Assessing Normality i) Normal Probability Plots: Look for the observations to fall reasonably close to the green line. Strong deviations from the line indicate non- normality.

Normal P-P Plot of BLOOD Normal P-P Plot of V1 1.00 1.00

.75 .75

.50 .50

.25 .25

0.00 0.00 Expected Cummulative Prob Expected Cummulative Expected Cummulative Prob Expected Cummulative 0.00 .25 .50 .75 1.00 0.00 .25 .50 .75 1.00 Observed Cummulative Prob Observed Cummulative Prob

The observations fall very close to the There is clear indication that the data line. There is very little indication of do not follow the line. The assumption non-normality. of normality is clearly violated. ii) Histogram: Look for a “bell-shape”. Severe skewness and/or outliers are indications of non-normality.

5 16

14 4 12

10 3

8

2 6

4 1 Std. Dev = 60.29 Std. Dev = 992.11 2 Mean = 274.3 Mean = 573.1 0 N = 20.00 0 N = 25.00 150.0 200.0 250.0 300.0 350.0 0.0 1000.0 2000.0 3000.0 4000.0 175.0 225.0 275.0 325.0 375.0 500.0 1500.0 2500.0 3500.0 4500.0

BLOOD V1

Although the histogram is not perfectly There is a clear indication that the data symmetric and bell-shaped, there is no are right-skewed with some strong clear violation of normality. outliers. The assumption of normality is clearly violated.

Caution: Histograms are not useful for small sample sizes as it is difficult to get a clear picture of the distribution. iii) Boxplots: It is hard to detect normality using a box-plot. But, at the very least, look for symmetry. Severe skewness and/or outliers are indications of non-normality.

400 5000

25 4000

8 300 3000

2000

7 200 1000

0

100 -1000 N = 20 N = 25 BLOOD V1

Although the box-plot is not perfectly There is a clear indication that the data symmetric, there is no clear violation are right-skewed with some strong of normality. outliers. The assumption of normality is clearly violated. Assessing Equal Variability

Boxplots: Look for roughly an equal spread of the data.

9 100

8

7

0

6

5

3

-100 4 RESP RESP2 N = 18 8 N = 19 32 1.00 2.00 No Yes

VAR00001 VAR

There is a clear difference in the There is no severe difference in the spreads. The assumption of equal spreads. The assumption of equal variability seems violated. variability seems to be satisfied.