Topic 6: Hypothesis Testing with 3+ samples, ANOVA Flashcards

1
Q

Multiple Group designs

A
  • Have one independent variable with three or more levels and a continous DV

*extension of the two-group designs

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2
Q

As with the two-group design, multi-group designs…

A

can be experimental or ex post facto

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3
Q

One-way Analysis of Variance (ANOVA)

A
  • A hypothesis-testing technique used to compare means from three or more possible populations
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4
Q

ANOVA hypothesis

A

Ho= All population means are equal (u1=u2u3=…uk)
Ha= At least one of the means is different from the others

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5
Q

What is ANOVA? (2)

with the diagram+ overall in words

A

In ANOVA we compare:
- How much the sample means differ (on average) from the overall mean (of all scores) to how much individual score differ from their own sample means (on average)
- Aka: How much are we as a group differing from overall average?

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6
Q

x double bar

A

Overall mean for all the mean of the score in the study

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7
Q

If there is more between than within group variability then…

A

samples are not all from the same population thus, we reject null that they are from the same population

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8
Q

In anova, bigger the green arrow, smaller the red the more sure we are that

A

This group is diff

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9
Q

Explain the F value+formula

+error

A
  • error between and within groups should be similar assuming no confounds
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10
Q

If the IV has no effect (does not lead to variability between groups), the variability due to the IV will be

A

close to 0

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11
Q

The higher the F-value,

A

the greater the likelihood that the IV caused an effect

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12
Q

Assumptions of the one-way ANOVA (3)

A
  1. The samples are independent of eachother
  2. Each sample comes from a normal (or approximately normal) population. Fairly robust against violations of this assumptions unless n is small
  3. Each population has the same variance. Also fairly robust against violations of homogeneity of variances
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13
Q

F distrubution is —- skewed and you shouldnt get a —– number

A
  • positively
  • negative
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14
Q

The degrees of freedo for the F-test are:

A

dfN=k-1
dfD=N-k

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15
Q

k

A

The number of groups

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16
Q

N

A

Total sample size

17
Q
A

Average variation of each score (from own sample means. Tells us how much each participant deviate from their own condition.

18
Q
A

Tells us overall mean from all participants

19
Q

Calculating F for one-way ANOVA

20
Q

SD and variance relationship

A

Square SD to get variance

21
Q

Performing a one way ANOVA Test

A
  • determine the critical value from the F-distribution table
  • Calculate the F value with formula.
  • If F is in the rejection region, reject H0. Otherwise, fail to reject H0
22
Q

Denominator is the

A

bottom number

23
Q

Effect size for ANOVAs

A

Small = 0.01
Medium = 0.06
Large = 0.14

24
Q

Multiple comparisons

A

Test suitable for the simultaneous testing of several hypotheses concerning the equality of three or more population means.

25
Significant F only shows that ------. Multiple comparisons tell us ----
- Not all groups are equal - which group differ
26
Why not just run a series of t-test? Why use multiple comparisons?
We run into issues with the family-wise error rate. The more you run a study, the higher chance of making a type 1 error. Everytime you run, you increase type 1 by 5%.
27
The reason we use multiple comparison procedures is because
They control the familywise error rate
28
Liberal multiple comparison tests (4)
1. More chance of type 1 error 2. More likely to find a significant difference 3. More power 4. Less chance of type 2 error
29
Conservative multiple comparison tests (2)
1. Less chance of type 1 error (every scared of making) 2. More chance of making type 2 error (missing a significant difference)
30
The Tukey procedure
Tells you which population means are significantly different from eachother Ex: No difference between 1 and 2 but a difference between 3 and the other 2
31
We only used a Tukey procedure after ------ if .......
- after we found a significant result woth the ANOVA - If your F is not significant, you cant do Tukey as you will find no difference
32
Tukey procedure what do we do?
- We find the mean difference between each of the groups being compared. - If the mean difference is greater than the critical rangel than the two groups are significantly different
33
Critical range degree of freedom calculations
- amount of groups (K) - N-K