Week 2 ANOVA (Text books) Flashcards

To supplement the lecture content and underpin our knowledge of ANOVA First slides from Andy Field, Pallant, G& W

1
Q

Rather than run an ANOVA, why don’t we simply use multiple t-tests when we have more than 2 groups/conditions?

A
  • because of an increased type 1 error rate - each time we test a group the probability of falsely rejecting the null hypothesis is 5%; which with 3 groups would rise to 14.3%
  • ANOVA hold the risk of a type 1 error at 5%
  • If 5 conditions rather than 3 error rate rises to 40% if run t-tests!
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2
Q

What is the name for this error rate across statistical tests conducted on the same experimental data?

A

*Familywise error rate
or
*Experimentwise error rate

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3
Q

What is the equation for the familywise error rate?

A

familywise error = 1 - (-.95) to the power of n

n = number of groups

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4
Q

In a nutshell, what does ANOVA do?

A
  • ANOVA tells us whether 3 or more means are the same
  • so it tests the null hypothesis that all group means are equal
  • ANOVA tests for an overall experimental effect
  • ANOVA is a special type of regression
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5
Q

The F ratio of ANOVA tells us if there is an overall experimental effect, what next?

A

Post hoc tests, such as Tukey’s HSD, tell us if where the significance is

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6
Q

So, what does ANOVA do?

A

ANOVA compares the ratio of systematic variance to unsystematic variance in an experimental study (using the F ratio)
*The F ratio assesses how well a regression model can predict an outcome compared to the error within that study

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7
Q

Why is it important to have a control group in social science experiments?

A
  • They act as a baseline for other groups, which is a reference point.
  • when I compare the results, I will see how different each treatment condition is to the control/baseline group to determine if that treatment is effective
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8
Q

What are Andy’s wise words regarding the difference between balanced (equal) and unbalanced (unequal) groups when running ANOVA’s?

A

*In unbalanced designs, it is important to have a fairly large number of cases to ensure that the estimates of the regression coefficients are reliable.

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9
Q

Post hoc tests are designed to reduce the likelihood of a type 1 error rate, but what is the downside according to Pallant?

A

With post hoc tests the approach is stricter making it more difficult to obtain statistically significant differences

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10
Q

How do G & W partition the degrees of freedom for an independent measures ANOVA?

A

df total = N - 1
df between = k - 1
df within treatments = N - k

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11
Q

According to G & W what do SSbetween & MSwithin provide?

A

SSbetween and MSwithin provide a measure of how much difference there is between treatment conditions

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12
Q

What are the H0 and H1 for ANOVA?

A
  • The Null hypothesis (H0) is that in the general population there are no mean differences among the treatments
  • The H1 (Experimental hypothesis) is that at least one mean is different from another
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13
Q

What are the effect sizes for Cohen’s d?

A
d = 0.2: Small effect (mean difference around 0.2 standard deviation)
d = 0.5: Medium effect (mean difference around 0.5 standard deviation)
d = 0.8: Large effect (mean difference around 0.8 standard deviation)
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14
Q

When is ANOVA considered to be robust?

A

When n is large (20-30+ in each group)
Therefore, violation on the normality assumption would have little effect on its accuracy.
P.93

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15
Q

Characteristics of large sample sizes in ANOVA

A

With large and equal groups in ANOVA =
Also robust against heterogenous variances.
P.93

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16
Q

When is Kruskal-Wallace test used?

A

When the assumptions underlying ANOVA are not met:
Normality and homogeneity
Sample size small and unequal
DV measured on an ordinal scale

17
Q

What is the null hypothesis in ANOVA?

A

Is that the population means for the groups are equal;

the alternative hypothesis is that they are unequal.

18
Q

When is the F ratio close to 1?

A

If the variation BETWEEN groups is of the same order of magnitude as the naturally occurring level among individuals WITHIN GROUPS (I.e. Individual differences or error variance).

The F-ratio will be close to 1 and the null hypothesis of no real difference between the groups will be retained.
P.93.

19
Q

What if the variation between groups is much higher than the variation within groups?

A

The F ratio will be much greater than 1 and the null hypothesis of no difference between the groups will be rejected.
P.93

20
Q

Variance between groups is also known as…

A

ERROR VARIANCE

21
Q

What is an OMNIBUS F?

A

A significant or overall omnibus F indicates that there is a difference SOMEWHERE among the groups.

To find out where the differences are… Post hoc analytical comparisons must be conducted.