Correlation won't answer your question. As Dr. Iyisoy said, if you want to know which gender is more productive in your sample all you need to do is compare the two means. If you want to see if one gender is significantly more productive you could use a t-test or any other related method for comparing means. Either way, you don't need correlation for either of these.

You can calculate average of productivity variable within each gender and understand which gender is more productive. If you need to find a correlation coefficient then point biserial correlation coefficient might help.

Correlation won't answer your question. As Dr. Iyisoy said, if you want to know which gender is more productive in your sample all you need to do is compare the two means. If you want to see if one gender is significantly more productive you could use a t-test or any other related method for comparing means. Either way, you don't need correlation for either of these.

If your objective is what you indicated in your last sentence of your explanation that you want to ....see which gender is more productive in your sample. This suggest that you want to do comparison between "men Vs Females" if this is the case then the proper test is a comparison model i.e. T-test (Parametric test) or Man Whitney U test (non Parametric test). Which model between the two to use will depend on the nature of your data and compliance to other assumptions especially this is applicable to parametric test which are associated with a set of stringent assumptions.

In event where your data does not meet a minimum assumptions for the parametric test then you go for the non parametric test (Man Whitney U Test) despite of being relatively weaker that the parametric test but will still serve the purpose. 

I hope this helps you to move forward,

Hi,

How to find the Point-Biserial Correlation Coefficient Related to Other Correlation Coefficients?

In distinguishing the point-biserial from other correlation coefficients, I must first point out that the point-biserial and biserial correlation coefficients are different. The biserial correlation coefficient (or rbi) is appropriate when you are interested in the degree of relationship between two interval (or ratio) scales but for some logical reason one of the two is more sensibly interpreted as an artificially created dichotomous nominal scale.

For instance, you might be interested in determining the degree of relationship between passing or failing a first year university ESL course and language aptitude test scores.

To do this, grades at the end of the course (A, B, C, D and F, often converted to a 4.00, 3.00, 2.00, 1.00, & 0.00 interval scale) might be artificially separated into a nominal scale made up of two groups: pass (A to D, or 1.00 to 4.00) and fail (F or 0.00). The degree of relationship between this new, artificially created dichotomy and the interval scores on the language aptitude test could then be determined by using the rbi coefficient.

Thus the biserial correlation coefficient is appropriately applied when the nominal variable is artificially created (as in the pass-fail variable created from grade points), while the point-biserial correlation coefficient is appropriately applied when the nominal variable occurs naturally (as in the naturally occurring male-female gender distinction).

Hi Ruba,

for correlations between interval and nominal variables, usually (partial) eta squared is used and it is the best approach for your question. You get the amount of variance explained by the nominal variable. The square root of eta can be used as a correlation coefficient. When using SPSS, you can conduct an ANOVA with gender as the independent variable and the outcome as the dependent. You have to activate "effect size" under the options menu.

This way, you as well can test, if gender has a significant contribution and to what degree.

Best regards,

Wolfgang

Check out MCA in MicrOsiris (microsiris.com) or use the Stat decision tree http://microsiris.com/Statistical%20Decision%20Tree/default.htm to find alternatives epending on characteristics of the nominal and interval variable.

thank you Mehmet, i was planning actually to use it but i've been told that my sample must ‎meet the assumptions 1) data must be normally distributed and mine is approximately normal, ‎‎2) mine has outliers..few about 2 or three but ...exist...any alternatives? 

Dear Stephen, i've included your suggestion, i actually conducted a t-test of independent samples and it supports the results i found from conducting the point bi-serial correlation; there is a significant difference between the two genders. I also compare the means and Males were slightly higher than Females; p value for the correlation was low and negative interpreted as (productivity decline as we moved to the higher value of gender: M=1, F=2). so, females have lower productivity levels. 

do you think that providing all these test together will support the results or will be just a repetition of the same findings? 

thank you 

If you have a problem with outliers and non-normality, you can consider a non-parametric test (like Wilcoxon, bootstrapping, etc.).

As for the results, these sound redundant to me; I don't see how the correlation adds anything that the comparison of means doesn't already show. It's also harder to understand (because "higher value of Gender" is not inherently meaningful, Gender doesn't have a natural order, so a reader can't understand what that means without knowing how you coded gender; if you coded it was F=1,M=2 then the correlation would be in the opposite direction).

Ruba

In my point of view, it is artificial to check normality of scale data, since scale variables are not even continuous. So I would be against your told argument that you need to check normality. Yes outliers may effect correlation coefficient but not point biserial in the same sense I guess. Because in point biserial coefficient one of your variables is categorical and it has only two values. Whatever outliers might happen in the second continuous one, and you should be more explicit in what sense you consider an observation in your continuous variable an outlier. Do you mean an outlier to normality of your continuous data?

You say there is a slight difference between male/female scores. If that slight difference is considered large enough by a subject matter expert then you could have enough evidence that there is a difference between genders in addition to significance of your p value. So this means p value being significant does not imply that observed effect is theoretically big and meaningful.

I guess one of your aims is to show that your found effect is big enough. One way of expressing this, is using effect sizes. For your case an effect size indicator might be Cohen's d. So I suggest you calculate Cohen's d and evaluate it in addition.

if your nominal variable is broken into 2 categories then use simple simple regression

 As Abdulrazzak says: this is a linear regression with one factor. Your research question is clearly very applied, which makes this whole NHST and p-value approach completely useless. Run a regression and interpret the parameters quantitative, with an added statement on uncertainty, your confidence or credibility limits.

http://rpubs.com/schmettow/school

nice informations

I think in your case you don't need correlation it will be t-test or other techniques. However, since your data failed the parametric assumptions as I see you explaining in a response as you face problem with outliers and non-normality, you can consider a non-parametric test. You can achieve that with SPSS

correlation eta statistics can serve your purpose. you can do it in spss.

See MicrOsiris:

MCA examines the relationships between several categorical independent variables and a single

dependent variable using an additive model.

MNA performs a multivariate analysis of nominal-scale dependent variables, using a series of

parallel dummy-variable regressions derived from each of the dependent variable codes,

dichotomized to a 0-1 variable.

To do correlation between nominal variable and a scale, make sure the nominal is variable is dichotomy, then you can do point biserial correlation.

When the nominal variable is more than 2 categories, correlation test violate the assumption of linearity. it is not the correct test.

With a binary outcome variable (gender) and continuous scale-independent variable, you can use logistic regression to measure the relationship between the 2 variables.

You can run simple regression

Or you can use recode command to change the contineous variable into a dichotous vaiable and then run Chi- square test.

Bout always go back to theory and review of literature in determining the number of independent variables in the multilpe regression equations. We dont have two variables in isolation. I do believe that productivity is determined by more variables and gender could be just one variables among others determined by theory and / or previous research