Finishing up:Statistics & Developmental designs

Psych 231: Research Methods in Psychology

Announcements

Remember to turn in the second group project rating sheet in labs this week

Statistics Summary

Real world (‘truth’)

H0 is correct

H0 is wrong

Experimenter’s conclusions

Reject H0

Fail to Reject H0

Type I error

Type II error

Example Experiment: Group A - gets treatment to improve memory Group B - gets no treatment (control)

After treatment period test both groups for memory Results:

Group A’s average memory score is 80% Group B’s is 76%

Example Experiment: Group A - gets treatment to improve memory Group B - gets no treatment (control)

After treatment period test both groups for memory Results:

Group A’s average memory score is 80% Group B’s is 76%

XAXB

76% 80%

Is the 4% difference a “real” difference (statistically significant) or is it just sampling error?

Two sampledistributions

H0: there is no difference between Grp A and Grp B

H0: μA = μB

About populations

Observed difference

Difference from chance

Computed test statistic

=

set α-level

Make a decision: reject H0 or fail to reject H0

Some inferential statistical tests

The Design of the study determines what statistical tests are appropriate

1 factor with two groups T-tests

• Between groups: 2-independent samples

• Within groups: Repeated measures samples (matched, related)

1 factor with more than two groups Analysis of Variance (ANOVA) (either between groups or

repeated measures)

Multi-factorial Factorial ANOVA

T-test

Design 2 separate experimental conditions Degrees of freedom

• Based on the size of the sample and the kind of t-test

Formula:

T = X1 - X2

Diff by chance

Based on sample error

Observed difference

Computation differs for between and within t-tests

XAXB

T-test

Reporting your results The observed difference between conditions Kind of t-test Computed T-statistic Degrees of freedom for the test The “p-value” of the test

“The mean of the treatment group was 12 points higher than the control group. An independent samples t-test yielded a significant difference, t(24) = 5.67, p < 0.05.”

“The mean score of the post-test was 12 points higher than the pre-test. A repeated measures t-test demonstrated that this difference was significant significant, t(12) = 5.67, p < 0.05.”

Analysis of Variance

Designs More than two groups

• 1 Factor ANOVA, Factorial ANOVA• Both Within and Between Groups Factors

Test statistic is an F-ratio

Degrees of freedom Several to keep track of The number of them depends on the design

XBXA XC

Observed variance

Variance from chanceF-ratio =

Can’t just compute a simple difference score since there are more than one difference

A - B, B - C, & A - C

1 factor ANOVA

Null hypothesis: H0: all the groups are equal

XA = XB = XC

Alternative hypotheses

HA: not all the groups are equal

XA ≠ XB ≠ XC XA ≠ XB = XC

XA = XB ≠ XC XA = XC ≠ XB

The ANOVA tests this one!!

Do further tests to pick between these

XBXA XC

1 factor ANOVA

Planned contrasts and post-hoc tests:

- Further tests used to rule out the different Alternative

hypothesesXA ≠ XB ≠ XC

XA ≠ XB = XC

XA = XB ≠ XC

XA = XC ≠ XB

Test 1: A ≠ B

Test 2: A ≠ C

Test 3: B = C

Reporting your results The observed differences Kind of test Computed F-ratio Degrees of freedom for the test The “p-value” of the test Any post-hoc or planned comparison results

“The mean score of Group A was 12, Group B was 25, and Group C was 27. A 1-way ANOVA was conducted and the results yielded a significant difference, F(2,25) = 5.67, p < 0.05. Post hoc tests revealed that the differences between groups A and B and A and C were statistically reliable (respectively t(8) = 5.67, p < 0.05 & t(9) = 6.02, p <0.05). Groups B and C did not differ significantly from one another”

1 factor ANOVA

Factorial ANOVAs

We covered much of this in our experimental design lecture

More than one factor Factors may be within or between Overall design may be entirely within, entirely between, or mixed

Many F-ratios may be computed An F-ratio is computed to test the main effect of each factor An F-ratio is computed to test each of the potential interactions

between the factors

Factorial ANOVAs

Reporting your results The observed differences

• Because there may be a lot of these, may present them in a table instead of directly in the text

Kind of design• e.g. “2 x 2 completely between factorial design”

Computed F-ratios• May see separate paragraphs for each factor, and for interactions

Degrees of freedom for the test• Each F-ratio will have its own set of df’s

The “p-value” of the test• May want to just say “all tests were tested with an alpha level of

0.05” Any post-hoc or planned comparison results

• Typically only the theoretically interesting comparisons are presented

Non-Experimental designs

Sometimes you just can’t perform a fully controlled experiment Because of the issue of interest Limited resources (not enough subjects, observations are too

costly, etc). • Surveys

• Correlational

• Quasi-Experiments

• Developmental designs

• Small-N designs

This does NOT imply that they are bad designs Just remember the advantages and disadvantages of each

Developmental designs

Used to study changes in behavior that occur as a function of age changes Age typically serves as a quasi-independent

variable Three major types

Cross-sectional Longitudinal Cohort-sequential

Developmental designs

Cross-sectional design Groups are pre-defined on the basis of a pre-

existing variable • Study groups of individuals of different ages at the

same time• Use age to assign participants to group

• Age is subject variable treated as a between-subjects variable

Age 4

Age 7

Age 11

Cross-sectional design

Developmental designs

Advantages:• Can gather data about different groups (i.e., ages)

at the same time• Participants are not required to commit for an

extended period of time

Cross-sectional design

Developmental designs

Longitudinal design

Developmental designs

Follow the same individual or group over time• Age is treated as a within-subjects variable

• Rather than comparing groups, the same individuals are compared to themselves at different times

• Changes in dependent variable likely to reflect changes due to aging process• Changes in performance are compared on an

individual basis and overall

Age 11

time

Age 20Age 15

Longitudinal Designs

Example Wisconsin Longitudinal Study (WLS)

• Began in 1957 and is still on-going (50+ years)• 10,317 men and women who graduated from Wisconsin high schools

in 1957

• Originally studied plans for college after graduation• Now it can be used as a test of aging and maturation

Longitudinal design

Developmental designs

Advantages:• Can see developmental changes clearly• Can measure differences within individuals• Avoid some cohort effects (participants are all from

same generation, so changes are more likely to be due to aging)

Longitudinal design

Developmental designs

Disadvantages• Can be very time-consuming• Can have cross-generational effects:

• Conclusions based on members of one generation may not apply to other generations

• Numerous threats to internal validity:• Attrition/mortality

• History

• Practice effects• Improved performance over multiple tests may be due to

practice taking the test

• Cannot determine causality

Developmental designs

Measure groups of participants as they age• Example: measure a group of 5 year olds, then the

same group 10 years later, as well as another group of 5 year olds

Age is both between and within subjects variable

• Combines elements of cross-sectional and longitudinal designs

• Addresses some of the concerns raised by other designs• For example, allows to evaluate the contribution of cohort

effects

Cohort-sequential design

Developmental designs

Cohort-sequential designTime of measurement

1975 1985 1995

Cohort A

Cohort B

Cohort CCro

ss-s

ectio

nal c

ompo

nent

1970s

1980s

1990s

Age 5 Age 15 Age 25

Age 5 Age 15

Age 5

Longitudinal component

Developmental designs

Advantages:• Get more information

• Can track developmental changes to individuals• Can compare different ages at a single time

• Can measure generation effect• Less time-consuming than longitudinal (maybe)

Disadvantages:• Still time-consuming• Need lots of groups of participants• Still cannot make causal claims

Cohort-sequential design