The research question: Does gender influence the educational level of a person?
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The research question is relevant to the chi-square test because gender and education level are the two variables that exist on a categorical scale. While gender exists in two categories (male and female), educational level exists in four categories (ordinary level, advanced level, college level, & university level). According to David and Sutton (2004), the chi-square test is applicable in testing the existence of a relationship between two categorical variables. In this case, gender is one categorical variable while education level is another categorical variable. Since the research question seeks to establish if gender influences educational level, it compares observed and expected education level in a given population. Concerning the research question, one can expect that education level does not vary according to gender, but observations may show otherwise. Thus, the establishment of the relationship between gender and the education level requires a chi-square test.
The null hypothesis
H0: There is no significant gendered difference in education level.
The null hypothesis predicts that gender and the education level are two categorical variables, which are independent and unrelated. In essence, the null hypothesis holds that gender has no association with the education level of an individual. In the chi-square test, the null hypothesis holds if the chi-statistic is less than the critical value and the p-value is greater than a given significant level.
The alternative hypothesis
H1: There is a significant gendered difference in the education level.
The alternative hypothesis assumes that gender influences the education level of an individual. Essentially, the alternative hypothesis holds that gender and the education level are related or dependent variables. For the alternative hypothesis to be true, the chi-square statistic must have a value greater than the critical value and p-value that is less than a certain significant level.
Types of Error
In the interpretation of the hypothesis, type I and II errors are prone to occur. Rejection of a true null hypothesis results in the commission of type I error. The rejection of a true null hypothesis indicates an outcome of false positive. In this study, if the null hypothesis is true, its rejection implies there is a gendered difference in education level, which is a false positive. In contrast, failure to reject a false null hypothesis makes one to commit a type II error, which shows false negative. Type II error prevents researchers from ascertaining the existence of certain relationships. In this case, failure to reject a false null hypothesis prevents one from accepting a true alternative hypothesis. Therefore, hypothesis testing at significant levels such as 0.05 and 0.01 is appropriate in reducing rejection of a true null hypothesis.
The study will sample 100 participants from the population in Chicago city. In selecting participants, the study will employ the convenience method of sampling because it is cheap and easy to conduct. Since the study seeks to establish if gendered difference exists in the education level among people who are in the city of Chicago, it will select 50 men and 50 women (N = 100). Moreover, the study will sample individuals between the ages of 30 and 40 years. People who fall under the age bracket will participate in the study irrespective of their racial and ethnic backgrounds.
In the research question, gender is the independent variable. Gender is an independent variable because it does not depend on the education level. In an experiment, researchers manipulate the independent variable for it to influence the other variables (Jackson, 2012). In this case, the researcher manipulates gender by ensuring that study participants have equal gender for the findings to be statistically valid. Gender is a discrete variable because one can be either a male or a female; there is no intermediate value or category. Moreover, gender is a qualitative variable because it describes certain qualities of people that are not measurable in terms of digits. The scale of measuring gender is a nominal scale, which exists in categorical form (male and female). Operationally, gender is a nominal variable that gives an attribute of a person as either male or female.
The education level is a dependent variable according to the research question. The education level is a dependent variable because it varies from one person to another. Given that it is a qualitative data, the level of education has discrete values, which have no intermediates. In this view, the level of education is a categorical variable with categories such as ordinary level, advanced level, college level, and university level. The scale of measurement applied in the educational level is ordinal because the education level progresses from the lowest level to the highest level. Thus, the ordinal scale is the appropriate scale for the education level as per the research question. Operationally, the level of education comprises of ordinary level, advanced level, college level, and university level.
The appropriate statistical test for the analysis of the collected data is the chi-square test. Since the chi-square test is applicable in testing if there is an association between two categorical variables, the study seeks to use it in establishing if gender has any significant relationship with the educational level of people in Chicago city. Thus, the chi-square test will present a contingency table that shows relationships between gender and educational level. Romesburg (2004) states that the contingency table provides a detailed view of the relationships between two categorical variables, which expound the chi-square test. Moreover, the chi-square test will present the chi-square value (Pearson Chi-square) and p-value. Therefore, the chi-square value and the p-value is important in testing the null hypothesis and drawing the conclusion of the study.
The biases of the study emanate from the sampling method that study will employ. Since the study will employ the convenience method of sampling, there is a high probability that the potential participants will have high levels of education due to their confidence to participate. Also, as the study targets participants between the ages of 30 and 40 years, there is a high probability that most will have high levels of education. Regarding the test, chi-square requires that the collected data must exist as nominal or ordinal data in compliance with one of the assumptions. Additionally, another assumption requires variables to have two or more categories, which are independent. In hypothesis testing, one can conclude that there is a significant relationship between gender and education level if the p-value is less than 0.05 (p<0.05). In contrast, if the p-value is greater than 0.05 (p>0.05), it implies that there is no significant association between gender and education level. Given that the chi-square test measures the association between two variables, one cannot derive the existence of causal relationships between gender and education level. However, the results of the study are significant in establishing if the gendered difference in the education level is present in Chicago city.
David, M., & Sutton, C. (2004). Social Research: The Basics. New York: SAGE Publisher.
Jackson, S. (2012). Research methods and statistics: A critical thinking approach (4th ed.). Belmont: Wadsworth.
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Romesburg, C. (2004). Cluster Analysis for Researchers. New York: Lulu Publisher.