Analysis of variance - Lecture 7 Flashcards
When is analysis of variance ANOVA used for ?
Used to compare the mean of an interval scale variable between three or more independent groups
The ANOVA test assesses whether the variability between groups (SSB) is significantly larger than the variability within groups (SSW)
What are the assumptions when completing a one way ANOVA and sample size is less than 30 ?
Normality - the interval scale variable of interest should be normally distributed in the k populations from which the samples came. This can be checked using histograms or a box plot of the data from each sample.
Equality of variance - the standard deviation in each of the k populations should be similar. This can be checked by comparing the standard deviation in each of the samples
How is total variation calculated ?
Total Variation = Between group variation + Within group variation
Describe how a one way ANOVA works ?
The one-way ANOVA divides the total variation about the pooled group mean into two sources - a between groups portion and a within groups portion and then compares their magnitudes.
If the between group portion is sufficiently large relative to
the within group proportion then there is evidence that group means differ
What is the significance of the F value ?
Under the null hypothesis that the population means from the various groups are the same we would expect the variance between groups to be equal to the variance within groups
Therefore we would expect the F ratio to be 1.
The greater the F-ratio the more evidence we have against the null hypothesis
How do you complete a one way ANOVA on SPSS ?
Use Analyse>Compare Means> One-Way ANOVA
Move the interval scale variable into Dependent List and group variable into Factor
Click Options then Descriptive to also get summary statistics by group
When completed look for column labelled “Sig” in the between groups row for P-value
When is further analysis required ?
If there is evidence of a difference in population means (i.e., ANOVA P-value less than 0.05), further analysis can be conducted to help determine which groups differ
What are the 2 different types of hypotheses ?
A priori:
* comparisons which the experiment was designed to test and which have been formally stated in the study protocol
* a straightforwardcomparison of two means may be conducted using a modified t-test
* In SPSS this option is described as LSD
A posteriori:
* comparisons which have been suggested by the data
* Correction for multiple testing is therefore necessary
* a number of multiple comparison procedures are available to correct to prevent Type 1 statistical errors e.g Student– Newman–Keuls
What does the Student–
Newman–Keuls test do ?
Places groups with no statistically significant
difference in mean in the same column and groups with a statistically significant
difference in mean in two different columns
Understand the relationship between the independent samples t-test and one-
way Analysis of Variance (ANOVA)
T-test:
- directly tells if the two
groups differ
- Provides t-statistic and p-value
- comparing exactly two groups
ANOVA:
- comparing three or more groups
- Provides F-statistic and p-value
- Identifies if there is a difference among groups but does not specify which groups differ. Post-hoc tests required
Describe the evidence needed top reject the null using ANOVA
High F-ratio and low
P-value → evidence against
H0 (group means are likely different)
Describe the degrees of freedom aspect of ANOVA
Between groups (dfB) - (k - 1) where k = is the number of groups
Within groups (dfW) - (n - k) where n is the total number of observations
