My colleague's thesis consists of a situation where she has performed a t-test to analyse the differences between male and female respondents' responses with respect to all the independent and dependent variables in the study. Is it right to do so? If yes, please elicit references.
Is Chi-square a more appropriate test in this situation? If yes, please elicit references.
To be precise, the thesis proposed to compare male and female respondent differences across all their independent and dependent variables measured through a structured questionnaire of 55 items on a 5-point likert scale of respondents' self-reported opinions of agree/disagree and neutral types through that particular hypothesis
Your question, "Is gender dichotomous?" depends on how you measure it. How many options were respondents given? Gender is a complex construct and many people are discussing this outside of the statistical question, which Mehmet has answered.
Chi square test requires 2 categorical variables. T test requires 1 categorical and 1 continuous variables.You can't use them interchangeably.
If it is right to do comparisons between male's and female's answers depends on the hypotheses and research questions.
Your question, "Is gender dichotomous?" depends on how you measure it. How many options were respondents given? Gender is a complex construct and many people are discussing this outside of the statistical question, which Mehmet has answered.
I don’t know what the thesis of your colleague is, so it’s difficult to get too specific. However, if this person is simply wanting to know if there are statistically significant differences between males and females across a set of variables then the choice of test depends on the non-gender variable. In other words, you have gender, a dichotomous variable, which is compared to a set of other variables which may be categorical (Smoking: yes/no; Race: White/Black/Hispanic/Asian/…; etc.) or continuous (Age, height, measures of psychological or physiological constructs, etc.).
Of course, the concept of gender has altered somewhat recently (at least in the west) and it is possible you could have more than the two levels of male and female (i.e., transgender). But because, you have not suggested this to be relevant, it is sufficient to say that gender is indeed a dichotomous variable.
When assessing the statistical significance of gender and a categorical variable (i.e., smoking), you have two categorical variables and would use the chi-square test of independence. This is a non-parametric test to evaluate the relationship between two categorical variables. More specifically, it provides a probability that the two categorical variables are related. In the gender/smoking example, a significant chi-square test would indicate a person’s gender is related to whether or not they smoke. Of course, this is just an example, but the logic would follow for any analysis of gender and other categorical variables.
On the other hand, if one were to assess the statistical significance of gender and a continuous variable such as IQ, then the independent samples t-test would be the appropriate test. A significant test would suggest the differences in IQ between the genders exist beyond the theoretical probability that IQ between males and females is merely due to chance. Of course, the same type of thinking applies when assessing the statistical significance between gender and any other continuous variable (assuming they meet the assumptions required for this parametric test).
Unless I am missing something, the information in this post can be found by using a search engine for chi-square test of independence and independent samples t-test. I consulted a statistics text book (Gravetter and Wallnau, 2007).
I apologize for the brevity and lack of detail of this post, but unfortunately, I have to attend to something. However, feel free to post back if you would like me to further clarify anything.
To summarize, gender is typically considered a dichotomous variable, it is certainly a categorical variable. However, the choice of a parametric test such as the t-test or a non-parametric test such as the chi-square test depends not on gender, but on the other variable. If the variable is also categorical than the chi-square test is appropriate; if the variable is continuous, then the t-test is appropriate. I hope this answer provides what you are looking for.
References:
Gravetter F.J., Wallnau L. B. (2007). Statistics for the Behavioral Sciences(7th ed.). Belmont, CA: Thomson Higher Education.
one type of ttest is indpendent sample ttest, it is used to compare for example male vs. female on a dependent variable which should be meausred on a continious level scale.
Ref.
Kellar, Sacey & Kelvin, Elizabeth. (2013). Munro’s Statistical methods for health care research. 6th. ed. Philadelphia: Lippincott.
Thank you all for your valuable responses!
To be precise, the thesis proposed to compare male and female respondent differences across all their independent and dependent variables measured through a structured questionnaire of 55 items on a 5-point likert scale of respondents' self-reported opinions of agree/disagree and neutral types through that particular hypothesis.
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