Ch. 4

Scales of Measurement

• Nominal = numbers as representative of categories



• qualitative differences between categories

Examples from your q're?

• Ordinal=number as representative of categories
• quantitative difference = ranking

Examples?

When to use which: identity versus magnitude

• Interval scale=numbers represent quantities



• equal intervals



• no absolute 0

Examples?

• Ratio scale=numbers represent quantities
• equal intervals
• absolute 0

Relevance to your Results section

• Coding sheet

Frequency Distributions=

How often does each score appear?

Y-axis: frequency

X-axis: category/score

• nominal/ordinal

• interval/ratio

Types of Frequency distributions:

• Normal





• Bimodal





• Positively skewed





• Negatively skewed

In SPSS:

Using Frequencies in your Participants Section

-analyze frequency of sex, ethnicity

"Participants

The sample consisted of 120 participants, approximately half of whom were women (N = 62) while the rest were men (N = 58). Further, approximately 42 percent of participants were White, and the remaining participants were evenly distributed across African American (17%), Latin Amercian (20%), Asian American (14%) and other (7%) (See Table 1)"

Measure of Central Tendency

• Mean

• Median





• Mode



• when to use which

Variability=how dispersed/ spread out scores are from the mean

• range



• standard deviation



• applying the concept to the math

In SPSS:

hit statistics button, and click all that apply

Sample Results section:

-analyze means, and standard deviation (interval data)

-report:

"Table 1 shows the means and standard deviations of high school and college GPAs by gender. The means and standard deviations of high school GPAs were relatively similar for men and women. However, it appears that on average, women had higher college GPAs than men"*

Table 1

Means and Standard Deviations for College and High School GPA Scores for each Gender

High School GPA	M 2.53	SD .92	M 2.55	SD .82
College GPA	2.25	.40	2.73	.37

Standard (Z-)Scores: transforms raw scores into a score depicting your position in the distribution:____ standard deviations above/below the mean.

Purpose: To compare different scales

e.g., Did you perform as well on a quiz as an exam?

e.g., Test Mean Std. Dev raw score

Assignment 15 2.5 16 (80%)

Test 36 6 48 (80%)

Correlation: the extent to which two variables are related

• strength





• direction--see "scatterplots"

SPSS

Sample Results section

" ...means, sd's...

Correlation coefficients were computed to assess the relationship between perceived personal and group discrimination. Results indicated there was a positive correlation, r = .65, p = >01, such that the more women perceived their group to be discriminated against, the more they perceived themselves to personally experience discrimination"

Regression analysis=used to predict one variable (Y) from several (X1, X2 etc.)

• How much do we understand the predicted variable by knowing other variables (Do we need to investigate more variables?)

Answer:

r²=% of variability explained in the predicted (Y) by the predictor (X) variable

• which variable predicts Y best?

Answer: regression coefficient

SPSS

Sample Results section

"...means, sd's, correlations...

To assess the predictors of collective action, a regression analysis was conducted whereby collective action was regressed onto personal and group discrimination. Together, personal and group discrimination explained 24.8% of the variability in collective action, F(2, 110) = 18.17, p = .01. However, only perceiving personal discrimination uniquely predicted collective action, B = .50, p =.01, such that the more women perceived themselves to be victims of discrimination, the more action they took"