Chapter 14 Flashcards
Describe the difference between a parametric technique and a nonparametric technique.
Nonparametric techniques is used to make inferences about populations rather than population parameters.
Parametric tests: Infer population parameters from sample statistics
Parametric techniques assume that the data follows a certain distribution (usually normal). In contrast, nonparametric techniques do not make such assumptions and can be used with data that does not meet these criteria.
How do you determine degrees of freedom for a chi-square test for goodness of fit?
For a chi-square test for goodness of fit, degrees of freedom are calculated as the number of categories minus one (df = k - 1), where k is the number of categories.
How does a chi-square test differ from parametric tests?
A chi-square test is a non-parametric test that allows for inferences about population frequencies from sample frequencies, making it suitable for analyzing data measured on nominal and ordinal scales without as many assumptions as parametric tests.
Define the context in which nonparametric techniques are preferred over parametric techniques.
Nonparametric techniques are preferred when research questions do not involve specific parameters of a distribution but rather the entire frequency distribution, such as when analyzing the popularity of different car models based on sales data.
Describe the relationship between obtained frequencies and chi-square value.
The chi-square value increases when the obtained frequencies are either larger or smaller than the expected frequencies, indicating a greater discrepancy.
How is the sampling distribution of chi-square constructed?
The sampling distribution of chi-square is constructed by randomly selecting a sample from a population, recording the frequencies, and then calculating the squared differences between observed and expected frequencies divided by the expected frequencies.
Define the significance of comparing obtained chi-square values with the distribution of values under the null hypothesis.
Comparing obtained chi-square values with the distribution of values under the null hypothesis helps determine whether the observed outcome is likely or unlikely, based on the assumption that the null hypothesis is true.
Describe how the shape of the chi-square distribution changes.
The shape of the chi-square distribution changes depending on the degrees of freedom, which are related to the number of independent discrepancies (O - E) that are free to vary.
Define the two types of chi-square tests discussed.
The two types of chi-square tests are: (1) the chi-square test for goodness of fit, used for one variable, and (2) the chi-square test for independence, used to determine if two variables are related.
How is the region of rejection characterized in a chi-square test?
The region of rejection in a chi-square test appears in the upper tail of the distribution, indicating that the test is nondirectional and a low chi-square value suggests that obtained frequencies are closer to expected values than chance would predict.
Define the Chi-Square Test for Goodness of Fit.
The Chi-Square Test for Goodness of Fit is used to determine if the observed frequencies of categories in a sample match the expected frequencies specified by the null hypothesis.
How are null and alternative hypotheses established in a Chi-Square Test for Goodness of Fit?
Null and alternative hypotheses are determined a priori, based on the research question. The null hypothesis typically states that there is no difference in preference among categories, while the alternative hypothesis suggests that preferences differ.
Describe a practical example of using the Chi-Square Test for Goodness of Fit.
A tavern owner may test customer preferences for four types of beer by having 100 customers taste each type. If the null hypothesis states no preference, the expected frequency for each type would be 25, while the alternative hypothesis would suggest that preferences differ from this expectation.
Describe the process of comparing the obtained chi-square value with the critical value.
To compare the obtained chi-square value with the critical value, first calculate the chi-square statistic using the observed and expected frequencies. Then, determine the degrees of freedom based on the number of comparisons that can vary. Finally, consult the chi-square distribution table for the critical value corresponding to the calculated degrees of freedom and significance level. If the obtained value is equal to or greater than the critical value, the null hypothesis is rejected.
Define the significance of the critical value in a chi-square test.
The critical value in a chi-square test serves as a threshold that the obtained chi-square statistic must exceed to reject the null hypothesis. It is determined based on the degrees of freedom and the chosen significance level (alpha). If the obtained value is greater than or equal to the critical value, it indicates a statistically significant difference in the observed data.
