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Finishing up: Statistics & Developmental designs. Psych 231: Research Methods in Psychology. Remember to turn in the second group project rating sheet in labs this week. Announcements. About populations. Real world ( ‘ truth ’ ). H 0 is correct. H 0 is wrong. Type I error. Reject H 0.

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Finishing up: Statistics & Developmental designs

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## Finishing up:Statistics & Developmental designs

Psych 231: Research Methods in Psychology

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

### Announcements

About populations

Real world (‘truth’)

H0 is correct

H0 is wrong

Type I error

Reject H0

Experimenter’s conclusions

Fail to Reject H0

Type II error

76%

80%

XB

XA

• 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%

H0: μA = μB

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

• Is the 4% difference a “real” difference (statistically

significant) or is it just sampling error?

Two sample

distributions

set α-level

### Statistics Summary

Observed difference

Computed

test statistic

=

Difference from chance

Make a decision: reject H0or fail to reject H0

• 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

### Some inferential statistical tests

Observed difference

X1 - X2

T =

Diff by chance

Based on sample error

• Design

• 2 separate experimental conditions

• Degrees of freedom

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

• Formula:

XB

XA

Computation differs for

between and within t-tests

### 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.”

### T-test

Observed variance

F-ratio =

XA

XC

XB

Variance from chance

• 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

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

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

### Analysis of Variance

The ANOVA tests this one!!

Do further tests to pick between these

XA = XB = XC

XA ≠ XB ≠ XC

XA ≠ XB = XC

XA = XB ≠ XC

XA = XC ≠ XB

XA

XC

XB

Null hypothesis:

H0: all the groups are equal

Alternative hypotheses

• HA: not all the groups are equal

### 1 factor ANOVA

XA ≠ XB ≠ XC

XA ≠ XB = XC

XA = XB ≠ XC

XA = XC ≠ XB

• Planned contrasts and post-hoc tests:

• - Further tests used to rule out the different Alternative hypotheses

Test 1: A ≠ B

Test 2: A ≠ C

Test 3: B = C

### 1 factor ANOVA

• 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

• 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

### Factorial ANOVAs

• 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

### Non-Experimental 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

### 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

• Disavantages:

• Individuals are not followed over time

• Cohort (or generation) effect: individuals of different ages may be inherently different due to factors in the environmental context

• Are 5 year old different from 15 year olds just because of age, or can factors present in their environment contribute to the differences?

• Imagine a 15yr old saying “back when I was 5 I didn’t have a Wii, my own cell phone, or a netbook”

• Does not reveal development of any particular individuals

• Cannot infer causality due to lack of control

• Cross-sectional 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

• Longitudinal design

time

Age 11

Age 15

Age 20

### Developmental 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 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

• Longitudinal design

### 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 design

Time of measurement

1975

1985

1995

Cohort A

1970s

Age 5

Age 5

Age 5

Cross-sectional component

Cohort B

1980s

Age 15

Age 15

Cohort C

1990s

Age 25

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