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- Creighton University
- Psychology
- Psychology 315
- Skovran
- Unit 4 and Final Study Guide

asha r.

Null hypothesis for a repeated measures ANOVA

The mean of the groups are equal

Alternative hypothesis for a repeated measures ANOVA

The mean in *at least one *of the groups is different from the others

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When to use a repeated measures design:

To compare the means on a **quantitative variable**, from each participant, who is in **all** of the conditions if the qualitative variable

- You are investigating
__differences over time__of the same group

Repeated measures ANOVA vs. Dependent t-test

Similarity:

- Both a t-test and a repeated measures ANOVA can be used when collecting data from a
**group of participants that were in two conditions**

- A
**t-test is only for 2 conditions**, while an**ANOVA is for 2 or more conditions/ levels**

Repeated measures ANOVA vs. One-way ANOVA

Similarity:

- Both a repeated measures ANOVA and a one-way ANOVA can be used
**in a study with 2 or more conditions/ levels**

- A
**RM ANOVA is for participants in all conditions** - A
**one-way ANOVA is for participants in only one of the conditions**

Process of Statistical Analysis for Multiple IV Condition Designs

- Perform the Omnibus
*F*test - Compute all Pairwise comparisons - if your
*F*test was significant - Reject the null: mean differences > minimum mean
- Check that the significant mean difference is in the hypothesized condition
- SPSS computes the math for you

Repeated measures ANOVA - reporting results format

Include:

- Significant mean difference or not
- APA Results Ex.:
*F*(2, 412) - 15.62,*p*= .00 - Information revealed brought the LSD comparisons
- (
*M = ____, SD = _____*)

Benefits of Factorial Analysis of Variance

Multicausality: the idea that behavior has *multiple causes* and can be better studied using *multivariate *research designs

Multivariate Research

Involves multiple IVs and one DV

3 variable is a 2x2 factorial design

- The DV
- One IV
- The other IV

3 effects involves in a 2x2 factorial design

- Interaction
- The main effect of one IV
- The main effect of another IV

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Interaction

Differences __between simple effects__

Main Effects

Differences __between marginal means__

5 important terms involves in a factorial design

- Cell means
- Marginal means
- Main effects
- Simple effects
- Interaction

Cell means

The mean DV score of all the people __with a particular combination of IV treatments__

Marginal mean

The mean DV score of all the people __in a particular condition of the specified IV__

Simple effects

Involves the __comparison of cell means __

Why do we need to be careful when we interpret main effects?

When there is an interaction, the pattern of the interaction may influence the interpretability of the description of the marginal means

**The main effect may be misleading**

5 basic patterns of results for a 2x2 factorial design

3 patterns *have an interaction*:

*no interaction:*

- = vs. <
- < vs. >
- < vs.
_{<}

- < vs. <
- = vs. =

What patterns are potentially misleading?

= vs. <

- One null simple effect and one simple effect

< vs. >

- Simple effects in opposite directions

Factorial hypotheses: main effect

- Involves
**a single IV** - Tells how one IV is expected to relate to the DV ignoring the other IV

Factorial hypotheses: interaction

- Involves
**both IVs** - Tells the expected differences in how one IV relates to the DV for different conditions of the other IV

Main effect research hypothesis: descriptive

- Telling the expected pattern of this RH, this involves a single IV
- This suggests that the effects of that IV are the same for all levels of the other IV

Main effect research hypothesis: misleading

- While telling the expected pattern of this RH, it is essentially the same as describing an interaction
- This suggests that important differences between the effects of that IV are at different levels of the other IV

Main effect research hypothesis: associative

- Type of research hypothesis that can always be tested
- States whether or not there is a statistical relationship between one IV and the DV

Main effect research hypothesis: causal

- Requires that the conditions of that IV were randomly assigned, properly manipulated and there was good experimental control
- States that the DV value is a direct result of the value of that IV

Interaction research hypothesis: associative

Interaction research hypothesis: causal

- States that the DV value is a direct result of the value of the combination of IV conditions

Describe how each "effect" in a 2x2 factorial design is statistically examined

- Tell the IVs and the DV
- Present data in table
- Determine if the interaction is significant
- Determine whether the first main effect is significant
- Determine whether the second main effect is significant

Main effects *F *tests

Sufficient in telling us about the *relationship of each IV to the DV*

The corresponding significance test

Tells us whether the two *marginal means are significantly different*

- Check and make sure if two marginal means are significantly different that they are different in the
*expedited direction*

Interaction *F *tests

Tells us whether there is a *statistically significant* interaction, but *not where* it is significantly significant

- Does not tell us the pattern and which simple effects (cell means) are different from each other
- Does not tell us
*how much difference is necessary*to conclude that they are significantly different

LSD pairwise comparisons

Can be used to determine *how large of a cell mean is required* to treat it as a *statistically significant mean difference*

4 things you need to know to compute the LSD pairwise comparisons

- # of conditions
- 2x2 is always going to have
**4 conditions** - df
_{error} **N - 4**- MS
_{error} - Look on the spss printout
- n
- N / 4

How do you compare cell means?

LSDmmd

How do you compare marginal means?

Using the main effects *F *tests

3 type of factorial designs

- Between-groups factorial design
- Within-groups factorial design
- Mixed factorial design

Between-groups factorial design

- Each IV uses a
*between-groups comparison* - Each participant complete
*only one condition*of the design

Within-groups factorial design

- Each IV uses a
*within-groups comparison* - Each participant completes
*all conditions*of the design

Mixed factorial design

- One IV uses a between-groups comparison
- The other IV uses a within-groups comparison
- Each participants completes
*both conditions*of the within-groups IV,*but*completes*only one condition*of the between-groups IV

Main effects and the interaction are 3 separate effects and...

Each must be separately interpreted

- Three parts of a story

How is an interaction different than main effects?

An interaction is the comparison of simple effects

A main effect is the difference between marginal means

A main effect is the difference between marginal means

You cannot reject the null if...

The simple effects mean difference is greater than the required mean difference

- Simple effects are only relevant
*when referring to an interaction*

Order of Operations

- Enter cells means & marginal means
- Main effect of one IV?
*F*test sig.- Descrip. or mislead.?
- Main effect of the other IV?
*F*test sig.- Descrip. or mislead.?
- Significant interaction?
*F*test sig.- Calculate LSDmmd
- Enter < = > for SE

Write up your results - Factorial ANOVA (interaction - part 1)

Rating in the various cond. of the study are in Table 1. As hypo., there was an interaction of IV1 and IV2, as they related to DV, *F *(1, 28) - 21.19, P < .05. Further analyses from LSD follow ups of the cell means (min. mean diff. = ) revealed ...

Write up your results - Factorial ANOVA (main effect - part 2)

There was also a main effect for IV, *F *(1, 28) - 31.62, p < .05. As hypothesized, ... (if this is qualified by simple effects state that here)

Contrary to the RH, there was not main effect for the other IV,*F* (1, 28) = 6.54, p = .16

Contrary to the RH, there was not main effect for the other IV,

How do we know if we can causally interpret the effects?

- Both main effects must be causally interpretable to have a causally interpretable interaction
- Can we causally interpret the results?
- Main effect of one IV?
- Main effect of the other IV?
- Interaction effect?

Definition of correlation (r)

Summarizes the **direction and strength of a linear relationship** between *two quantitative *variables

Range of correlation

-1.00 to +1.00

Type of variables for correlation

2 quantitative variables

Definition of chi square (X^{2})

Summarizes the **relationship** (pattern) between *two qualitative *variables

Range of chi square

0.00 to infinity

Type of variables for chi square

2 qualitative variables

How do we visually display correlation data?

Through a scatter plot

How do we visually display chi square data?

Through a **contingency table**

Contingency table

A chi square table reports the *frequencies or counts*, and not the means of those in each cell

Types of relationships for correlation

- No relationship
- Linear
- Non-linear

Types of direction for correlation

- Positive
- Negative

Types of strength for correlation

- Strong
- Moderate
- Weak

Correlation research hypothesis must specify:

- Variables
- Direction of the expected linear relationship
- Population of interest
- In generic form
- There is a positive or negative relationship between X and Y in the population represented by the sample

Correlation null hypothesis must specify:

- Variables
- No linear relationship is expected
- Population of interest
- Generic form
- There is
**no linear relationship**between X and Y in the population represented by the sample

When you retain the null for a correlation you are concluding that...

The linear relationship between these variables in the sample **is not strong enough** to conclude there is a linear relationship between the population represented by the sample

When you reject the null for a correlation you are concluding that...

The linear relationship between these variables in the sample **is strong enough** to conclude that there is a linear relationship between them in the population represented by the sample

Chi square research hypothesis must specify:

- Variables
- Specific pattern of the expedited relationship
- Population of interest
- Generic form
- There
**is a pattern of relationship**between X and Y in the population represented by the sample

Chi square null hypothesis must specify:

- Variables
- No pattern of relationship is expedited
- Population of interest
- Generic form
- There
**is not pattern of relationship**between X and Y in the population represented by the sample

When you retain the null for chi square you are concluding that...

The pattern of the relationship between these variables in the sample **is not strong enough** to conclude there is a relationship between them in the population represented by the sample

When you reject the null for chi square you are concluding that...

The pattern of the relationship between these two variables in the sample **is strong enough** to conclude there is a relationship between them in the population represented by the sample

Can we causally interpret a correlation?

Most application of Pearson's r involve quantitative variables that are subject variables measured *by the participants*

- Usually can't be because it is normally a natural groups design...
- No random assignment
- No manipulation of IV
- No procedural control

Parametric tests

Assume that the data has come from a type of probability distribution and makes inferences about the parameters of the distribution

- Everything we have covered so far is parametric statistics

Non-parametric tests

Make few assumptions about the distribution

- Chi square is non-parametric
- Used with
**categorical**data - Considered distribution free tests
- Not robust
- Can be
*misleading*but gives us*something*to do with nominal/ ordinal data

To eyeball what the pattern of differences show in a chi square you are going to have to look where?

At your contingency table

Write up your results: Chi square

As hypothesized, cats ho recieved food as reinforcement learned to dance. However, contrary to the RH, cats who recieved affection as reinforcement also learned to dance *X*^{2}(1) = 8.44, p < .05.

Describe the pattern of a correlation

- 0.00 absolutely - no pattern of relationship
- "smaller" X
^{2 }- weaker pattern of relationship - "larger" X
^{2}- stronger pattern of relationship

One sample t-test: chart

# of IVs: 1

# of levels of IVs: 1

Types of IVs: qualitative

Independent or related: independent

# of DVs: 1

Types of DV: quantitative

Comparison being made: whether or not that sample likely belongs to the population

# of levels of IVs: 1

Types of IVs: qualitative

Independent or related: independent

# of DVs: 1

Types of DV: quantitative

Comparison being made: whether or not that sample likely belongs to the population

Independent t-test: chart

# of IVs: 1

# of levels of IVs: 2

Types of IVs: qualitative

Independent or related: independent

# of DVs: 1

Types of DV: 1

Comparison being made: whether 2 samples likely belong to the same population - i.e. 2 samples are significantly different

# of levels of IVs: 2

Types of IVs: qualitative

Independent or related: independent

# of DVs: 1

Types of DV: 1

Comparison being made: whether 2 samples likely belong to the same population - i.e. 2 samples are significantly different

Dependent t-test

# of IVs:

# of levels of IVs:

Types of IVs:

Independent or related:

# of DVs:

Types of DV:

Comparison being made:

# of levels of IVs:

Types of IVs:

Independent or related:

# of DVs:

Types of DV:

Comparison being made:

One-way ANOVA

# of IVs: 1

# of levels of IVs: 2+

Types of IVs: qualitative

Independent or related: independent

# of DVs: 1

Types of DV: quantitative

Comparison being made: whether 2+ samples belong to the same population - i.e. 2+ samples significantly differ

# of levels of IVs: 2+

Types of IVs: qualitative

Independent or related: independent

# of DVs: 1

Types of DV: quantitative

Comparison being made: whether 2+ samples belong to the same population - i.e. 2+ samples significantly differ

Repeated measures ANOVA

# of IVs: 1

# of levels of IVs: 2+

Types of IVs: qualitative

Independent or related: relation

# of DVs: 1

Types of DV: quantiative

Comparison being made: difference scores of 1 sample over 2+ measurements (levels of the IV)

# of levels of IVs: 2+

Types of IVs: qualitative

Independent or related: relation

# of DVs: 1

Types of DV: quantiative

Comparison being made: difference scores of 1 sample over 2+ measurements (levels of the IV)

Factorial ANOVA

# of IVs: 2+

# of levels of IVs: 2+

Types of IVs: qualitative

Independent or related: independent and/ or related

# of DVs: 1

Types of DV: quantitative

Comparison being made: testing for the combined effect of 2+ IVs on the DV

# of levels of IVs: 2+

Types of IVs: qualitative

Independent or related: independent and/ or related

# of DVs: 1

Types of DV: quantitative

Comparison being made: testing for the combined effect of 2+ IVs on the DV

Correlation

# of IVs: 2

# of levels of IVs: 1

Types of IVs: quantitative

Independent or related: independent and/ or related

# of DVs: -

Types of DV: -

Comparison being made: whether two quantitative variables are linearly related - does not prove causation

# of levels of IVs: 1

Types of IVs: quantitative

Independent or related: independent and/ or related

# of DVs: -

Types of DV: -

Comparison being made: whether two quantitative variables are linearly related - does not prove causation

Chi square

# of IVs: 2

# of levels of IVs: 1

Types of IVs: qualitative

Independent or related: independent and/ or related

# of DVs: -

Types of DV: -

Comparison being made: whether there is a pattern between the frequency counts of 2 qualitative variables

# of levels of IVs: 1

Types of IVs: qualitative

Independent or related: independent and/ or related

# of DVs: -

Types of DV: -

Comparison being made: whether there is a pattern between the frequency counts of 2 qualitative variables

Attributive hypothesis

States that **a behavior exists**, can be measures, and distinguished from similar other behavior

Ex. Flying saucers have been seen in our skies

Ex. Flying saucers have been seen in our skies

Associative hypothesis

States that a relationship exists between two behaviors

*is related* to how many hours you work each week

- Knowing the amount or kind of one behavior helps you
**predict**the amount or kind of another behavior

Causal hypothesis

States that differences in the amount or kind of one behavior causes/produces/creates/changes/etc., differences in the amount or kind of another behavior

Ex. IQ is a better predictor of graduate school performance than college GPA

Ex. IQ is a better predictor of graduate school performance than college GPA

Population sampling frame

Includes the entire population

- Not always feasible
- First step of the sampling procedures
- Target population: defining people/ animals we want to study

Sampling frame

"Best list" we can get of population members

- Second stage of selection/ sampling

Ex. Students enlisted with the registrar

Selected sample

Sampling frame members who are selected to participate in research

- Third stage of selection/ sampling

Ex. 100 students from the registrar's list

Data sample

Participants from who useful data are collected

- Fourth stage of selection/ sampling

Independent variable

The variable manipulated by the researcher

- May be qualitative (in most cases) or quantitative (r)

Common approaches to manipulating the IV include...

- Changing a physical aspect of stimuli or changing the meaning of stimuli
- Manipulate the environment
- Change attributes of the stimuli or task

Dependent variable

The variable *expected to change* as a result of the manipulation of the IV

- The one in which scores are presumably caused or influences by the iV
- Also called the
**dependent measure**

Control

Another way to simply the situation by eliminating factors that might influence the behavior being observed and thus create confusion

Controlling extraneous variables:

- Employ a more precise operational definition of each component
- Eliminate the extraneous variable
- Keep the extraneous variable constant
- Balance out the extraneous variable

Internal validity

Must **take control of the potential confound** so that they become controls and *not confounds*

- ...if we are going to causally interpret our results

True experiments

Can be used to test a *causal research hypothesis*

**Random assignment**of participants*before*IV manipulation- by experimenter
**Treatment/ manipulation**of IV by the*experimenter*- Provides temporal precedence
**Good control**of procedure during task completion

Non-experiment

No version can be used to test a causal research hypothesis

- Includes both quasi-experiment and natural groups design

Quasi experiment

- No random assignment of individuals
- No treatment/ manipulation of the IV performed by the researcher
- Poor/ no control over procedural variable during task

May have one or two of these, but not all

Natural groups design

- No random assignment of individuals
- No treatment manipulation by the researcher
- No procedural control over variables during task

Between-groups experiment

- Also called
*between subjects*experiment - Each participant is only in
**one of the conditions** - Typically used to study "differences"

Advantages to a between-groups experiment

- Has a ‘control’ or ‘comparison group that helps control for extraneous variables
- Can randomly assign participants to groups or conditions
- Can be used when other designs cannot
- Ex. Married vs. not married

Disadvantages to a between-groups experiment

- Cannot always assign individuals to groups or conditions
- SES, gender, personality, etc.
- Need more participants

Within-groups experiment

- Also called
*within subjects, repeated measure, or longitudinal* - Participants complete
**all conditions**of the experiment - Typically used to study "changes" within a participant

Advantages to within-groups experiment

- Takes fewer participants
- Participants serve as their own control group
- More powerful statistical tests available

Disadvantages to within-groups experiment

- Attrition
- Practice/ carryover effects
- Solution - counterbalancing

Types of data collection procedures

- Self report
- Naturalistic observation
- Undisguised participant observation
- Disguised participant observation

Self report

- Mail questionnaire
- Group administered interview
- Computer administered interview
- Personal interview
- Phone interview

Naturalistic observation

- Requires "camouflage" or distance
- Researchers can be very creative

Undisguised participant observation

- The researcher is in plain view
- Participant is likely to know they are collecting data

Disguised participant observation

Participant looks like someone who belongs there - such as a confederate

Types of data collection setting

- Laboratory setting
- Structured setting
- Field setting

Laboratory setting

Helps with control (internal validity) but can make external validity more difficult

Structures setting

A "natural appearing" setting that promotes "natural behavior" while increasing opportunity for control

- An attempt to blend the best attributes of field (external) and laboratory (internal)

Field setting

Usually defined as "where the participants naturally behave"

- Helps external validity, but can make control (internal validity) more difficult
- Random assignment and manipulation are possible with some creativity

Type I error

- A "false alarm"
- Reject the null when you should have retained it
- p = alpha

Type II error

- A "miss"
- Retained the null when you should have rejected it
- p = 1 - alpha
- Power

Type III error

- A "mus-specification"
- The results show that there is a significant relationship, but in the opposite direction than originally hypothesized

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