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
How do you find out if the F‐ratio is significant?
• SPSS can calculate whether the effect of the IV is
sufficiently larger than the effect of the errors
• SPSS will report the exact p‐level for a given F‐ratio
-It takes into account the number of observations
(degrees of freedom)
. The p value needs to be equal to or less than 0.05 for the F ratio to be regarded as significant
What is the p-value when calculating the f-ratio?
• The p value is the probability of getting this F ratio by
chance alone
What are factors in ANOVA?
• These are the independent variable(s) e.g. music type
What are the level of factors in ANOVA?
• These are like conditions. e.g. three levels of the factor: constant low level of music, no music and intermittent music
What are between-subjects factors?
- Factors that vary between participants. e.g. each participant will only experience one level of a factor
- Like an independent samples t-test
What are within-subjects variance?
- factors that vary within a participant e.g. administering all levels of factors to participants
- like a repeated-measures t-test
What are mixed ANOVA designs?
- when a study design includes one or more within subjects factors and one or more between-subjects factors.
- e.g we want to look at male and female test scores (between‐subjects) for each of the facial expressions (within‐subjects)
What needs to be done when describing an ANOVA design?
We need to specify:
- How many factors are involved in the design
- How many levels there are in each factor
- Whether the factor(s) are within or between subjects
What are the different types of ANOVA test in terms of the number of factors?
• One‐way ANOVA (one factor, e.g. facial
expression)
• Two‐way ANOVA (two factors, e.g. facial
expression and gender)
• Three‐way ANOVA (three factors, e.g. facial
expression, gender and age group)
• and so on
What are the different types of ANOVA test in terms of the number of levels in each factor?
e.g. We could describe our 2-way ANOVA example
(two factors, e.g. gender and facial expression)
as a 2 x 4 ANOVA
• Gender has 2 levels (male or female)
• Facial expression has 4 levels (neutral, angry,
happy, and sad)
