Hello,
I have calculated an average z-score. Now I want to analyze the differences between men and women. Can I use a t-test? If so, how to interpret it. For example: p-value = 0.028; mean men: 0.428; mean women: -0.467. How to interpret it? what does the minus sign mean? Who achieved the higher average score, men or women?
If any other way to solve my problem. I work from a z-score, because originally the data may have completely different boundaries for men and women. It would not be possible to compare them adequately.
Thank you for advice.
Yes, you can use a t-test if you think the data is normally distributed, which it probably is. The fact that p is < 0.05 shows that there is is a significant difference between mean values of men and women. I think your mean values might be in error because it's not possible to get a negative value unless there were negative values in the original data. So recheck the mean values.
You must know the standard deviation of the population and your sample size should be above 30 in order for you to be able to use the z-score. Otherwise, use the t-score.
https://www.statisticshowto.com/probability-and-statistics/hypothesis-testing/t-score-vs-z-score/
Well thank you. I understand, but the z-score can have negative values. Therefore, when I use them in the t-test, those means are negative. And I can't interpret that.
It sounds like you are confused about the z-score itself. In simplified terms, the z-score is a measurement of how far each value is from the mean (average). Therefore, if a group has an average Z score that is negative, that means that overall the group was below the average. In your example, if the men have a positive z-score and the woman have a negative z-score, that means that the women were below the overall average (of both men and women, I assume) and the men were above the overall average (of both men and women, I assume). That means that the men were higher in average than the women in this case.
Dávid Miško , The Z-statistic and the T-statistic are different. They are two different probability distributions from which you can make inferences. In general, T statistics is not recommended if the number of samples is> 50.
If you use z-score you are transforming your variable on another variable with mean 0 and sd 1. Using t-test on z-score is not useful because both men's and women will have a mean close to 0. You can use a t-test directly.
It seems like the p-value is significant; the negative mean just means the average for women is -0.467(but we dont have any information about your data).
Remember, the z-score tells you the number of standard deviations away from the mean (negative means below). To interpret the z-score, you can compare it to the mean. So for men, the mean is 0.428. Let’s say for instance one of the men has a score of 0.892 and his z-score is 2.3. That means for that particular man, his score of 0.892 is 2.3 standard deviations above the mean, which can be interpreted as really good. Same for negative values then, -2.3 sd’s below the mean, which can be interpreted as below the average.
Hope this helps, good luck
It is better to conduct the test on the Raw data. Since, when you convert the data to Z score you have change the mean and the Standard deviation of the data.
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