independent one-way ANOVA Flashcards
when to use an independent one way anova?
Using statistics to examine the influence of an IV (with more than 2 levels) on the DV
-between subjects/ independent design
what does a independent one-way anova look at?
Are the mean scores under each IV significantly different?
-if they are, we assume the IV has caused this difference
Interested in whether there is a difference in population means
-examine the difference in sample means to estimate the difference in population means
when is a one-way anova used?
Used when we have an IV with more than 2 levels
what does a one-way anova estimate?
Estimates if the population means under the different levels of the IV are different
estimate is based on the difference between the measured sample means
why use a one-way anova instead of a t-test
When p<.05 we reject the null hypothesis because it’s unlikely to find a difference of the magnitude we’ve measures if the null hypothesis were true
There is still a 5% chance we have made a type 1 error
-measured results from sampling error rather than reflecting a true difference in the underlying population means
With 3 IV levels you would run 3 t-tests
- A vs B, A vs C, B vs C
For each of these t-tests there would be a 5% chance of making a type 1 error
The overall type 1 error rate across all t-tests would be higher
what does the family wise error rate adjustment reduce?
the chance of a type 1 error
familywise error rate
The probability that at least one of a ‘family’ of comparisons, run on the same data, will result in type 1 error
Provides a corrected significance level (a), expressing the probability of making a type 1 error
what control the familywise error rate?
omnibus tests
null hypothesis of independent one way anova
there is no difference between the population means under different levels of the IV
H0: U1=U2=U3
variance when F value is close to 0
small variance between IV levels relative to within IV levels
variance when F value is further from 0
large variance between IV levels relative to within IV levels
variance between IV levels t/F ratio (independent)
includes variance ‘caused’ by our manipulation of the IV and error variance
variance within IV levels t/F ratio (independent)
includes only error variance
total variance (independent one way ANOVA)
total of modal variance and residual variance
model variance
variance caused by manipulation and error variance
deviations of the sample means from the grand mean
residual variance
only error variance
deviations from the mean of a sample
grand mean
sum of the IV level means, divided by the number of IV levels
residual variance
sum of squared differences between individual values and the corresponding IV level mean
partitioning the variance
1) Calculates the means for each IV level
2) Calculates the grand mean
-sum of the IV level means, divided by the number of IV levels
3) Calculates the within IV levels variance
-sum of squared differences between individual values and the corresponding IV level mean
4) Calculates the between IV levels variance
sum of squared differences between each IV level mean and the grand mean
assumption of independent one way ANOVA
Normality: the DV should be normally distributed, under each level of the IV
Homogeneity of variance the variance in the DV, under each level of the IV, should be (reasonably) equivalent
Equivalent sample size
Independence of observations
independence of observations
scores under each level of the IV should be independent
what can correct for heterogeneity of variance independent one way anova
welches f statistic
what is the levene’s test null hypothesis
there is no difference between the variance under each level of the IV (homogeneity)
what do we do when levene’s p value is <0.05
we reject the null hypothesis (heterogeneity)
which column of levene’s statistic do we read from?
based on mean
what should we report for independent one way anova when homogeneity is violated
welch’s F instead of ANOVA F
degrees of freedom have been adjusted to make the test more conservative
non parametric equivalent independent one way anova
Kruskal Wallis Test
model sum of squares (SS M)
sum of squared differences between IV means and grand mean
residual sum of squares (SS R)
sum of squared differences between individual values and corresponding IV level mean
df for independent one-way anova
The difference between the number of measurements made and the number of parameters estimated
We need to calculate df for our estimates of:
-between IV level (model) variance
-within IV level (error/residual) variance
N is total sample size, K is number of IV levels
Between: df(model): k-1
Within: df(residual): N-k
post hoc tests (independent one way ANOVA)
Secondary analyses used to assess which IV level mean pairs differ
Only used when F value is significant
Run as a t-test but include correction for multiple comparisons
Choice corrections, vary in their risk of type I and type II errors
Tukey honestly significant difference (HSD) type I error risk
low
Tukey honestly significant difference (HSD) type II error risk
high
Tukey honestly significant difference (HSD) classification
reasonably conservative
partial n2
how much variance in the DV is explained by the manipulation of the IV overall
