Analyzing Statistical Data: Parametric & Nonparametric Tests - Unit V

This document is a comprehensive worksheet and take-home exam solution focusing on parametric and nonparametric statistical procedures. It begins by defining and differentiating between parametric and nonparametric tests, outlining their characteristics and providing examples such as the t-test and Mann-Whitney U-test. The solution details the assumptions, applications, and research questions addressed by the independent t-test and the Mann-Whitney U-test, including hypothesis formulation and conceptual understanding. Furthermore, the document analyzes two research articles, applying the learned statistical concepts to real-world studies, including the analysis of lipid profiles, BMI, and glucose levels in patients, and the impact of research utilization training on nurses. The analysis includes study designs, inclusion/exclusion criteria, statistical procedures, and a discussion of the results and limitations of each study. The assignment provides a practical application of statistical knowledge, encompassing hypothesis testing, data analysis, and critical thinking skills.

Unit V, Part 2 Work Sheet &Take Home
Exam
Student Name: Student ID:
Subject Name: Subject ID:
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.
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f. Single assumption is independent observation with identical distribution of population data.
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.
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c. Variances of the variable for two populations should be equal.
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
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12. Significance of two-tailed test:
ANS: Two-tailed test distributes the alpha value equally in both the tails. If the level of
significance is 5% then alpha value of 0.05 is distributed in both tails as 0.025. In two-tailed test
the alternate hypothesis tests the probability of sample mean being greater or less than that of
population mean. This is a two directional test method.
Figure 2: Two-tailed test alpha value distribution
Critical Thinking
(Note article by Wali &Wali)
1. The aim of this study is:
ANS: The aim of the study was to underline the relationship among lipid profile, BMI, glucose,
HbA1c and leptin levels in patients with STs(Wali, 2016).
2. The design of the study is:
ANS: The design of the study was controlled study based on the samples taken from a tertiary
care hospital in south India from April 2013 to May 2014.
3. Inclusion criterion for this study:
ANS: The patients with at least three STs were chosen for the study.
4. Exclusion criteria for the subjects:
a. Patient who was on scheduled medicines that could affect the level of glucose metabolism
or leptin levels were excluded.
b. Patients with irregular lipid profile were excluded. Possible reasons were diabetes mellitus,
gastroentropathy, mal absorptive disorders and hepatic diseases.
c. Patients with liver or kidney disease were excluded. Some of the patients with
endocrinopathies such as acromegaly or Cushing’s syndrome and other medical disorders
were also excluded.
d. The study also excluded pregnant women and lactating mothers.
5. Parameters measured and level of measurement:
a. Waist circumference, Height and weight of the patients were measured.BMI level was
evaluated as a ratio of weight (in kg) and square of height (in meters).
b.By the help of an enzyme related immune-sorbent assay leptin serum level was calculated.
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c. Total triglycerides (TG) and serum total cholesterol (TC) and were measured by an
enzymatic method
d. After applying enzymatic method, Serum high density lipo-protein (HDL) and Serum low
density lipo-protein (LDL) were found by phosphotungstate precipitation.
6. Statistical analysis procedures for the study:
ANS:Two tailed independent student’s t-test was used for analysis in the study. the analysis was
done using SPSS software platform.
7. Step 1: Null and Alternative Hypotheses for this article:
Ho: ST cases and control group have same mean values of the study parameters.
HA:ST cases and control group have significantly different mean values of study parameters.
8. Step 2: The significance level (a-level), degrees of freedom and the critical value:
a. The a-level is: 0.05
b. The total degrees of freedom are __124___ (n1+n2-2 ___)
9. Patients were screened __171____. Patients satisfied the criteriafor inclusion ___126___.
10. Summarization of the major findings of the study:
ANS: There was significant relation of STs with some of the parameters. The significantly
associated parameters were Leptin levels, LDL, VLDL and Triglycerides. Other parameters such
as glucose levels, HDL and BMI had statistically insignificant relation with STs of the patients.
11. Study limitations:
ANS: Insulin level of the patients was not measured. The samples were not collected at the different
collection centres. Only one collection centre had been used to collect raw data and the sample size was
also small.
Critical Thinking
(Note article by Tsai)
1. ANS: The aim/objective of this study was to analyze the effect of research utilization training.
An eight week course was conducted for the nurses, which was based on research utilization
training.
2. Description of the design of this study:
ANS: The research work included eighty nine participants who completed the initial six months of
course work successfully. Their age and educational level were noted down and later matched
with that of the control group. The participants went through an eight week research utilization
course. The sixty five hour course work was divided into three stages(Tsai, 2003). Research
participation and utilization based questionnaire were distributed to participants and their
approach toward nursing was recorded.
3. Selection criteria for the study subjects:
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ANS: The selection criterion was based on marks obtained in the questionnaire by Tsai et al.
(1998b).
4. Description of the study procedure:
ANS: Experimental group participated in an eight week (2 month) at the medical center. The
course was a classroom program based on research utilization. The subjects were tested at the
beginning, immediately after the course completion and finally six months after the course
completion.
5. Research tools:
ANS: Structured questionnaires were used which covered five sections of the study.
6. Number of enrollments in the study and how many completed the study:
ANS: One hundred and five participated in the study and after successful completion of six
months of coursework eighty nine of them completed the study.
7. Statistical analysis procedures used for this study:
ANS: Mann-Whitney U –test and repeated measure ANCOVA were used for statistical
analysis(Nachar, 2008).
8. Step 1: Null and Alternative Hypotheses for this article:
1. Ho:Research utilization course attending nurses and control group had equalamount of positive
attitude toward nursing research.
HA:Research utilization course attending nurses had more positive attitude toward nursing
research compared to control group.
2. Ho: Research utilization course attending nurses and control group had equal amount of
support for nursing research.
HA:Research utilization course attending nurses had more support toward nursing research
compared to control group.
3. Ho: Research utilization course attending nurses and control group had equal score of
participation for nursing research.
HA:Research utilization course attending nurses had more score of participation toward nursing
research compared to control group.
4. Ho: Research utilization course attending nurses and control group had equal score of research
utilization for nursing research.
HA:Research utilization course attending nurses had more score of research utilization toward
nursing research compared to control group.
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9. Step 2: Significance level (a-level) for this study.
a. The a-level was 0.05
10. Description and discussion of the results of the Mann-Whitney U-test:
ANS: Mann-Whitney U-test revealed that no significant difference was there between
experimental and control group as p-value was greater than 0.05 (z = -0.7). The second and third
stages of the study were significantly performed better by experimental group compared to control
group with p-value less than 0.05.
11. Study limitations:
ANS: Short duration of the study and probable biasness of the institution towards research utilization
were the limitations of the study.
Chapter 6
1. Paired t Test:
ANS: Paired t-test is used for several pairs of observations where only a single measurement
variable and two nominal variables are present(Strong, 2014). Paired t-test hypothesizes the mean
difference for the pair of observations as zero.
2. Define the Wilcoxon Matched-Pairs Rank Test:
ANS: Wilcoxon Matched-Pairs Rank Test is a non-parametric test which compares sample
median with hypothetical population median. Difference of each pair along with the sign of the
difference is noted and ranked. The ranks are then used to compute the test statistic ( z ~ N ( 0,1 )
3. a. Type of data required for the Paired tTest:
ANS: Two sets of Nominal data from normally distributed sampling distribution (for mean
difference) are required for paired t-test.
b. Type of data required for the Wilcoxon Matched-Pairs Test:
ANS: For Wilcoxon Matched-Pairs Test the data should come from a symmetrical distribution of
the differences for the pairs of observations ordinal in nature(Woolson, 2008).
4. Choosing between the Paired tTest and the Wilcoxon Matched-Pairs Test
The paired t test can be used when:
a. Sampling distribution for mean difference is approximately normally distributed.
b. Selection is unbiased or random.
c. Sample data has no inaccurate values.
The Wilcoxon Matched-Pairs Signed Rank Test
a. Sampling distribution for mean difference is severely not normally distributed
b. Sampling distribution of the differences for the pairs of observation is symmetric.
c. Paired differences and signs of paired differences can be given rank.
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5.Research question(s)answered by Paired tTest and the Wilcoxon Matched-Pairs Signed
Rank Test:
ANS: Both the tests analyses a sample with paired data to test whether they originated from a
population of specific mean or median.
6. Assumptions for the Pairedt Test and the Wilcoxon Matched-Pairs Test:
ANS: Paired t Test assumes that sampling distribution for mean difference is approximately
normally distributed and sample selection is unbiased or random without any inaccuracy.
Wilcoxon Matched-Pairs Test assumes that sampling distribution of the differences for the pairs
of observation is symmetric and paired differences are independent.
7. Example of a Null and Alternative Hypothesis for the PairedtTest:
ANS: H0: Diabetic patients respond do not change when treatment A is imparted.
HA: Diabetic patients respond significantly positive when treatment A is imparted
8. Conceptual understanding of the Paired tTest:
ANS: Paired t-test is nothing but one sample t-test which takes the difference of paired
observation as sample data.
9. Conceptual understanding of the Wilcoxon Matched-Pairs Signed Rank test:
ANS: Wilcoxon Matched-Pairs Signed Rank test is similar to a paired t-test where the difference
of paired observations is symmetric but not normal. Difference along with their signs are ranked
and used for calculation of test statistic which is normal in nature.
Critical Thinking
(Note article by Kim, Junes & Song)
1. The aim/purpose of the study is:
ANS: The aim of the study was to make elderly women habitual to examine changes in health performance
and cardiovascular risk factors along with life satisfaction.
2. The design of the study is:
ANS: A pretest-posttest method was used for the apparently experimental group.
3. Selection criteria for the study subjects:
ANS: Subjects were selected based on three criteria. Ability to carry out daily activities without help and
ability to follow lectures in education classes with minimum interaction skills(Kim, 2003). No subjects
having chronic diseases were selected.
4. Measurement instruments used in this study:
ANS: Three instruments namely the life satisfaction scale developed by Choi (1986), a health behavior
scale (Song and Lee, 2001) and a cardiovascular risk factor profile (AHA, 1996) were used.
5. Step 1: Null and Alternative Hypotheses for this article:
ANS: H0: The health promotion program did not have significant effect on the health behaviors of
elderly women
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HA: The health promotion program had significant positive effect on the health behaviors of elderly
women
6. Step 2: The a-level was 0.05
7. Summarization of the major findings of this study:
ANS: The health program had significant positive effects on all three aspects of elderly women health. All
the three factors had positive changes in their total scores, significant improvement in overall health of
elderly women were also noticed for six weeks.
8. Study limitations:
ANS: Absence of individual cardiovascular training program and comprehensive physiological assessment
program were identified as the limitations.
Critical Thinking
(Note article by Ellis, Charlett& Bendall)
1. The aim of the study is:
ANS: The aim was to test the appropriateness of primary gel separation tubes. The tubes were studied for
the storage of frozen sera proposed for serological testing.
2. Materials and methods:
ANS: The sera were separated from blood samples of 102 patients after collection of blood in gel
separation tubes. The blood sera were later distributed in gel separation and plastic tubes(Ellis, 2004). All
the samples were frozen and studied one year later for anti-rubella IgG concentrations.
3. Selection criteria for the study subjects:
ANS: The patients were randomly selected from adult patients at the genitourinary medicine clinic.
4. Measurement instruments used in this study:
ANS: Vacutainer 3.5 ml Plus SST gel separation tube and 1.8 ml plastic micro tube were used.
5. Step 1: Null and Alternative Hypotheses for this article:
ANS: H0: There is no significant difference in anti-rubella IgG activity between gel sera of gel separation
and plastic tubes.
HA: There is significant difference in anti-rubella IgG activity between gel sera of gel separation and
plastic tubes (two tailed).
6. Step 2: The a-level is: 0.05
7. Major findings of this study:
ANS: The study found that gel separation tubes were a realistic alternative to plastic micro tubes for
freezing blood samples in laboratory. Sera separation costs and sample handling errors were reduced by the
use of gel separation tubes.
8. Limitation of the study:
ANS: Extensive testing procedures and storage problem for large size gel separation tubes were
some limitations of the study.
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SPSS Exercises for Chapters 5 & 6
Independent t Test
Data Set 1
a. ANS: The frequency distributions for both the treatments for insomnia patients were generated
in SPSS and has been represented in frequency tables given below (table 1 and table 2)
Table 1: Frequency table for Placebo treatment
Hours of Sleep placebo
Frequency Percent Valid Percent Cumulative Percent
Valid
2 1 10.0 10.0 10.0
4 4 40.0 40.0 50.0
5 3 30.0 30.0 80.0
7 2 20.0 20.0 100.0
Total 10 100.0 100.0
Table 2: Frequency table for Formula treatment
Hours of Sleep formula
Frequency Percent Valid Percent Cumulative Percent
Valid
4 3 30.0 30.0 30.0
5 5 50.0 50.0 80.0
6 2 20.0 20.0 100.0
Total 10 100.0 100.0
b. ANS: Both the treatment results for insomnia patients were represented graphically in
following (figure 3 and figure 4) histograms.
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Figure 3: Histogram for hours of sleep due to Placebo treatment
Figure 4: Histogram for hours of sleep due to formula treatment
c. ANS: The measures of central tendency (i.e., mean, median, and mode), dispersion (i.e.,
range, standard deviation), the Fisher’s measure of skewness of the distribution and the Fisher’s
measure of kurtosis were calculated in SPSS and given in table 3 for both the treatments.
Table 3: Descriptive Statistics table for both treatments
Hours of Sleep
placebo
Hours of Sleep
formula
N
Valid 10 10
Missing 0 0
Mean 4.70 4.90
Median 4.50 5.00
Mode 4 5
Std. Deviation 1.494 .738
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