Databases Reference
In-Depth Information
Potpourri
: A/B testing can certainly trace its origins in advertising back to the
days of the mail-order business [
47
,
48
,
49
].
However, it can be traced back even further to Sir Francs Bacon [
50
] in 1620,
who is considered the father of empirical research and the first known proponent
of the what is now considered scientific variable testing.
There are multiple formulas for sample size depending on the type of sample on
uses. However a general formula for sample size is:
2
Z
α
σ
2
n
=
E
Equation 7.1. Sample size calculation
Where n = sample size, E is the desired margin of error, σ is the population stan-
dard deviation, and z
α/2
is the critical value. α represents the confidence level required
(for a 95 percent confidence level, one would choose α of 0.05). E represents the
margin of error as chosen by the analyst; the exact value of this will depend to the
research being done. z
α/2
is obtained by looking at a z-table.
As an example of the calculation if α = 0.05, E = 5, σ = 15, then z
α/2
= 1.960 and
n = 34.5744, which is rounded up to 35. Thus, one would need a sample size of 35.
Typically for any quantitative analysis, one needs 35 to 40 subjects as a rule of thumb.
Potpourri
: Much of quantitative statistical analysis is based on analysis of vari-
ances (ANOVA), which is based on normal distributions, means, and standard
deviations.
This type of quantitative statistical analysis was developed by Sir Ronal A. Fisher,
whose work laid nearly the entire foundation of modern statistical science [
51
].
You must be aware in any statistical analysis what the probability is of being
wrong. As Schwab [
52
] points out, the law of probability can lead to large errors if
the sample size is too small.
Potpourri
: The law of probability is really interesting, as it is a more precise
description of our actions as we strive for success.
Basically, the law of probability is about the chances of something occurring.
So, when we select a sample size that gives of a certain confidence interval, it is
a probability of being correct (or valid or successful) and a probability of being
incorrect (or invalid or unsuccessful).
There is rarely any guarantee of 100 percent either way.
Reliability is a term used to describe the stability of the measurement. Will the
measurement measure the same thing in the same way in repeated tests? Or phrased
