Q-test

• is used to detect an outlier, a data that is different from the other data
• may be used to delete only a single data
• data is an outlier if  Q  =   | suspect data - nearest data | ÷ (largest data - smallest data)  >  Qc

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

• is the probability of a type I error (see below table); uses calculus & numerical methods to determine its value
• is used in various statistical test
• types of p-value , where comparing groups A versus B, where the mean of A > mean of B
• 1-tail p-value
• if p-value > 0.05, then  A  ≤  B
• if p-value < 0.05, then  A  >  B
• 2-tail p-value
• if p-value > 0.05, then  A  =  B
• if p-value < 0.05, then  A  ≠  B
Table 2. Types of errors in a statistical test.
 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

• is used to compare the variance (i.e. square of the standard deviation) of two groups of data
• generates the 2-tail p-value

t-test 1:  independent sample or unpaired samples

• is used to compare the means of 2 groups of data
• use the F-test prior to the t-test - to determine if you use the same versus different variance t-test
• generates 1-tail and 2-tail p-values; investigator picks appropriate p-value

t-test 1:  correlated sample or paired samples

• is used to compare the mean difference between 2 groups of data
• use the F-test prior to the t-test - to determine if you use the same versus different variance t-test
• generates 1-tail and 2-tail p-values; investigator picks appropriate p-value

1-anova (1 factor analysis of variance)

• is used to compare 3 or more groups of data that differ by 1 factor
• detects the presence of any differences among pair(s) of groups
• does not identify the different pair(s) of groups
• generates 2-tail p-value

Tukey's test

• is used after 1-anova to identify pair(s) of groups that differ

2-anova 1

• is used to compare 2 or more groups of data that differ by 2 factors
• detects the presence of any differences among pair(s) of groups
• does not identify the different pair(s) of groups
• generates 2-tail p-value

regression analysis 1

• is used to "curve-fit" experimental data in a graph, i.e. determines the value of the parameter(s) of an equation that describes the data
• uses calculus to determine the value of the parameter(s) (i.e. least-squares analysis)

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.