Differences between Marginal, Joint, and Conditional Distributions - Assignment Example

Marginal (unconditional) distribution is used to examine the distribution of a single variable (row or column variable) in a two-way table. The row totals and the column totals in a two-way table give the marginal distributions of the two variables separately. There are two marginal distributions in a two-way table and each marginal distribution from a two-way table is a distribution for a single categorical variable.

The joint distribution of the row and column variables is found by dividing the count in each cell by the total number of observations.
The conditional distribution of the row variable for one specific value of the column variable is each entry in the column as a percent of the column total. The conditional distribution of the column variable for one specific value of the row variable is each entry in the row as a percent of the row total. The complete conditional distribution gives the proportions or percentages for all possible values of the conditioning variable. The conditional distribution reveals the nature of the association between two categorical variables. 

M7 Chi-Square Discussion

Define chi-square. When is it appropriate to use? What are the two models for using a chi-square test?
The chi-square statistic (denoted by χ2) measures the relative difference between expected and observed frequencies (cell counts). It is a measure of how much the observed cell counts in a two-way table diverge from the expected cell counts. The Chi-square statistic is computed by first taking the difference between each observed count and its corresponding expected count, Taking the Square of these values, then dividing each squared difference by the expected count, and finally taking the sum of all the values.
The chi-square is appropriate to use when the variables are simple random samples (SRSs), measured on the categorical level and the average expected cell count is 5 or greater and all individual expected counts are 1 or greater, except in the case of 2 × 2 tables. All four expected counts in a 2 × 2 table should be 5 or greater.

The two models for using a chi-square test are ‘Comparing several populations: the first model’ and ‘Test independence: the second model’. In the first model, independent SRSs are drawn from each of the c populations, and each observation is classified according to a categorical variable with r possible values. The first model tests the hypothesis that the distribution of the response variable is the same in all c populations. In the second model, a single SRS is drawn from a population, and observations are classified according to two categorical variables having r and c possible values. The second model tests the association (or independence) between two variables. Read More