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Application: Chi-Square Study: Intelligence and Self-Esteem


Previously in this course, you worked with parametric statistics like t tests, ANOVAs, and correlations. In order to use parametric procedures, your dependent variables must be measured on either an interval or a ratio scale. For this Assignment you will examine the nonparametric procedure called chi-square, which allows you to analyze nominal data compared to parametric tests that allow you to analyze interval and ratio data. Consider this example: You are curious whether males report that they like statistics more frequently than females report that they like statistics. You decide you will ask them a yes-or-no question, and that involves nominal data. You would then count the numbers of responses of yes and no for males and for females.


Nonparametric procedures allow you to compare the male responses to the female responses and determine if gender and enjoyment of statistics are independent from each other (not related). Understanding chi-square will help you to more fully understand research studies that utilize nominal variables.




To prepare for this Assignment, imagine that you have information about 30 other participants’ self-esteem and intelligence, but for these individuals you only have data on whether they have average or above average intelligence, and whether they have high or low self-esteem. You do not have their actual scores for each variable. The observed frequencies are reported here:

Above Average
Self-Esteem Low




To complete this Assignment, submit by Day 7 your answers to the following. Based on the scenario, use SPSS to determine if intelligence is related to self-esteem in your sample by computing the appropriate chi-square test. Save and submit both the SPSS data and output files.


  • Explain what scale of measurement is used to measure intelligence in this example. How do you know?
  • Explain what scale of measurement is used to measure self-esteem. How do you know?
  • Before computing the chi-square, state your null and alternative hypotheses in words (not formulas).
  • Based on the hypotheses you stated, explain whether you should conduct a one-way or two-way chi-square test and why.
  • Identify the obtained ?2.
  • Identify the degrees of freedom and explain how it is calculated.
  • Identify the p value.
  • Explain whether you should retain or reject the null hypothesis and why.
  • Explain what you can determine about the relationship between self-esteem and intelligence, based on this set of data.
  • Submit three documents for grading: your text (Word) document with your answers and explanations to the application questions, your SPSS Data file, and your SPSS Output file.
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