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# Res 342 Week 3 DQ 2.

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Week 3 DQ 2: Why do you use the chi-square statistic? What type of data is used with
chi-square analysis? What are the nonparametric tests that correspond to each type
of parametric test in Weeks One and Two?
The chi-square statistic is used to measures the relative difference between expected
and observed frequencies. When two variables are independent, the fjk should be close
to ejk, which leads to a chi-square test statistic near zero. The large differences
between fjk and ejk will lead to a large chi-square test statistic. The chi-square test statistic
cannot be negative because of squaring; therefore it is always a right-tailed test. If the test
statistic is far enough in the right tail, we will reject the hypothesis of independence. Squaring
each difference removes the sign, so it does not matter whether ejk is above or
below fjk because each squared difference is expressed relative to ejk.
The type of data used with chi-square analysis follows: independent variable, probability
distributions, frequency distribution, good-of-fit test, and data measurement scales (e. g.,
nominal, ordinal, interval, and ratio). The nominal measurement scale contains only qualitative
data. Interval measurement deals with quantitative data. Ordinal measurement scale has the
same properties as the nominal data except we can determine rankings such as popcorn as
good, fair or poor. The ratio measurement scale can be used to perform all four mathematical
operations to compare values.
The nonparametric tests that correspond to each type of parametric test in week one
and two follows: one sample hypothesis tests (e. g., testing a proportion, testing a mean with a
known population variance, testing a mean with an unknown population variance, test for one
variance), two sample hypothesis test (e. g., comparing two variances, comparing two
proportions, and comparing two means: paired samples), analysis of variance (e. g., one factor
ANOVA, two factor ANOVA without replication – randomized block model, tests for homogeneity
of variance – optional), and hypothesis testing.
Nonparametric operations are used in rank data. This form of data details the level to
where a variable scores on a scale or in a table. For example, colleges are concerned with
where their football team ranks in the top ten. Rank data is ordered from lowest to highest, the
integer values are from 1 to the sample size. In large samples, nonparametric techniques can
be shown as normal-theory based procedures applied to ranks.
Reference
Doane, D., & Seward, L. (2007). Applied Statistics in Business and Economics. Burr
Ridge, Illinois: McGraw-Hill.

Glasserman, P. (2001). Hypothesis testing. Retrieved October 9, 2004,
from http://www-1.gsb.columbia.edu/faculty/pglasserman/B6014/HypothesisTesting.pdf
Lind, D.A., Marchal, W.G., & Wathen, S.A. (2005). Statistical techniques in business
and economics (12
th
ed.). Boston: Irwin/McGraw-Hill.
Orris, J. (2007). Basic Statistics Using Excel and MegaStat. Burr Ridge, Illinois:
McGraw-Hill.

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