According to data obtained from the General Social Survey...

According to data obtained from the General Social Survey (GSS) in 2014,1644 out of 2532 respondents were female and interviewed in person, 551 were male and interviewed in person, 320 were female and interviewed over the phone and 17 were male and interviewed over the phone. a. Explain how we could regard either variable (gender of respondent, interview type) as a response variable. b. Display the data as a contingency table, labeling the variables and the categories. c. Find the conditional proportions that treat interview type as the response variable and gender as the explanatory variable. Interpret. d. Find the conditional proportions that treat gender as the response variable and interview type as the explanatory variable. Interpret. e. Find the marginal proportion of respondents who (i) are female, (ii) were interviewed in person.

According to data obtained from the General Social Survey (GSS) in 2014,1644 out of 2532 respondents were female and interviewed in person, 551 were male and interviewed in person, 320 were female and interviewed over the phone and 17 were male and interviewed over the phone.
a. Explain how we could regard either variable (gender of respondent, interview type) as a response variable.
b. Display the data as a contingency table, labeling the variables and the categories.
c. Find the conditional proportions that treat interview type as the response variable and gender as the explanatory variable. Interpret.
d. Find the conditional proportions that treat gender as the response variable and interview type as the explanatory variable. Interpret.
e. Find the marginal proportion of respondents who (i) are female, (ii) were interviewed in person.

Key Concepts

Marginal Proportions

Marginal proportions are the overall percentages calculated for each individual category of a variable, regardless of the other variable's categories. These are obtained by dividing the total count in a category by the overall sample size. Marginal proportions provide a summary of the distribution for each variable and are useful for describing the overall structure of the data.

Conditional Proportions

Conditional proportions refer to the fractions or percentages calculated within subsets of the data defined by one of the variables. When one variable is treated as the explanatory variable, the proportions of each response category are computed within each level of the explanatory variable. This approach helps in understanding how the distribution of the response variable changes across different categories of the explanatory variable.

Response and Explanatory Variables

In studies involving categorical data, one variable may be designated as the response (or outcome) variable, while the other is considered the explanatory (or predictor) variable. However, in contingency table analysis, the distinction can be arbitrary or based on the research question. This flexibility highlights that the status of a variable can change depending on which aspect of the association you wish to explore and interpret.

Contingency Table

A contingency table is a matrix used to display the frequency distribution of variables. It provides a systematic way to show the counts (and sometimes percentages) of observations that fall into each combination of category levels from the two variables. This tool is fundamental in categorical data analysis as it allows researchers to quickly assess the relationship between the variables.

Transcript

00:30 We're going to look at a poll that took respondents that were in classified them, broke them down based on their gender of male and female, and how they viewed their level of risk as it being important when choosing a retirement investment.

00:49 So this is question 54.

00:55 And part a wanted to know the probability of taking whether or not the level of, low risk was important.

01:09 You looked at that table, we're going to look at a poll that took respondents that were in classified them, broke them down based on their gender of male and female and how they view their level of risk as it being important when choosing a retirement investment.

01:54 So this is question 54 and part a wanted to do.

02:05 And it was 0 .49.

02:07 And that's for both male and female janitors.

02:12 Okay, if we look at b, they wanted to know what the importance of the males, when the males responded, saying that it was important.

02:25 Now, because this is males only that we're looking at, we're going to use the number of the table of the total males that responded, which was 0 .50.

02:35 Row and then the no probability of taking whether or not the level of risk was important.

02:46 You looked at that table, the number from the male's row, that said it was important, and that was 0 .22.

02:56 You calculate that out, the probability then of being male and saying that the risk is important is 0 .44.

03:05 They did the same thing for the females then.

03:10 They looked at females that said it was important what the probability of a female saying that is important again because there was point and it was 0 .49 and that's for both male and female genitors okay if we look at b they wanted to know what the importance of the males when the males responded saying that it was important now because this is males only that we're looking at we're going to use the number of the table of the total males that responded, which was 0 .50, and then the number 50 for the number of respondents that were female, and the importance part in the table was 0 .27.

04:05 You calculate that out, and that's going to have a probability of 0 .54...

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