W5 - 1-Way Independent ANOVA Flashcards
Define experimental power
Ability to detect an effect of a certain size
What do underpowered studies leave you unable to do?
Detect small effects
What can you do to ensure the study has enough power?
Test plenty of people
Type 1 error
Incorrect rejection of the true null hypothesis
When 1 concludes a relationship or effect exists when it actually doesn’t.
What is the level of type 1 error we are willing to risk called?
Alpha
Type 1 errors will occur 5% of the time (1 in 20).
Type 2 error
Failure to reject false null hypothesis
When 1 concludes a relationship or effect doesn’t exist when actually it does.
What is the level of type 2 error we are wiling to risk called?
Beta
What are statistical tests based on the assumption of?
That variance is due to true and random effects
List reasons as to why you may have a p value larger than 0.05
No actual effect
Lack of power - Too small a sample to detect an effect of a certain size
Inadequate variability w/in IV
Measurement error
Nuisances variance
List some sources of measurement error
Inadequate measurement instruments
Response error from participants
Contextual factors
Equation for family wise error
1-(1-alpha)^no. tests conducted
What happens to familywise error with the increasing number of tests we run
More inflation of familywise error rate
How can the increased family wise error/error rate be corrected?
By the bonferroni, Tukeys HSD, Holm & Scheffe tests
What do the bonferroni, Tukeys HSD, Holm & Scheffe tests do?
Reduce your ability to detect a true effect
Lower experimental power
Increase chance of making a type 2 error
What is a solution to the bonferroni, Tukeys HSD, Holm & Scheffe tests lowering experimental power + increasing chance of making a type 2 error?
1-way independent ANOVA
What does the 1-way independent ANOVA allow you to do?
Compare many groups w/ a single test
Positives to a 1-way independent ANOVA
No inflated familywise error rate
No reduction in experimental power
Assumptions to the 1-way independent ANOVA
Samples are independent
Data is interval or ratio
Normally distributed
Homogeneity of variance
What is the variance in ANOVA tables?
Mean Square (MS)
What does ANOVA ask the question of?
How successful the experimental manipulation has been in comparison to the natural variability that exists.
Compares the type of variance you want (effect variance) with the variance you do not want (error variance).
What is the F ratio
Ratio between wanted (effect) variance and unwanted (error) variance.
What does the 1-way independent ANOVA do specifically?
Examines the ratio of variance between groups + variance within groups
MS between / MS within
When do significant effects occur in the 1-way independent ANOVA
When you have 4 times as much variance between groups than within.
What does an F ratio close to 1 mean?
Treatment creates little variability in scores
When can a significant difference be shown in regards to the F ratio
When theres a large F statistic but depends on the df
Can the F ratio ever be negative?
NO
Is the F ratio ever less than 1
Hardly ever
What size are most F ratios
Medium
What does a small F ratio usually indicate
No effect
What does a large F ratio usually indicate?
A sig effect but depends on df
How can you find out if the F ratio is sig?
Calculate df between groups (effect/treatment)
Calculate df within groups (Error)
Find values on critical value table.
If F value is larger than the critical value for our df then there IS a sig difference at the p<0.05 level.
Why is error variance (a.k.a measurement error) always present?
Due to variables not being able to be measured perfectly + there being ind differences
Error variance (MSE) in independent ANOVA
Always occurs within each group (MSwithin)
Calculating the F ratio
How to calculate the SS within
Mean of each group
Subtract mean from a dataset from each value in that dataset.
Square the differences
Total the squared differences to get the SS within.
Calculating the F ratio
How to calculate the SS between
Sum of means
Square of means
Total the squared means
Calculate SS for means of the groups (SSm)
Multiply SSm by no. of ppl in each group to give the between group effect (variance)
What must happen if the F value is greater than the critical value of 3.68?
Reject null hypothesis as there IS a sig difference at the p<0.05 level
Meaning 1 of our mean values is sig different from 1 of the other sample means. but don’t know which as theres more than 2 groups so we need to carry out a POST HOC TEST
What are post hoc tests used to determine?
Which pairs of means are different from 1 another
List the post hoc tests
Tukeys HSD test
Bonferroni Correction test - Usually this one
Scheffe test
LSD test
How is effect size reported?
Partial eta squared
Define effect size
% of variability in the DV explained by the IV.
Which post hoc tests provides the most conservative correction?
Bonferroni
What does the Bonferroni post hoc test do?
Counteracts inflated familywise error by creating a new alpha.
Does this by dividing original alpha by no. of tests conducted.
When must you avoid using the Bonferroni post hoc test
When theres lots of conditions
What does the Tukey HSD post hoc test do?
Calculates a new critical value
When should the Games-Howell test be used?
When you have unequal variances between groups due to levenes test p value being <0.05.
What does the LSD post hoc test stand for?
Least sig difference
Should be avoided
