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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

Finishing up:Statistics & Developmental designs

Psych 231: Research Methods in Psychology

Statistics summary

About populations labs this week

Real world (‘truth’)

H0 is correct

H0 is wrong

Type I error

Reject H0

Experimenter’s conclusions

Fail to Reject H0

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%

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


set α-level

Statistics Summary

Observed difference


test statistic


Difference from chance

Make a decision: reject H0or 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

Some inferential statistical tests

T test

Observed difference are appropriate

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:



Computation differs for

between and within t-tests


T test1

  • Reporting your results are appropriate

    • 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

Observed variance are appropriate

F-ratio =




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

1 factor anova

The ANOVA tests this one!! are appropriate

Do further tests to pick between these

XA = XB = XC

XA ≠ XB ≠ XC

XA ≠ XB = XC

XA = XB ≠ XC

XA = XC ≠ XB




Null hypothesis:

H0: all the groups are equal

Alternative hypotheses

  • HA: not all the groups are equal

1 factor ANOVA

1 factor anova1

X are appropriateA ≠ 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

1 factor anova2

  • Reporting your results are appropriate

    • 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 are appropriate

  • 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

Factorial anovas1

  • Reporting your results are appropriate

    • 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

Non experimental designs

  • Sometimes you just can are appropriate’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

Developmental designs

  • Three major types

    • Cross-sectional

    • Longitudinal

    • Cohort-sequential

Developmental designs

Developmental designs1

  • Cross-sectional design of age changes

    • 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

Developmental designs2

  • Advantages: of age changes

    • 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

Developmental designs3

  • Disavantages of age changes:

    • 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

Developmental designs4

  • Follow the same individual or group over time of age changes

    • 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


Age 11

Age 15

Age 20

Developmental designs

Longitudinal designs

  • Example of age changes

    • 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

Developmental designs5

  • Advantages: of age changes

    • 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

Developmental designs6

  • Disadvantages of age changes

    • 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

Developmental designs7

  • Measure groups of participants as they age of age changes

    • 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

Developmental designs8

Time of measurement




Cohort A


Age 5

Age 5

Age 5

Cross-sectional component

Cohort B


Age 15

Age 15

Cohort C


Age 25

Longitudinal component

Developmental designs

Developmental designs9

  • Advantages: of age changes

    • 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

Developmental designs