DT

Question 1

Ungrouped data is?
What type of analyses?
What to consider?

Answer 1

One or more continuous independent variable (e.g. hight)
• Use correlations, regressions
• Need to check for normality/skewnwss

Question 2

Grouped data

What type of analyses?

What to consider? (2 things)

Answer 2

One or more categorical independent variables

t-test, ANOVA

(1) Normality is assumed if sample sizes within cells are 20 or greater (central limit theorem)
BUT sample sizes within cells tends to be small
(2) outlines can exert too much influence

Question 3

What is central limit theorem?

Answer 3

The central limit theorem states that if you have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed

Question 4

What techniques can be used for assessing normality?

Answer 4

1) Normal probability plots
2) Normality tests
3) Histograms

Question 5

What are the normality tests discussed in class?

Answer 5

1) Tests for skewness
2) Shapiro-Wilk
3) Kolmogorov-Smirnov

Question 6

What is the test for skewness and how is it interpreted?

Answer 6

skewness statistic
OVER
standard error of skewness

• > compared to a critical z value that varies based on sample size
• > positive = positively skewed, neg = negatively skewed (if outside of critical range)

Question 7

When is the Kolmogorov-Smirnov test valid? when is it not?

Answer 7

Valid when testing whether a set of observations are from a completely specified continuous distribution

Meaning: if one or more parameters must be estimated from the sample then the tables are not valid

Question 8

What types of probability plots are used to assess normality?

Answer 8

Q-Q Plot

P-P Plot

Detrended normal probability plots

Question 9

What is a Q-Q plot?

What are Q-Q plots better for?

Answer 9

The Q-Q is plotting the actual values of the variable against the theoretical values for the normal distribution.

Q-Q plot is better at finding deviations in the tails (Q has a tail)

Question 10

What are detrended normal probability plots?

Answer 10

Deviations from the diagonal are plotted meaning that the positive linear trend is eliminated

Question 11

What are the 4 steps for producing a normal probability plot?

Answer 11

1. arranging the data from smallest to largest.
2. determining the percentile of each data value.
3. determining the corresponding z-scores from these percentiles based on the normal distribution.
4. plotting each z-score against its corresponding data value.

Question 12

What is a P-P plot?

What are P-P plots better for?

Answer 12

A P-P plot plots the corresponding areas under the curve (cumulative distribution function) for those values.

P-P plot is better at finding deviations from normality in the center of the distribution

Question 13

Which plot tends to be preferred in research situations?

Answer 13

Q-Q (over P-P)

Question 14

What would need to be done if there is a large number of subjects that are contributing to the skew?

what would you consider if there is only a small number of subjects contributing to it?

Answer 14

Mathematical transformation

Winsorizing

Question 15

What is Winsorizing

Answer 15

a method for minimizing the influence of outliers by

(1) assigning the outlier a lower weight
OR
(2) changing the outlier value so that it is closer to the other values in the set

Question 16

What do then Kolmogorov–Smirnov test and Shapiro–Wilk test do?

How are they interpreted

What is a potential concern?

Answer 16

they compare the scores in the sample to a normally distributed set of scores with the same mean and standard deviation

If the test is non-significant (p > .05) it tells us that the distribution of the sample is not significantly different from a normal distribution

Larger sample sizes increase the chance of getting significant results from small deviations from normality that may not be important

Question 17

How do you interpret QQ or PP plots?

Answer 17

if a line sags consistently below or rises consistently above, the problem is kurtosis

if S shape the issue is skewness

Question 18

What side is the hump on in a positive skew?

Answer 18

left hand side (remember turn to the right and it makes a P for positive)

Question 19

What side is the hump on in a positive skew?

Answer 19

Right hand side

Question 20

What does positive kurtosis vs negative kurtosis look like?

Answer 20

positive kurtosis is tall and skinny (pointier than normal)

completely negative is a bowl shape (partly negative would be flatter thank normal)

Question 21

What are the 3 main types of transformations? What can be done with all of them?

Answer 21

1. Square root
2. Logarithmic
3. Inverse

They can all be reflected

Question 22

When would you use a reflection in a transformation? Why?

What to consider?

Answer 22

If you need to normalize a negative skew

• > a reflection turns it into a positive skew and then the positive skew transformations can be applied
• > must keep in mind that it was reflected in interpretation (or reflect back after not clear to me)

Question 23

What are Tabachnick and Fidell’s suggestions for Moderate, Substantial, and Severe positive skewness?

Answer 23

Moderate: square root
Substantial: logarithmic
Severe: inverse

Question 24

What is the Box-Cox Power Transformation?

Answer 24

A procedure for identifying the best exponent to use in a transformation in order to get the best normal shape

• > Lambda = the power that each value is raised to
• > Lambda is the best value between -5 and +5

Question 25

What is Templeton’s two stage approach to data transformation?

Answer 25

It is a procedure for transforming continuous variables to normal
Step 1: Rank the data
Step 2: match the ranks with the corresponding variables from a normal distribution

Question 26

What does excluding cases listwise mean? pairwise?

Answer 26

Listwise: Only subjects that have data for all the selected variables are included in the analysis (i.e. if you are looking at 4 variables and a participant only had data for 3 and has missing data for the other, this participant would be excluded from the analysis entirely - excluded for all 4 variables being looked at)

Pairwise: Variables are evaluated individually, therefore any subject with data for that variable will be included in the analysis for that variable -> this means you could have an unequal number of participants included in the analysis of each of the variables.

Question 27

What is Raynald’s implementation of the box cox transformation?

Answer 27

Looks at 31 values of lambda between -2 to 1 (increments of .1)