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2. From the contingency table values, calculate expected frequencies (see Exhibit
6.1 cell comments) under the assumption of independence. The calculation of
χ
2 is relatively simple and performed by the CHITEST(actual range, expected
range) function. The function returns the p-value of the calculated
2 .Note
χ
2 value, although it does calculate the value for
that it does not return the
χ
internal use.
3. By considering an explicit level of
α
, the decision to reject the null can be made
2 >
2
= χ
α
on the basis of determining if
χ
. Alternatively,
can be compared
α
= α
to the calculated p-value: p-value <
. Both rules are interchangeable and
α
equivalent. It is often the case that an
of 0.05 is used by investigators.
6.4 z-Test and t-Test of Categorical and Interval Data
Now, let us consider a situation that is similar in many respects to the analysis just
performed, but it is different in one important way. In the
2 test, the subjects in
our sample were associated with two variables, both of which were categorical.
The cells provided a count, or frequency, of the observations that were classiﬁed in
each cell. Now we will turn our attention to sample data that contains categorical
and interval or ratio data. Additionally, the categorical variable is dichotomous, and
thereby can take on only two levels. The categorical variable will be referred to as
the experimental treatment and the interval data as the response variable. In the next
section, we consider an example problem related to the training of human resources
that considers experimental treatments and response variables.
χ
6.5 An Example
A large ﬁrm with 12,000 call center employees in two locations is experiencing
explosive growth. One call center is located in South Carolina (SC) and the other is
in Texas (TX). The ﬁrm has done its own standard internal training of employees
for 10 years. The CEO is concerned that the quality of call center service is begin-
ning to deteriorate at an alarming rate. They are receiving many more complaints
from customers, and when the CEO disguised herself as a customer requesting call
center information, she was appalled at the lack of courtesy and the variation of
responses to a relatively simple set of questions. She ﬁnds this to be totally unac-
ceptable and has begun to consider possible solutions. Among the solutions being
considered is a training program to be administered by an outside organization with
experience in the development and delivery of call center training. The hope is to
create a systematic and predictable customer service response.
A meeting of high level managers is held to discuss the options and some skep-
ticism is expressed about training programs in general: many ask the question—Is
there really any value in these outside programs? Yet in spite of the skepticism, man-
agers agree that something has to be done about the deteriorating quality of customer
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