Analysis of Variance (ANOVA) Flashcards
When would ANOVA be used?
• In situations where we want to compare more than two
conditions (instead of T-tests)
•and / or more than one independent variable (factor)
What are the key functions of using an ANOVA test?
• it allows you to investigate the effect of multiple factors on your dependent variable at the same time (in combination)
• It tries to determine whether we have a true
effect of the IV rather than an effect of individual difference (variance between conditions greater than variance within conditions)
Why not use t-tests instead of ANOVA?
- If we just used t‐tests on each pair of groups we would carry out three separate tests:
- By running multiple tests you increase the chance of making a Type 1 error (not finished)
- AKA experiment wise error rate
How does ANOVA control for experiment wise error rate?
ANOVA controls for these errors so that the Type 1 error
remains at 5% and you can be more confident that any
significant result you find is not just down to chance
When are t-tests more efficient than ANOVA and vice versa?
• ANOVA and t‐test are similar • Compare means between‐groups • With 2 groups both work but: -t‐test more efficient -ANOVA inefficient • With more than 2 groups: - t‐test not efficient - ANOVA more efficient
What are the assumptions of ANOVA?
- DV is ratio/interval
- Normally distributed population
- Homogeneity of variance
- independent random samples taken from each population for independent groups
What is homogeneity of variance?
The samples being compared are drawn from populations with the same variance
-shape of distribution the same between groups
How does ANOVA work?
• Analyses the different sources from which variations in scores arise
• It looks at the variability between conditions (between‐
groups variance) and within conditions (within‐group
variance)
• It tries to determine whether we have a true effect of the IV rather than an effect of individual differences (variance between conditions greater than variance within conditions)
What is between-group variance?
The variation (difference) between mean scores in each condition
Explain between-group variance
- When the means are very different there is what is called a greater degree of variation between the conditions
- If there were no differences between the means, there would be no variation
What sources does between-group variance arise from?
- Individual differences
- Treatment effects
- Random errors
Explain the source of the treatment effects of between-group variance
• This is the effect of the IV(s) – what we are actually
trying to measure
• We want a difference between experimental conditions
– the scores of participants in one group are different to scores of participants in another group
• We are measuring whether the variable we are looking at is actually having an effect
Explain the source of the individual difference of between-group variance
- People naturally vary
- We don’t want a high amount of individual differences as this may suggest the IV is having an effect when it is actually due to differences between participants ability in different groups
Explain the source of the random errors of between-group variance
• Errors of measurement can arise from a variety of
sources such as:
-Varying external conditions – differences in time of
day at testing
- State of the participant – current focus of attention,
motivation
- Experimenter’s, or computer’s, ability to measure
and score accurately
What is within-groups variance?
Within‐groups variance is the variation (difference)
between people within the same group
Explain within-group variance
•Within‐groups variance can be called error variance
-The variability within the groups is not produced by the experiment and that is why it is considered error variance
What sources can within-group variance arise from?
- Individual differences
* Random errors
Explain the source of individual differnces of within-groups variance
• People within the same group differ even though they are treated the same
-It is highly likely to have some level of within‐groups
variance because people naturally differ e.g.,
knowledge, IQ, personality etc
Explain the source of the random errors of within-groups variance
• Errors of measurement can arise from a variety of
sources such as:
-Varying external conditions – differences in time of
day at testing
- State of the participant – current focus of attention,
motivation
- Experimenter’s, or computer’s, ability to measure
and score accurately
What is the logic of ANOVA?
- Subjects in different groups should have different scores because they have been treated differently (i.e. given different experimental conditions)
- but subjects within the same group should have the same score
What is ANOVA trying to find out in terms of the logic of ANOVA?
• Trying to find out if the variance or spread of
scores is larger between the groups (i.e. in the different
conditions) than the spread within the groups
• If variance between groups is much > within-group variance =IV having larger effect than individual differences
What is the partitioning of the variance?
The comparison of variance due to nuisance factors (error variance, individual differences) compared to variance due to our experimental manipulation
What is the f-ratio and formula?
- Calculation of the ratio of the variance due to our manipulation of the IV and the error variance
- F = between‐groups variance/within‐groups variance
What are the meaning’s of different f-ratios?
• An F ratio of less than 1 indicates that the effect of the
IV is not significant
• The greater the F‐ratio the better