The simplest approach would be to do a t-test for each protein at each age. There are some major problems with this approach, that are compounded by the problem that your different protein levels are not independent of each other. You could run a Bonferroni correction (simply devide your significance threshold (0.05) by the number of pairwise tests. This too is not a great solution, as the result will miss many significant differences. However, that is about the end of simple solutions.

Is there is a regular progression of protein levels at the different ages? If so, a regression model that includes a variable "male" versus "female" could provide a better solution. Maybe start by running a correlation analysis to see if the protein level at Age 2 is correlated with the protein level at Age 1, and so forth for however many ages you have.

A discriminant analysis. You know that you have males and females, can you use various protein levels to unmistakably identify male versus female for each age group? You also know ages, so can you find some combination of the protein levels at different ages to identify age within each sex?

The first main issue is sample size. If you have 2 or 3 replicates (e.g. 2 males and 2 females at each age), then you are stuck with the simplest approach, and you will have to hope that you get a reviewer that doesn't care (or know) about the problems. If you have a sample size of 20 or more replicates, then you can (with care) run your data through nearly every statistical method in the book if you have enough time.

Dear Parya

The first step you must test your data for normality distribution, in case of normal distribution, you can use ANOVA with factorial experiment 2 × 4 or ? ( gender × levels of different age), so you can test the main effect of each gender and age and the interaction between them.

Good Luck

Your question is not clear enough

1. Number of groups is not specified are there only 2 groups male and female if so apply t-test.

2. If number of groups are more like age range wise groups like 10-20 year 1 group, 20-30 years 2nd group , 30-40 years so on in both male and female then you will use ANOVA.

3. You have not mentioned variable just proteins needs clarification Albumin, globulin, their ratio what else etc

4. If some qualitative variable use Chi-Square for them in case of more numbers they can be tested in ANOVA as well

1) You should plot your data: can you see an effect?

2) Be clear on whether you are testing individual variables for normality which can be done before analysis, or if you are testing the residuals for normality (which can only be done after the analysis). In many cases, the statistical method only cares if the residuals are normally distributed.

If you have 2 replicates and the test for normality fails to reject the null hypothesis, what does that tell you about your data?

3) If there are problems in #2, will you rely on the robustness of the method, apply a transformation, or use a non-parametric method?

4) Do you need to test means, or medians? Is the mean a good representation of the data? You probably can't tell if there are only three replicates.

A great deal depends on your sample size.

Dear Timothy A Ebert

Thank you for your response. My data sets are not normally distributed. I have number of proteins for both male and female at different age. Protein levels have partial correlation and all protein numbers decrease by age. I tried to use effect size to make comparison between male and female. Next I employed spearman partial correlation in SPSS to test partial correlation between protein numbers. Since I could not consider gender as ordinal variable I was not able to consider that in spearman partial correlation and I was looking for a method to consider influence of gender on the proteins levels.

Dear Khalid hassan

Thank you for response. My data sets are not normally distributed. Is effect size (Cohen d) a good way to evaluate statistical difference between male and female?

Dear Ashique Ali

Thank you for your response.My data set is not normally distributed. I tried spearman partial correlation to evaluate correlation between protein levels and used effect size to see if difference between male and female is statistically significant or not.