Categorical Data Analysis

Definition

·       A two-dimensional table in which each observation is classified on the basis of two variables simultaneously

·       The simplest way to display the results of a study examining the association between two discrete variables

Degrees of freedom : Number of observations that are free to vary (once one value is in the table, the other values cannot vary)

®    df = (R-1) (C-1)

            Observed Frequencies

®    The numbers in the table that indicate the number of people that were observed to be in that category

·       The way that you choose to percentage the table affects the interpretations that you make about the information in the table

®    Percentage based on row totals = Can interpret the percentages by comparing between the columns within a row 

®    Percentage based on column totals = Can work out the percentage of this total that is in each category 

§  Does not provide information as to whether any difference is present between the variables

·       Does not tell you whether the association between variables is larger than you’d expect by chance or not 

Definition

Statistic that you calculate to help you determine the likelihood of the association found in the contingency table, having occurred by chance

1)      Calculate the expected frequency for each cell in the table

®    Divide the row total by the grand total

®    Multiply the result by the column total

®   (row total x column total)  grand total

2)      Subtract the expected frequency from the observed frequency for each cell in the table

3)      Square the value found in step 2 for each cell in the table

4)      Divide the result of step 3 by the expected value for each cell in the table

5)      Sum the results of step 4

1)      Research hypothesis

®    State H₀ vs H₁

2)      Sampling distributions and sample statistics

®    Collect data and construct and check the assumptions of the sampling distribution of a particular statistic

3)      Degree of compatibility data | null hypothesis

®    Compare the statistic to that distribution and find the probability of exceeding the observed statistic’s value

4)      Decision making

®    Reject or retain the null hypothesis (H₀) 

·       Independence

®    Observations are independent of each other

§  Example: you cannot have people who are studying degrees from more than one faculty

®    Mutually exclusive and exhaustive

·       Small expected frequencies

®    Expected frequencies (m_i) shouldn’t be smaller than 5 (20% of the observations allowed)

1)      Research hypothesis

®    State H₀ vs H₁

2)      Sampling distributions and sample statistics

®    Collect data and construct and check the assumptions of the sampling distribution of a particular statistic

3)      Degree of compatibility data | null hypothesis

®    Compare the statistic to that distribution and find the probability of exceeding the observed statistic’s value

4)      Decision making

®    Reject or retain the null hypothesis (H₀)

·       Independence

®    Observations are independent of each other

®    Mutually exclusive and exhaustive

·       Small expected frequencies

®    Expected frequencies (m_i) shouldn’t be smaller than 5 (20% of the observations allowed)