SECTION 1: CHI-SQUARE ANALYSIS a) When is the Chi-square test used? (hint: types
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SECTION 1: CHI-SQUARE ANALYSIS a) When is the Chi-square test used? (hint: types of variables?) b) What is the alternative hypothesis when we use the Chi-square test? SECTION 2: TABLES In the following SPSS output, is the relationship between the "class" and "race" significant? What is your evidence? What do you do with the null hypothesis? Crosstabs Case Processing Summary MissingN Total Valid NPercentNPercentNPercent Class Race 0% 741 100.0% Class Race Crosstabulation Count Total 20 17 37 38 36 74 Class1 14 Total 25 12 Chi-Square Tests Asymp. Sig Value Pearson Chi-Square 1.884 Likelihood Ratio N ofVald Cases 1.910 74 390 385 a. 0 cells (.0%) have expected count less than 5 The minimum expected count is 5.84Explanation / Answer
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Section 1
a) Chi-Square Test for Independence. This explains how to conduct a chi-square test for independence. The test is applied when you have two categorical variables from a single population. It is used to determine whether there is a significantassociation between the two variables.
The Chi-square test is intended to test how likely it is that an observed distribution is due to chance. It is also called a "goodness of fit" statistic, because it measures how well the observed distribution of data fits with the distribution that is expected if the variables are independent.
There are basically two types of random variables and they yield two types of data: numerical and categorical. A chi square (X2) statistic is used to investigate whether distributions of categorical variables differ from one another. Basically categorical variable yield data in the categories and numerical variables yield data in numerical form. Responses to such questions as "What is your major?" or Do you own a car?" are categorical because they yield data such as "biology" or "no." In contrast, responses to such questions as "How tall are you?" or "What is your G.P.A.?" are numerical. Numerical data can be either discrete or continuous. The table below may help you see the differences between these two variables.
Notice that discrete data arise fom a counting process, while continuous data arise from a measuring process.
The Chi Square statistic compares the tallies or counts of categorical responses between two (or more) independent groups. (note: Chi square tests can only be used on actual numbers and not on percentages, proportions, means, etc.)
b)
Suppose that Variable A has r levels, and Variable B has c levels. The null hypothesis states that knowing the level of Variable A does not help you predict the level of Variable B. That is, the variables are independent.
H0: Variable A and Variable B are independent.
Ha: Variable A and Variable B are not independent.
The alternative hypothesis is that knowing the level of Variable A can help you predict the level of Variable B.
Data Type Question Type Possible Responses Categorical What is your sex? male or female Numerical Disrete- How many cars do you own? two or three Numerical Continuous - How tall are you? 72 inchesRelated Questions
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