaps a particular man should be paired with a particular woman. These are two different questions with different data to look at so one p-value can't predict another. There are many issues associated with testimg differences between populations and correlation. We can help if you can be more specific about what you did. – Michael R. Chernick Dec 17 '16 at 12:03
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    What exactly are you correlating here? This is not clear from your question. – Ruben van Bergen Dec 17 '16 at 12:05
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    Tell us about the data. What units is performance measured in? Also pay attention to Nick's answer and my comments following his answer. – Michael R. Chernick Dec 17 '16 at 12:18
  • Performance is discrete not continuous. Totals vary 10(1)50 and means 1(0.2)10. Otherwise I don't think any of the new information contradicts points made by @Michael Chernick and myself. – Nick Cox Dec 17 '16 at 16:14
  • The additional description shows that the men and women are not paired, so where is correlation between men and women involved. Performance is discrete. But it seems to be derived in a complicated way based on ten questions. I don't understand. The original question was about the difference between statistical significance and correlation and whether non-significance based on a t test and non-significance in a test of correlation go hand in hand. I think that has been answered in the negative. Are you now going somewhere else with this question? – Michael R. Chernick Dec 17 '16 at 16:34
  • One more note: averaging 10 values that each can be 1, 2, 3, 4 or 5 will lead to values that are between 1 and 5 and are not necessarily integers But they still constitute a finite set of fractions. – Michael R. Chernick Dec 17 '16 at 16:41
  • Look at my answer here: http://stats.stackexchange.com/questions/131065/non-transitivity-of-correlation-correlations-between-gender-and-brain-size-and/131069#131069 Maybe this is what you encountered? – kjetil b halvorsen Dec 18 '16 at 10:15

1 Answers1

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You should say more about your exact data set-up.

A t-test could be applied in two quite different circumstances.

  1. You have one group of males and one group of females, and nothing else said.

  2. You have groups of males and females and males and females are paired. For example, each pair could be a couple in a relationship. If possibly, you have an experimental design selecting pairs, one male and one female, in otherwise comparable circumstances.

If your case is #1, then I can see no sense whatsoever in which a correlation makes sense. There is no pairing of values. You can't just call up a correlation on two sets of values. Shuffling of males relative to females would just change the result arbitrarily.

If your case is #2, the correlation can be calculated but it doesn't assess similarity or difference at all. For example, if each male has exactly the same performance level as each female, then the difference is 0 and the correlation is 1. If each female scores 42 points more on performance, then the correlation is 1. It's possible to imagine any combination of (difference, no difference) and (correlation, no correlation).

In short, for comparing performance of males and females, a t test might make sense, but either a correlation is meaningless or at best it is answering a quite different question.

Nick Cox
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  • As you can see here Nick and I hit one of the main points answering nearly simultaneously. With more information we can give you better answers and also refer you to posts where you can find some of your answers. Here are some issues related to your question. – Michael R. Chernick Dec 17 '16 at 12:08
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    What test is appropriate to compare two populations parametric or nonparametric? What does correlation mean? Is correlation related to causation? What is the right significance level for a test of hypothesis? Is 0.05 a magic number? Why is the p-value so commonly misunderstood? How is it related to the significance level? Also Nick has raised questions about how you should collect data to best answer your questions. This enters the are of design of experiments. – Michael R. Chernick Dec 17 '16 at 12:14