AP Statistics Tutorial Exploring Data • The basics • • • • • • Charts and graphs • • • • • • • • • Regression • • • • • • • • Categorical data • • Experimentation • Surveys • • • • Experiments • • Anticipating Patterns • Probability • • • Random variables • • • • • • • • Discrete variables • • • Continuous variables • • • • • Sampling distributions • • • Statistical Inference • Estimation • • • • • Confidence intervals • • • • • • • Hypothesis testing • • • • Hypothesis tests • • • • • • • • • Appendices • ■ • ■ • ■. AP Statistics Lessons The basics • • • • • Charts and graphs • • • • • • • • Regression • • • • • • • Categorical data • • Surveys • • • Experiments • • Probability • • Random variables • • • • • • • Discrete variables • • Continuous variables • • • • Sampling distributions • • • Estimation • • • • Confidence intervals • • • • • • Hypothesis testing • • • Hypothesis tests • • • • • • • • • Appendices • • • Chi-Square Test for Independence This lesson explains how to conduct a chi-square test for independence. The test is applied when you have two from a single population. It is used to determine whether there is a significant association between the two variables. Ventana De Microsoft Publisher 2010. For example, in an election survey, voters might be classified by gender (male or female) and voting preference (Democrat, Republican, or Independent). We could use a chi-square test for independence to determine whether gender is related to voting preference. The at the end of the lesson considers this example.

This test is performed by using a Chi-square test of independence. Recall that we can summarize two categorical variables within a two-way table, also called a r × c contingency table, where r = number of rows, c = number of columns. For a contingency table that has r rows and c columns, the chi square test can. Follow the link below to access a java-based program for calculating Chi Square. For a contingency table that has r rows and c columns, the chi square test can. Follow the link below to access a java-based program for calculating Chi Square.

When to Use Chi-Square Test for Independence The test procedure described in this lesson is appropriate when the following conditions are met: • The sampling method is. • The variables under study are each.

• If sample data are displayed in a, the expected frequency count for each cell of the table is at least 5. This approach consists of four steps: (1) state the hypotheses, (2) formulate an analysis plan, (3) analyze sample data, and (4) interpret results. State the Hypotheses Suppose that Variable A has r levels, and Variable B has c levels. The states that knowing the level of Variable A does not help you predict the level of Variable B. That is, the variables are independent.

H 0: Variable A and Variable B are independent. Serial Windows Server 2012 R2 Standard X64. H a: Variable A and Variable B are not independent. The is that knowing the level of Variable A can help you predict the level of Variable B. Note: Support for the alternative hypothesis suggests that the variables are related; but the relationship is not necessarily causal, in the sense that one variable 'causes' the other. Formulate an Analysis Plan The analysis plan describes how to use sample data to accept or reject the null hypothesis.

The plan should specify the following elements. • Significance level. Often, researchers choose equal to 0.01, 0.05, or 0.10; but any value between 0 and 1 can be used. • Test method. Use the to determine whether there is a significant relationship between two categorical variables.

Analyze Sample Data Using sample data, find the degrees of freedom, expected frequencies, test statistic, and the P-value associated with the test statistic. The approach described in this section is illustrated in the sample problem at the end of this lesson. • Degrees of freedom. The (DF) is equal to: DF = (r - 1) * (c - 1) where r is the number of levels for one catagorical variable, and c is the number of levels for the other categorical variable. Acer Aspire One D270-26dkk Drivers. • Expected frequencies. The expected frequency counts are computed separately for each level of one categorical variable at each level of the other categorical variable. Compute r * c expected frequencies, according to the following formula.