Q-test

Table 1. Q-test values for 90% confidence.

N (sample size)

Q c

3

4

5

6

7

8

9

10

0.94

0.76

0.64

0.56

0.51

0.47

0.44

0.41

 

For example, is the value of 25 an outlier in the following data set ?

10, 11, 13, 14, 25.

In this example,

Q   =  | 25 - 14 | / (25 - 10)  =  0.73 > Q c = 0.64

thus, the value of 25 is an outlier and may be deleted in subsequent data analysis

 

data characterization

mean,  X  =  Σ xi / n

standard deviation,  SD =  { Σ  (xi - X)2 / (n - 1) }½

standard error of the mean,  SEM = SD / (n)½    [see remarks about SEM:   Br. J. Anaesthesia  90(4): 514, 2002]

 

p-value 1

 

accept the null hypothesis

reject the null hypothesis

null hypothesis is valid

Correct decision

Type I error

null hypothesis is invalid

Type II error

Correct decision

null hypothesis = data is the "same"

 

F-test 1

 

t-test 1:  independent sample or unpaired samples

 

t-test 1:  correlated sample or paired samples

 

1-anova (1 factor analysis of variance)

 

Tukey's test

 

2-anova 1

 

regression analysis 1

 

1 for elaboration, see the statistics supplement (the version in my pickup folder in the school's (i.e. Galileo) folder is more rigorous (i.e. uses calculus) than the published version).  link for instructions to use various statistics software.  alternative presentation, using screen cast.