Everything discussed above cannot yield a meaningful answer because heteroskedasticity a has been ignored. The means whether tested by independent approaches or by binary approaches will lead to wrong inference because of nonconstant variance.

The first step is exploratory data analysis (EDA).

You need to draw boxplots.

For example draw the following boxplot:

x: salary

y: group

You will see outliers and means and medians for each group.

Then for each group you can conduct the following regression:

log(salary) ~ b1 * gender + b2 * GPA + ... + error term

The significance of coefficients will show you, for example, if expected salary depends on gender.

Good luck!

Mercedes Orús-Lacort

Thank you for an answer, Mercedes Orús-Lacort. I assume you recommend me to use t-test, because I have quite large samples and the sampling distribution of the mean for a variable will approximate a normal distribution due to central limit theorem. I think in such way I can explain why I choose t-test.

I’ve already done t-tests and calculated size effects for all my groups. But sometimes I have different variances in groups and the larger group, unfortunately, has a smaller variance. In such case what should you recommend?

(I mean the approximation is only correct when the larger group has also larger variance)

Andrey Davydenko Thank you very much! I got it! I haven't done linear regressions before but i will study hard.

As per your description it seems that your dependent variable is salary expectations (quantitative) and independent variables are Groups(situations),gender, both of which are qualitative.You can create a dummy variable for each situation so you shall have six categories in Groups(situations).

I hope you are using R for data analysis. If so use the aggregate function in R to find out the mean salary expectations across the various combinations of Groups(situations) and Gender . This gives you some clue about the salary expectations across different situations among males and females.From there you can decide the type of hypotheses and the appropriate statistical tests.

As your sample is pretty large the normality issues my not be a problem. If you still persist with normality you can use the non parametric alternatives to t-test like Wilcox-Test and for ANOVA the non parametric alternative is Kruskal-test.

The R code for aggregate function :

>aggregate(salaryexpect~gender+Group,data=data,mean)

store your data in a data.frame and run this code and as per your description you will get 12 means representing 2*6 situational groups. Comparison of theses group means will give you some clue of your further analysis.

Best of luck.

Srinivasa rao Dasaraju I am much obliged to you for your answer! Thank you very much!

Everything discussed above cannot yield a meaningful answer because heteroskedasticity a has been ignored. The means whether tested by independent approaches or by binary approaches will lead to wrong inference because of nonconstant variance.

Chuck A Arize No, it has not been ignored:

Here's the model I suggested:

log(salary) ~ b1 * gender + b2 * GPA + ... + error term

Since we work in logs, this should stabilize the variance. Should be tested though, so good point. But for salary, generally, logs will work.

Regarding the boxplots, it is just a visual tool to compare distributions, so nothing prevents from using boxplots.

Why is semi-log used? Could you explain differential dummy and differential slope were implemented to handle the key question with heteroskedasticity taken care of. I am interested in the t-test. Thanks

Usually salary is variable that has a log-normal distribution. Taking logs will make the assumptions of the classic linear regression more plausible. Maybe additional transformations will be needed for independent variables, hard to say in the absence of data.

Hi, Oleksandra,

There is a way to do exactly what you wish, without any distributional assumptions required to obtain exact p values. The method always identifies the most accurate answer which is possible for your data and hypothesis. There are numerous options for computing cross-generalizability to an independent random sample. Propensity scores can be computed to address possible threats to causal inference. If you are interested in learning more, here are some introductory articles.

The methodology always identifies the most accurate answer possible for your sample.

• https://odajournal.com/2014/04/06/a-statistical-guide-for-the-ethically-perplexed-chapter-4-panter-sterba-handbook-of-ethics-in-quantitative-methodology-routledge-2011-clarifying-disorientation-regarding/
• https://odajournal.com/2014/03/27/unioda-vs-students-t-test-comparing-two-migraine-treatments-2/
• https://odajournal.com/2015/12/02/unioda-vs-t-test-low-brain-uptake-of-l-11c5-hydroxytryptophan-in-major-depression/
• https://odajournal.com/2019/05/23/oda-vs-t-test-lysozyme-levels-in-the-gastric-juice-of-patients-with-peptic-ulcer-vs-normal-controls/

The methodology requires no distributional assumptions, achieved maximum accuracy is corrected to remove the effect of chance, and cross-generalizability is easily evaluated by a variety of methods.

• https://odajournal.com/2017/04/18/what-is-optimal-data-analysis/
• https://odajournal.com/2016/11/04/theoretical-aspects-of-the-d-statistic/
• https://odajournal.com/2016/05/02/using-unioda-to-determine-the-ess-of-a-cta-model-in-loo-analysis/

Propensity scores can be created and used to minimize threats to causal inference.

• Linden, A., & Yarnold, P.R. (2017). Using classification tree analysis to generate propensity score weights. Journal of Evaluation in Clinical Practice, 23, 703-712. DOI: 10.1111/jep.12744
• https://odajournal.files.wordpress.com/2019/01/v6a8.pdf

With respect to your specific objectives:

The methodology can compare two or more groups with respect to salary expectations:

• https://odajournal.com/2013/11/19/oda-range-test-vs-one-way-analysis-of-variance-comparing-strength-of-alternative-line-connections/
• https://odajournal.com/2014/08/18/globally-optimal-statistical-classification-models-i-binary-class-variable-one-ordered-attribute/

The methodology can identify the influence of subject variables (e.g., gender, GPA, etc.) on salary expectations for each of the six groups.

• https://odajournal.com/2016/09/19/novometric-analysis-with-ordered-class-variables-the-optimal-alternative-to-linear-regression-analysis/
• https://odajournal.com/2019/04/14/regression-vs-novometric-analysis-predicting-income-based-on-education/

Overfitting is not a problem

• https://odajournal.com/2019/03/21/some-machine-learning-algorithms-find-relationships-between-variables-when-none-exist-cta-doesnt/
• https://odajournal.com/2019/04/11/effect-of-sample-size-on-discovery-of-relationships-in-random-data-by-classification-algorithms/
• https://odajournal.com/2019/05/16/logistic-discriminant-analysis-and-structural-equation-modeling-both-identify-effects-in-random-data/
• https://odajournal.com/2019/04/22/multi-layer-perceptron-neural-net-model-identifies-effect-in-random-data/

And, your sample size is sufficient from a statistical power perspective:

• https://odajournal.com/2020/02/08/statistical-power-analysis-in-oda-cta-and-novometrics-invited/

The only statistical software which can conduct these analyses is available vis-à-vis

• http://ODAJournal.com

Paul Yarnold , Thanks a lot! I have not heard about ODA before.