Analysis on Parametric Test

Unit V, Part 2 Work Sheet &Take
Home Exam
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Due Date: Apr 3
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Section 2: Analyzing the Data
Parametric & Nonparametric Procedures
1. a. Parametric tests:
Parametric tests are those statistical tests which are based on postulations of the population. The
population parameters are taken as the basis of parametric test and null hypotheses are formed
based on those parameters(Corder, 2014).Hypotheses are constructed on the basis of equal mean
or equal variances. t- Test is one of the examples of parametric test which assume the normality of
population data.
b. Nonparametric tests:
Nonparametric tests do not assume any analytically strict conditions about the population. Non
parametric tests are more concerned about the order or rank of data instead of mean and variance.
Hence focus for these tests are not on the probability distribution of the population. Few examples
of non-parametric tests are Mann-Whitney test, Wilcoxon Signed-Rank test and Kruskal-Walis
test(Gibbons, 2011).
2. Seven common characteristics of Parametric Tests:
a. Sample data are collected from population observations independent in nature.
b. Collected sample data are normally distributed.
c. Population variancefor two or more groups has equal values.
d. Sampling technique is random in nature from a well-defined population.
e. Measurement of sample data is in ratio or interval scale.
f. Parametric tests compare sample means as a measure of central tendency.
g.Parametric tests compare two samples of equal sizes.
3. Examples of a Parametric Test:
ANS: Independent sample t-test, chi-square test are two examples of Parametric test(Hart,
2001).
4. Six common characteristics of Nonparametric Tests:
a. Non parametric tests are applicable to data in nominal or ordinal scale.
b. Probability distribution of the population is not required in non-parametric tests.
c. Non parametric tests use median as a measure of central tendency to compare between the
samples.
d. Rank of the sample data are used in non-parametric tests.
e.Parameter values for the population data are not required in non-parametric tests.
f. Single assumption is independent observation with identical distribution of population data.
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5. Examplesof Nonparametric Tests:
ANS: Three examples are Kruskal-Walis test, Mann-Whitney test and Wilcoxon Signed-Rank
test.
Chapter 5
1. Independent t Test:
ANS: The population data for independent t-test is assumed to follow normal
distribution.Independent sample t-test is a parametric test, which compares sample means as a
measure of central tendency between two independent samples(Samuels, 2012). The dependent
variables are hypothesized to have the same variances.
2. Mann-Whitney U-Test:
ANS: Mann-Whitney U-Test is non-parametric test. The basic requirements are similar to a t-test.
Medians of two populations are compared by the help of this test. Ordinal data is used for the test
with a sample size of five to twenty.
3. Choosing between the Independent Test and the Mann-Whitney U-Test
The Independent t test can be used when:
a. The population data is normally distributed.
b. Comparison between two independent sample means has to be done.
c. It is hypothesized that Variances of the two groups under observation are equal.
The Mann-Whitney U-test can be used when:
a. Ordinal variablesare to be measured is.
b. Two groups are tested which are independent.
c. Comparison of medians and differences in spread are done for two samples.
d. Observations of each group are independent in nature within the group.
4. Research question(s) Independent Samplest-test and the Mann-Whitney U-test address
ANS: Both the tests assumes that the observations of the study are independent in nature and
statistically infers whether two populations are significantly different or not. For normally
distributed populations t-test compares means of the populations(Pituch, 2013). Medians of two
populations are compared by Mann-Whitney U-test if the populations under the study are
normally distributed.
5. Assumptions for the Independent Samplest-test:
a. Observations of the population must be independent in nature.
b. The dependent variable should be normally distributed in the population data.
c. Variances of the variable for two populations should be equal.
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6. Example of a Null and Alternative Hypothesis for the Independentt-test:
a. H0: Mean score of mathematics and statistics are equal for class X 2017 batch. (Null)
b. H1: Mean score of mathematics is greater than mean score of statistics in class X (one tail
test) 2017 batch.
7. Conceptual understanding of the Independent Samplest-Test:
ANS: Populations are assumed to be infinite in size and follow normal distribution which is
inferred from the law of large numbers. The t-statistic is used instead of z-statistic when
population variance is unknown. Statistical inference about population characteristics are drawn
by comparing population means(Balducci, 2010). In comparison of two samples t-test is used to
find the information about the population, which is whether the samples are from same or
different populations.
8. For sample size with the t test the following must be determined:
a. Power of the test under study.
b.Probability of Type-I error of the study associated with the null hypothesis.
c. Probability of Type-II error of the study.
d. Relation between power and type-II error of the study.
9. Null and Alternative Hypothesis for the Mann-Whitney U-Test:
a. H0: Median of scores for mathematics and statistics are equal for class X 2017 batch.
(Null)
b. H1: Median of scores for mathematics is greater than mean score of statistics in class X
(one tail test) 2017 batch.
10. Conceptual understanding of the Mann-Whitney U-Test:
ANS: The Mann-Whitney U test is based on the relative ranks of the measurements in each group.
The difference in population distributions are assessed by comparing the medians of the
populations.
11. Significance of a one-tailed test:
ANS: In one-tailed test the critical region is set in any one of the tail of the probability curve. The
alpha value of the critical region of the test is assigned in either left or right tail(Hair, 2011). The
probability of the association is tested in either greater (right tail) or lesser (left tail) direction of
the probability curve.
Figure 1: Left and Right tail test alpha distribution
12. Significance of two-tailed test:
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