INCM 9102
Quantitative Methods
Ttests
Ttests
The term “Ttest” comes from the application of the t-distribution
to evaluate a hypothesis.
Note: a “t-statistic” and a “z-score” are conceptually similar
Ttests
A side note of interest from Wikipedia:
The t-statistic was introduced in 1908 by William Sealy Gosset, a
chemist working for the Guinness Brewery in Dublin, Ireland. Gosset
had been hired due to Claude Guinness's innovative policy of recruiting
the best graduates from Oxford and Cambridge to apply biochemistry
and statistics to Guinness' industrial processes. Gosset devised the t-test
as a way to cheaply monitor the quality of beer. He published the test in
Biometrika in 1908, but was forced to use a pen name by his employer,
who regarded the fact that they were using statistics as a trade secret.
Ttests
The t-table is effectively the inverse of the z-score table – the
“inside” of the table includes the t-statistics while the “outside” of
the table (the designation of the rows and columns) includes the
degrees of freedom and the alpha values.
To determine an appropriate t-statistic for a test, you must know
the alpha value and the degrees of freedom (n-1).
Note that as the number of observation increase, the t-distribution
is assumed to approach normality.
Ttests
Ttests take three forms:
1.One Sample Ttest - compares the mean of the sample to a given
number.
• e.g. Is average monthly revenue per customer who
switches >$50 ?
Formal Hypothesis Statement examples:
H0:   $50
H1:  > $50
H0:  = $50
H1:   $50
Ttests
Fun and exciting example:
After a massive outbreak of salmonella, the CDC determined that
the source was from a particular manufacturer of ice cream. The
CDC sampled 9 production runs if the manufacturer, with the
following results (all in MPN/g):
.593 .142 .329 .691 .231 .793 .519 .392 .418
Use this data to determine if the avg level of salmonella is greater
than .3 MPN/g, which is considered to be dangerous.
STAT3120 - Ttests
First, identify the Hypothesis Statements,
including the Type I and Type II errors…and
your assignment of alpha.
Do the computation by hand…
Then do the computation in SPSS…
Ttests
2.
Two Sample Ttest - compares the mean of the first sample
minus the mean of the second sample to a given number.
•
e.g. Is there a difference in the production output of two
facilities?
Formal Hypothesis Statement examples:
H0: a - b =0
H1: a - b  0
Ttests
When dealing with two sample, it is important to check the
following assumptions:
1.
2.
3.
The samples are independent
The samples have approximately equal variance
The distribution of each sample is approximately normal
Note – if the assumptions are violated and/or if the sample sizes
are very small, we first try a transformation (e.g., take the log
or the square root). If this does not work, then we engage in
non-parametric analysis: Wilcoxan Rank Sum or Wilcoxan
Signed Rank tests.
Ttests
3.
Paired Sample Ttest - compares the mean of the differences
in the observations to a given number.
e.g. Is there a difference in the production output of a
facility after the implementation of new procedures?
Formal Hypothesis Statement example:
H0: diff=0
H1: diff  0