# Statistics for Sociologists

## Goals of This Module

• Start with a discussion of looking at simple
relationships

between categorical dependent and independent variables

• Converting to proportions , percentages and ratios

• Contingency tables (cross-tabulation)

• Partial tables for multivariate relationships

• Problem of Simpson’s Paradox

• Revisit multiple regression , considering categorical

explanatory variables (dummy variables)

• Look at both main effects ( difference in intercepts ) and

interaction effects ( difference in slopes )

• Question of causation

• Establishing causation

## Converting Raw Numbers to Proportions , Percentages or

Ratios

• Raw numbers (i.e, simply the number of cases in a
particular

category) can often be difficult to interpret, especially if there

are several categories and an awkward number of total cases

• Percentages and proportions (and ratios) are also much easier

to compare both with variables and across variables

• Cautions:

• We must be careful not to over-interpret percentages (or

proportions) based on small total sample sizes

• Tables containing proportions or percentages should always

contain the sample size (n)

## Proportions

• It is often useful to convert raw numbers to
proportions,

especially when comparing categories

• The formula to find a proportion is simply:

• If there are 60 students in the class, 46 of whom are
women,

what is the proportion of women? Here count = 46 and

n = 60, therefore

p = 46/60 = .77

• In other words, the proportion of women in the class is
.77.

• Since the total equals 1, the proportion of men is 1-.77 = .23

## Percentages

• A percentage gives us the same information as a
proportion

except we now multiply the proportion by 100:

• Continuing from the proportions example, if there are 60

students in the class, 46 of whom are women, what is the

percentage of women? Here count = 46 and n = 60,

therefore

p = (46/60)*100 = 77%

• In other words, 77% of the class are women

• Since the total for percentages equals 100, the percentage of

men is 100-77 = 23%

## Ratios

• Ratios allow us to directly compare the relative number
of

cases in one category compared to another:

• If there are 46 women and 14 men, the ratio of women to

men is:

• In other words, there are more than 3 times as many
women

as men in the class

## Bar Graphs and Pie Charts revisited (1)

Bar charts should be used over pie charts – research
indicates

that people are better able to judge the relative difference in

size of straight lines than pie shapes

> plot (type, main="Bar chart for occupation type")

> pie(table(type), main="Pie chart for occupation type")

## Bar Graphs and Pie Charts revisited (2)

An Alternative to the Bar graph & Pie Chart: the Dot Chart

• The dot chart is an

alternative to the bar graph

or pie chart. It is especially

useful for displying

multivariate tables (see

later)

> par(pty="s")

> dotchart(table(type), main="Dot chart for occupation type")

Bar Graphs and Pie Charts revisited (3)

Critique of pie chart by Cleveland (1994, Figures 4.19 p. 262 and 4.20 p. 263)

## Contingency Tables

• Also called Cross-Tabulations

• Display relationships between categorical variables

• Remember: With qualitative variables we talk of relationships

or associations, but NOT correlations.

• Cells of the table represent the number of observations that

fall simultaneously into a particular combination of two

categories of the two variables .

• Tables can be presented in several ways:

1. Raw counts or frequencies

2. Percentages (or proportions) of total N

3. Percentages (or proportions) of column Ns

4. Percentages (or proportions) of row Ns

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