Topic 6: Hypothesis Testing with 3+ samples, ANOVA Flashcards
Multiple Group designs
- Have one independent variable with three or more levels and a continous DV
*extension of the two-group designs
As with the two-group design, multi-group designs…
can be experimental or ex post facto
One-way Analysis of Variance (ANOVA)
- A hypothesis-testing technique used to compare means from three or more possible populations
ANOVA hypothesis
Ho= All population means are equal (u1=u2u3=…uk)
Ha= At least one of the means is different from the others
What is ANOVA? (2)
with the diagram+ overall in words
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?
x double bar
Overall mean for all the mean of the score in the study
If there is more between than within group variability then…
samples are not all from the same population thus, we reject null that they are from the same population
In anova, bigger the green arrow, smaller the red the more sure we are that
This group is diff
Explain the F value+formula
+error
- error between and within groups should be similar assuming no confounds
If the IV has no effect (does not lead to variability between groups), the variability due to the IV will be
close to 0
The higher the F-value,
the greater the likelihood that the IV caused an effect
Assumptions of the one-way ANOVA (3)
- The samples are independent of eachother
- Each sample comes from a normal (or approximately normal) population. Fairly robust against violations of this assumptions unless n is small
- Each population has the same variance. Also fairly robust against violations of homogeneity of variances
F distrubution is —- skewed and you shouldnt get a —– number
- positively
- negative
The degrees of freedo for the F-test are:
dfN=k-1
dfD=N-k
k
The number of groups
N
Total sample size
Average variation of each score (from own sample means. Tells us how much each participant deviate from their own condition.
Tells us overall mean from all participants
Calculating F for one-way ANOVA
SD and variance relationship
Square SD to get variance
Performing a one way ANOVA Test
- 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
Denominator is the
bottom number
Effect size for ANOVAs
Small = 0.01
Medium = 0.06
Large = 0.14
Multiple comparisons
Test suitable for the simultaneous testing of several hypotheses concerning the equality of three or more population means.
Significant F only shows that ——. Multiple comparisons tell us —-
- Not all groups are equal
- which group differ
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%.
The reason we use multiple comparison procedures is because
They control the familywise error rate
Liberal multiple comparison tests (4)
- More chance of type 1 error
- More likely to find a significant difference
- More power
- Less chance of type 2 error
Conservative multiple comparison tests (2)
- Less chance of type 1 error (every scared of making)
- More chance of making type 2 error (missing a significant difference)
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
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
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
Critical range degree of freedom calculations
- amount of groups (K)
- N-K
