Week Seven

Question 1

sampling error

Answer 1

sampling error occurs when samples are drawn from the one population. If the null hypothesis is true all means should be equal, however, this may not always happen even if the null is retained.

Question 2

f distribution

Answer 2

the shape of the f distribution varies with df like t and is called a family of distributions.
has a mean of around 1
the further in the tail the result is the more likely it is to be significant.

Question 3

sampling error and sample size

Answer 3

more chance of sampling error in a small sample.

Question 4

conclusion of a significant difference

Answer 4

if Fobserved is larger than Fcritical there is a significant difference.

Question 5

type 1 error

Answer 5

rejecting the null when it is true.

= a = 0.05

Question 6

type 2 error

Answer 6

beta

retaining the null when it is false

Question 7

relationship between errors

Answer 7

when we reduce type 1 error, type 2 error increases. thus keep around 0.05
the more tests we do, the greater chance of making an error.

Question 8

power

Answer 8

power is usually kept around 80%

Question 9

independence of observations ANOVA assumption

Answer 9

a. Each participant is separate to the others, this is a research design issue.
Not possible to predict scores from the others.

Question 10

normality of distributions ANOVA assumption

Answer 10

a. Samples are drawn from normally distributed populations and that the error components is normally distributed within each treatment groups.
ANOVA is robust to breaches of assumption provided there is a similar number of participants in each group, there are at least 10-12 participants in each condition and the departure from normality is similar in each condition (kurtosis).

Question 11

normality testing in SPSS

Answer 11

• inspect frequency histograms for each conditions.

- complete skewness and kurtosis statistics. EXPLORE in SPSS.

Question 12

outliers

Answer 12

can impact normality and homogeneity.
can influence results as ANOVA is based on a ration of between and within groups variance.
outliers at each end of the scale can balance each other out.

Question 13

solutions to outliers

Answer 13

• remove the participants and state why.
• transform the data to remove the influence of outliers.
• windsorised: replaces outliers with the next most extreme score.
• logarithm of the square root.
• easiest way is to run the analysis with the outliers, then without, if the results are the same then the outliers have no influence.

Question 14

homogeneity of variance

Answer 14

• A rule of thumb is that the largest variance should be no more than 4 times the smallest variance.
  
  • Breaches of this assumption are more common with unequal group sizes.
  • Breaches can affect the type I error rate.
  • Levene’s test in SPSS can test homogeneity, a significant Levene’s test is bad as it means there is significant difference between the variances.

Question 15

homogeneity assumption in SPSS

Answer 15

• ANOVA
• options
• homogeneity of variance test
• continue
• sign levene’s means the variance is significantly difference and thus breached.

Question 16

ways to deal with a homogeneity breach

Answer 16

1. if there are equal group sizes and the breach is minor (less than 4 times), then run ANOVA as it is robust.
2. run ANOVA and use a lower alpha level to control for the possible impact on the type 1 error rate. HOWEVER THIS WILL INCREASE TYPE 2 ERROR
3. use an alternate statistic test without the assumption (nonparametric).
4. transform the data to remove the heterogeneity and run ANOVA again.
5. bootstrapping

Question 17

data transformation

Answer 17

• Data transformations involve performing an identical mathematical operation on all scores.
  
  • Transformations can change the shape of the distribution.
  • A suitable transformation can
    ○ Reduce heterogeneity
    ○ Achieve normality.

Question 18

types of transformation

Answer 18

○ Logarithmic transformations (long skews, outliers and breaches of homogeneity).
○ Square root (pos skew)
○ Reciprocal or reflect (neg skew)
○ Trimmed samples (outliers of heavy tailed kurtosis)
○ Logarithm and square root are essentially the same thing.

Question 19

log transformations

Answer 19

each score becomes equal to its log.

• it compresses large values but has less effect on small values.
• reduces the spread of scores, reducing skewness and variability.

Question 20

breaches of assumptions

Answer 20

• Breaches of these assumptions lead to either an inflated or deflated estimate of the true BG or WG variability.
  
  • As F=BG/WG, this will either inflate or deflate the obtained F value.
    This will either raise of lower the type 1 and type 2 error rates.