Simple Between Subjects ANOVA

Question 1

One way ANOVA

Answer 1

we are using ANALYSIS OF VARIANCE to tell us something about means
- Focus is on situations with a continuous, normally distributed dependent variable, and a nominal/categorical independent variable with 3+ different levels (e.g., a variable with 3 or more different groups)
ANOVA is basically the same as regression – they are both LINEAR MODELS. If you understand one you understand the other

Question 2

why don’t we just run multiple t-tests?

Answer 2

• Doing multiple t-tests would cause an inflated type 1 error rate
  ○ We inflate the chances of finding a significant p-value (a p-value less than 0.05).
  
  • P-value is the probability of observing results as extreme (or more) as observed, if the null hypothesis is true
  • We use the criteria p < .05 in psychology.
  • Running multiple t-tests would mean that we are getting multiple attempts to find a significant p-value
    ○ the more attempts, the greater the likelihood of obtaining a p-value less than .05.
    ○ This completely undermines the p <.05 criteria.

Question 3

how does ANOVA work?

Answer 3

• By looking at different types of variance – some of which is good variance that we want to have, and some of which is bad variance that we want to minimise – to determine whether our IV appears to have an effect on our DV
  
  • Pretty much just compares the amount of variability between groups (good variance; means our IV is doing something) to the amount of variability within groups (bad variance; error/noise caused by something outside of our IV)
  • ANOVA protects the familywise error rate
  • ANOVA is an OMNIBUS test
    ○ It tells us if there a significant effect, but does not tell us where the effect is (i.e. is there a difference between group A and B, group B and C, group A and C… etc.
    If our ANOVA is not significant we are not justified in examining group contrasts individually.

Question 4

assumptions of 1 way ANOVA

Answer 4

• DV should be at the scale level
  
  • Data should be normally distributed
  • Equal variances between groups
  • GROUPS must be INDEPENDENT
    ○ Scores at one level do not influence scores at another level
    ○ For example, the same person shouldn’t be in multiple groups

Question 5

hypotheses of a typical ANOVA

Answer 5

• H0: There is no significant difference between mean 1, mean 2 and mean 3 (or more if you have them)
  
  • H1: There is a significant difference between the means.
    ○ If we have a specific direction it could be ‘scores for mean 1 are greater than scores for mean 2’.
    ○ Whether the hypothesis is directional or not is important for the test you perform!

Question 6

what to do when conducting an ANOVA on R

Answer 6

• Step 1: Install (if necessary) and load in necessary packages
  
  • Step 2: Load the data
  • Step 3: Look at and format the data
  • Step 4: Test assumptions (normality and equal variances between groups)
  • Step 5: Run the ANOVA
  • Step 6: Get the important information
  • Step 7: Run post-hoc tests (non-directional hypothesis) and/or planned comparisons (directional hypothesis)
    Step 8: Get the important information

Question 7

How do report the results of a simple one way ANOVA

Answer 7

• Non-directional
  
  • ‘A one-way ANOVA was conducted to compare the effect of [IV: in this case lecture type] on [DV: in this case subjective well-being]. There was a statistically significant effect of lecture type on subjective wellbeing (F(2,87) = 16.77, p < .001, ηp2 = .278). Bonferroni adjusted post-hoc tests demonstrated a significant difference between Statistics Lectures and Zoology (p = .006), Statistics lectures and Sports Science (p < .001), and Sports Science and Zoology (p = .032).
  • Directional
  • ‘A one-way ANOVA was conducted to compare the effect of [IV: in this case lecture type] on [DV: in this case subjective well-being]. There was a statistically significant effect of lecture type on subjective wellbeing (F(2,87) = 16.77, p < .001, ηp2 = .278). Planned contrasts demonstrated a significant difference between Statistics Lectures and Zoology and Sports Science (t(87) = 5.17, p < .001, d = 2.31). There was also a significant difference between Zoology and Sports Science (t(87) = 2.61, p = .011, d = 0.67).
    REMEMBER, WE ALSO HAVE TO PROVIDE INTERPRETATION OF THE DIFFERENCES! PROVIDE MEANS/SDS IN A TABLE OR A FIGURE, OR IN THE TEXT.

Question 8

summary

Answer 8

• One-way ANOVA is a useful tool when you want to compare the means of more than two groups, without increasing the likelihood of TYPE 1 ERROR
  
  • Data should be continuous and normally distributed.
  • Alone, one-way ANOVA tells us only that an effect exists. We have to use planned contrasts or post-hoc tests to identify where the difference(s) is / are.
    Provides us with an effect size (partial eta squared), which tells us how much variance can be explained by our groups. This is very similar to R squared in regression.