Categorical Data! • Frequency Table – Records the totals (counts or percentage of observations) for each category. If percentages are shown, it is a relative frequency table. • Distribution – Shows the possible values of the variable and the relative frequency of each value
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Categorical Data! Frequency Table –Records the totals (counts or percentage of observations) for each category. If percentages are shown, it is a relative.
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Categorical Data!• Frequency Table
– Records the totals (counts or percentage of observations) for each category. If percentages are shown, it is a relative frequency table.
• Distribution– Shows the possible values of the variable and
Contingency Table• Displays counts and sometimes percentages of
individuals falling into named categories on two or more variables. Shows how individuals are distributed along each variable contingent on the value of another variable.– Marginal distribution: distribution of either variable by
itself (last row or column)– Conditional Distribution: distribution of 1 variable for
those individuals satisfying a condition on another variable. Considers a smaller group isolated from the whole.
Independence???• Independence…think impact!
– Variables are independent (one variable does not influence the value of the other variable) if the conditional distribution of 1 variable is the same for each category of the other.
Slide 3 - 8
Contingency Tables
• A contingency table allows us to look at two categorical variables together.
• It shows how individuals are distributed along each variable, contingent on the value of the other variable.– Example: we can examine the class of ticket and whether
a person survived the Titanic:
Slide 3 - 9
Contingency Tables (cont.)
• The margins of the table, both on the right and on the bottom, give totals and the frequency distributions for each of the variables.
• Each frequency distribution is called a marginal distribution of its respective variable.– The marginal distribution of Survival is:
Slide 3 - 10
Contingency Tables (cont.)
• Each cell of the table gives the count for a combination of values of the two values.– For example, the second cell in the crew column tells us
that 673 crew members died when the Titanic sunk.
Slide 3 - 11
Conditional Distributions
• A conditional distribution shows the distribution of one variable for just the individuals who satisfy some condition on another variable.– The following is the conditional distribution of
ticket Class, conditional on having survived:
Slide 3 - 12
Conditional Distributions (cont.)
– The following is the conditional distribution of ticket Class, conditional on having perished:
Python Eggs
Cold Neutral Hot
Number of Eggs
27 56 104
Number hatched
16 38 75
1) What percent of cold eggs hatched?
2) Neutral eggs hatched represent what percent of the total?