# Chapter 2 Variability

by Mark Pezzo
# 1. Systematic vs Error Variance

## 1.1. SYSTEMATIC

### 1.1.1. Variability that reflects consistent (predictable) changes

### 1.1.2. We hope that manipulating our IV will systematically account for some of the total variance

### 1.1.3. EXAMPLE: The drug treatment produced a consistent decrease in blood pressure among patients

## 1.2. ERROR

### 1.2.1. Variability that makes scores hard to predict (aka ''noise'' or ''chance'')

### 1.2.2. EXAMPLE: There are systematic reasons why women are shorter on average (M = 5'4'') than men (M = 5'10''), but chance is responsible for the fact that not all women are exactly 5'4''. We typically refer to these ''within-group'' differences as ''error variance'' (the typical deviation from the mean height for both men and women is +/- 2'')

### 1.2.3. Error Variance is predictable in one sense; It causes scores to be NORMALLY distributed

## 1.3. TOTAL

### 1.3.1. TOTAL VARIANCE = SYSTEMATIC VARIANCE + ERROR VARIANCE

### 1.3.2. Use the GRAND MEAN (mean of ALL scores, regardless of what group they're in) to calculate TOTAL variance

# 2. Between vs Within

## 2.1. SUBJECTS

### 2.1.1. Between-subject Variability

2.1.1.1. Differences between people attributed to their personality traits.

2.1.1.2. EXAMPLE: Introverts are quieter than extraverts

### 2.1.2. Within-subject Variability

2.1.2.1. Differences in a single person that occur over time or in different situations

2.1.2.2. EXAMPLE: I'm more ''extraverted'' after drinking a Red Bull

## 2.2. GROUPS

### 2.2.1. Between-Group Differences

2.2.1.1. Difference between the MEANS of the groups

2.2.1.2. Often too much emphasis on these differences even when very small

2.2.1.3. EXAMPLE: The mean spatial skills for men is greater than for women, but the difference is VERY small.

### 2.2.2. Within-Group Differences

2.2.2.1. Differences between people WITHIN a group

2.2.2.2. Often bigger than the differences between group means

2.2.2.3. EXAMPLE: Men are about 6 inches taller than women, but the tallest and shortest women are much more than 6 inches apart.

2.2.2.4. EXAMPLE: Much is sometimes made of differences between racial groups, but the differences within each race are MUCH bigger than the mean differences between

2.2.2.5. this is new

2.2.2.5.1. one

2.2.2.5.2. two

# 3. Formulas & Definitions . . . . .

## 3.1. VARIANCE FORMULA

### 3.1.1. Variance measures the ''average'' dispersion of scores; (dispersion = squared distance from the mean)

### 3.1.2. MEAN: the ''central tendency'' of a group of scores; Literally the ''balancing point'' of the scores in a FREQ CHART

### 3.1.3. SUM OF SQUARES: Expression used to refer to the top of the variance formula (i.e., sum of the squared deviations from the mean)

## 3.2. STANDARD DEVIATION

### 3.2.1. RISK MEASURE : SD is often used by investors to measure risk (volatility) of a stock; the more a stock's returns vary from the stock's average return, the more volatile the stock.