Test 3

Evaluates the mean difference between two measurements taken from a single sample

• within-subject

• related-samples

• dependent-samples design

Repeated-measures designs require FEWER participants than needed for an independent-measures design

• Individual differences in performance from one participant to another are eliminated.

• Reduces the variance between subjects → reduces the

  estimated standard error → increases power

Repeated-measures designs are well suited for examining CHANGES THAT OCCUR OVER TIME (such as learning or development)

Testing effects

Floor and ceiling effects

Exposure to the first condition may influence scores in the second condition

Occur when an individual has such a high score in condition 1 there is nowhere to go but down in condition 2

when comparing groups made up of the same people

(before vs after treatment)

There is no consistent or systematic difference between the two conditions

μDifference = zero

There is a systematic difference between conditions that produces a non-zero mean difference

The alternative hypothesis is that the sample mean difference represents a true mean difference in the population.

μDifference ≠ zero

Degrees of freedom (df) for the repeated-measures t test = n - 1

• For example, a study with 50 participants measured twice

• df = n – 1 = 50 - 1 = 49

Look up the corresponding value in t-distribution table

When the t value is farther from 0 than the critical value

.54500

8.8867

.62838

.867

199

.387

Cohen’s D

r-squared

(Know how to calculate)

A hypothesis testing procedure used to evaluate mean differences between two or more populations

Purpose is similar to t-test

Can examine more than 2 groups at the same time

Protects researchers from excessive risk of a Type I error in situations when comparing more than two population means

It automatically adjusts for the effect testing multiple hypotheses has on Type I errors

The independent variable that splits participants into groups

The individual conditions or values that make up a factor

Number of levels indicated by k

Same basic structure as the independent-measures t-statistic

measures the size of the differences between each level’s sample mean

By computing the variance of the means (MSbetween), we can test the size of the differences

Effects of the IV: could cause the mean for one level to be higher (or lower) than the mean for another level.

Chance or Sampling Error: If there is no effect of the IV at all, we would still expect some differences in the DV values between levels due to random, unsystematic sampling error

Measures the size of the differences that exist inside each of the treatment levels

Non-directional

Since F is a ratio of variances, we can never have a negative F.

• Variances can’t be negative.

• Therefore, there is only a single tail to the distribution

All the μ’s are equal

μ1=μ2=μ3

There is at least one mean difference

df between = k – 1 = Number of levels – 1

df within = N – k = Total number of participants – number of levels

We go to the F-Distribution table in the book

df between is in the columns (labeled across the top)

df within is in the rows (labeled down the side)

• So an ANOVA with 3 levels and 11 participants would have df = (2, 8)

• Regular type = .05

• Bold type = .01

• Critical Value = 4.46

Locate The Critical Region

Use an ANOVA table

Compare F value to critical value.

• If F is more extreme we reject H0 Hypothesis Testing with the Independent

However, ANOVA simply states that a difference exists

• It does not indicate which levels are different

• Need to follow the ANOVA with post hoc tests to determine

  exactly which groups are different and which are not.

  • Tukey & Scheffé tests are common post hoc tests.

  • Done after an ANOVA where H0 is rejected.

• The tests compare the treatments, two at a time, to test the mean differences while correcting for concerns about experiment-wise Type I error inflation.

91.467

276.400

2

27

45.733

10.237

4.467

Compare the treatments, two at a time, to test the mean differences while correcting for concerns about experiment-wise Type I error inflation

compute the percentage of variance accounted for by the independent variable (group)

A statistical method used to measure and describe the relationship between two (X and Y) as they exist naturally

No because there’s no attempt to manipulate on of the variables

when changes in X tend to be accompanied by consistent and predictable changes in Y

Correlation does not prove causation

the extent to which two variables are linearly related (meaning they change together at a constant rate)

The two variables tend to change in the same direction

As one increases the other tends to increase

The two variables tend to change in the opposite direction

As one increases the other tends to decrease

r

The most frequent method of measuring the common form of correlation as a straight line or linear relationship.

Perfect positive relationship

Perfect negative relationship

No relationship at all

-1.00

0.00

-0.4

+0.9

make sure you know how to calculation SSx and SSy

• Outliers

• Restriction of Range

Individuals with X and/or Y values that are substantially different than the other individuals in a sample

Relationship between X and Y is obscured when the data are limited to a restricted range of values

Ex: Only able to get 100 on a test

Spearman correlation

Variations of pearson’s

• point-biserial correlation

• phi-coefficient

• When examining the relationship between two ordinal variables (or one ordinal and one interval/ratio)

  • e.g: birth order and high school class rank

• When the form of the relationships between two, variables are curvilinear or exponential

  • variable get converted to rank

1. the observations for each variable are rank ordered

2. after the variable have been ranked, the Spearman correlation is computed by using the Pearson formula but with ranked data

When one variable is dichotomous and the other is on an interval or ratio scale

When variables are dichotomous

In both cases you use the same Pearson formula but recode the dichotomous variable values as 0 or 1

Ho: There is no association between X and Y (ρ = 0)

H1: X is associated with Y (ρ ≠ 0)

Ho: Greater X is not associated with greater Y (ρ ≤ 0)

H1: Greater X is associated with greater Y (ρ>0)

df=n-2

Then look at chart

Compare r to the critical value.

• Reject the null if r is more extreme than the critical value.

r squared (you square the r value)

the proportion of variance in the dependent variable that can be explained by the independent variable