Non Parametric Testing Flashcards
The investigator have no prior knowledge about the distribution of the sampled population and attempts to guess the distribution which result to serious error of the decision.
non parametric test
does not identify or specify the distribution of the population from which the sample were drawn
non parametric test
is a statistical procedure in which no hypothesis is made about a specific values of the population parameters
non parametric test
advantages of non parametric test
involve easy computation, fewer mathematical details, and easier to understand and to apply;
make it possible to work with small sample size, and very helpful to the experimenter involved in a pilot studies or dealing with rare types of characteristics
. In multi-sample cases, there are available nonparametric tests for testing hypothesis concerning observations drawn from several different populations without checking the assumptions about the population;
Probability statements associated with most nonparametric are exact probabilities, which are ____ of the shape of the population.
independent
- disadvantages of non parametric testing
may be used to test data that are measured only on a nominal or ordinal data;
that if in fact all parametric assumptions were satisfied in the data the values were of the required level of measurement, nonparametric tests would disregard much of the information contained in the data.
nonparametric tests when applied to data which are nearly normal or nearly normal are not so powerful as the equivalent parametric method.
major characteristics of the chi-square distribution are:
positively skewed
non-negative
there is a family of chi-square distribution
Chi square hypothesis
H1: There is a difference between the observed and expected frequencies.
Ho: There is no difference between the observed and expected frequencies
critical value in chi-square test
k-1 where k is the number of categories
- The U.S. Bureau of the Census indicated that 63.9% of the population is married, 7.7% widowed, 6.9% divorced (and not re-married), and 21.5% single (never been married). A sample of 500 adults from the Philadelphia area showed that 310 were married, 40 widowed, 30 divorced, and 120 single. At the .02 significance level can we conclude that the Philadelphia area is different from the U.S. as a whole?
what is the null hypothesis
The distribution regarding marital status in Philadelphia is the same as the rest of the United States
- The U.S. Bureau of the Census indicated that 63.9% of the population is married, 7.7% widowed, 6.9% divorced (and not re-married), and 21.5% single (never been married). A sample of 500 adults from the Philadelphia area showed that 310 were married, 40 widowed, 30 divorced, and 120 single. At the .02 significance level can we conclude that the Philadelphia area is different from the U.S. as a whole?
what is the alternative hypothesis
The distribution of marital status in the Philadelphia area is different from that in the U.S. population
- can be used to test for a relationship between two nominal scaled variables, where one variable is independent of the other.
chi-square test
is used to investigate whether two traits or characteristics are related.
contigency table
contigency table analysis according to two criteria:
usual hypothesis testing with
- degrees of freedom
- expected frequency
when to use chi-square?
When you want to know if there is an association between two categorical (nominal) variables (i.e., between an exposure and outcome)
Smoking (yes/no) and lung cancer (yes/no)
what test is used
chi-square test
Obesity (yes/no) and diabetes (yes/no)
what test is used
chi-square test
What does a chi-square test tell you?
If the observed frequencies of occurrence in each group are significantly different from expected frequencies (i.e., a difference of proportions)
Usually, the ___ the chi-square statistic, the greater likelihood the finding is significant,
higher
Chi square requires that there be ___ or more in each cell of a 2x2 table and 5 or more in 80% of cells in larger tables. No cells can have a zero count.
5
Chi-squared formula is not applicable in ___
smal samples
If fewer than 5 observations are used per cell, what is used instead of Chi-square test?
Fisher’s exact test
Applicable in the case of two dependent or related samples which aimed to detect significant differences between the two groups.
wilcoxon signed test
Applicable in the case of two dependent or related samples which aimed to detect significant differences between the two groups.
wilcoxon signed test
Alternative of the t-test for the two dependent or correlated samples.
wilcoxon signed test
- A researcher wishes to determine if there is systematic difference between the readings of the two digital weighing scales
what is the null and alternative hypothesis
Null Hypothesis
There is no systematic difference between the readings of the two digital weighing scales.
Alternative Hypothesis
There is a systematic difference between the readings of the two digital weighing scales.
- The Gagliano Research Institute for Business is comparing the research and development (R&D) as a percent of income for a sample of glass manufacturing firms for 2000 and 2001. At the 0.05 significance level, has the R&D expense declined?
what is the null and alternative hypothesis
null: The R&D expense as a percent of income for glass manufacturing firms in 2001 is equal to or greater than that in 2000.
alternative: The R&D expense as a percent of income for glass manufacturing firms in 2001 has declined compared to 2000.
Used to determine if two independent samples came from the same or equal populations.
wilcoxon rank-sum test
No assumption about the shape of population is required.
Each sample must contain at least 8 observations.
The data must be at least ordinal scale.
what test
wilcoxon rank-sum test
for wilcoxon rank-sum test, at least ___ observations should be present
8
the data must be at least ___ in wilcoxon rank-sum test
ordinal
Hills Community College purchased two vehicles, a Ford and a Chevy, for the administration’s use when travelling. The repair costs for the two cars over the last three years is given. At 0.05 significance level, is there a difference in the two distributions?
what is the null and alternative hypothesis
null: There is no difference in the distributions of repair costs for the Ford and Chevy vehicles.
alternative: There is a difference in the distributions of repair costs for the Ford and Chevy vehicles.
- Used to compare three or more samples to determine if they came from equal populations
kruskal-wallis test analysis of variance by ranks
The ___ scale of measurement is required for Kruskal-Wallis Test Analysis of Variance
ordinal
It is an alternative to the one-way ANOVA
Kruskal-Wallis Test
for Kruskal Wallis, each sample should have how many observations
at least five
The chi-square distribution is the test statistic for this
Kruskal-Wallis Test Analysis of Variance By Ranks
Keely Ambrose, director of Human Resources for Miller Industries, wishes to study the percent increase in salary for middle managers at the four manufacturing plants. She gathers a sample of managers and determines the percent increase in salary from last year to this year. At the 5% significance level can Keely conclude that there is a difference in the percent increases for the various plants
what is the null and alternative hypothesis
null: There is no difference in the percent increases in salary for middle managers across the four manufacturing plants.
alternative: At least one plant has a different percent increase in salary for middle managers compared to the others.
- tests the hypothesis that k repeated measures or matched groups come from the populations with identical medians.
friedman two-way anova
Decision rule for Friedman Two-way ANOVA
Reject the Ho if the computed Fr is greater than tabulated chi-square value.
The following data represent the grades of 8 students in Math, Science, and Filipino. Test the hypothesis that there is no significant difference between the performance of students in the three subjects.
state the null and alternative hypothesis
null: There is no significant difference in the performance of students across the three subjects (Math, Science, and Filipino).
alternative: There is a significant difference in the performance of students in at least one of the three subjects.
- Reports the association between two sets of ranked observations
spearman’s coefficient of rank correlation
Similar to Pearson’s coefficient of correlation, but is based on ranked data.
spearman’s coefficient of rank correlation
Ho and Ha of Spearman’s coefficient of rank correlation
Ho: Rank correlation in population is 0
H1: Rank correlation in population is not 0.
Non-parametric tests are not based on the restrictive normality assumption of the
population or any other specific shape of the population.
T/F
True
A study was conducted to determine the relationship between gender (male, female,
LGBT) and buying behavior (complex buying behavior, Dissonance-reducing buying
behavior,Habitual buying behavior, Variety seeking behavior) of consumers who are
patronizing online stores. Using Chi-square test, what is the correct null hypothesis?
Gender and buying behavior of consumers who patronize online stores are
independent.
Nonparametric tests generally are more powerful than parametric tests when normality
cannot be assumed.
T/F
True
A clinic has four doctors. They wish to compare the amount of time that doctors spend
with their patients. It is suspected that times may not be normally distributed but are
otherwise assumed similar except in center, so a nonparametric test was chosen. The
Kruskal-Wallis test results are shown below. H = 15.78 P-value = 0.022At 0.01 level of
significance, what is the correct conclusion?
The doctors have the same median times at α = .01
Most nonparametric tests assume ordinal data.
T/F
True
Which nonparametric test has no parametric counterpart?
Chi-square test
Non-parametric tests can be applied to nominal and ordinal scaled data.
T/F
True
The Mann-Whitney test can be used as a test for equality of two population medians.
T/F
True
Which nonparametric test is best use to compare ratings assigned to n pairs of bonds
by two different rating agencies, if the bonds are rated on an ordinal scale
Wilcoxon Signed Rank Test
Philippine Air Lines wants to determine if the number of no-shows for flights
originating from Manila is higher than from Cebu. A sample of 20 flights from each
city is taken and the number of no-shows is determined for each flight. Which
nonparametric test would you use to determine whether the number of no-shows is
greater in Cebu?
Mann-Whitney Test
spearman p
0.81 to 1.00
very strong relationoship
spearman p
0.61-0.80
strong relationship
spearman p
0.41-0.60 means
moderate relationship
spearman p
0.21-0.40 means
weak relationship
spearman p
0.00-0.20 means
no or negligible relationship
The Wilcoxon signed-rank test is an alternative to the t test for paired observations.
T/F
True
Chi- Square test is can be used to test association of two variables in nominal scales.
T/F
True
Chi-square test can be used even if the variables to be tested are in interval scale.
T/F
True
Most nonparametric tests require data measured on a ratio or interval scale.
T/F
False
Chi-square test is used to test significant differences among median of 2 or more
groups.
T/F
False
Interpretation of Spearman’s rank correlation is not similar to the interpretation of the
Pearson correlation coefficient r.
T/F
False
Which of the following nonparametric test is best to utilize when we want to test
relationship between 2 nominal scale variables?
chi-square test
The Kruskal-Wallis test is based on the independency of the group assumption.
T/F
True
In case of large samples, sampling distribution of the U statistics cannot be
approximated by normal distribution.
T/F
False
A study was conducted to determine the relationship between gender (male, female,
LGBT) and buying behavior (complex buying behavior, Dissonance-reducing buying
behavior,
Habitual buying behavior, Variety seeking behavior) of consumers who are patronizing
online stores.
The result of the Chi-square test is given below.
χ2 = 24.557 P-value = 0.059
What is the correct conclusion
: There is no significant relationship between gender and buying behavior of
consumers who patronize online stores.
The degrees of freedom for the Chi-Square test statistic when testing for independence
in a contingency table with 4 rows and 4 columns would be
df=(rows−1)×(columns−1)
df=(4−1)×(4−1)=3×3=9
chi-square degrees of freedom formula
df = (rows-1)x(columns-1)
Returns on an investor’s stock portfolio (n = 19 stocks) are compared for the same
stock in each of two consecutive quarters. The test results are shown below. W = 67, Z
= 1.336 P-value = 0.1835Which is the best conclusion?
The medians are the same at α = .05.
Rejection of a hypothesis using a nonparametric test is less convincing than using an
equivalent parametric test, since nonparametric tests generally make fewer
assumptions.
T/F
True
A non-parametric test that is used to test difference between medians of 2 independent
groups
Mann-Whitney Test
Which nonparametric test is analogous to a parametric k-sample test for means?
Kruskal Wallis Test
The Wilcoxon signed-rank test is useful to compare one sample median with a
benchmark.
T/F
True
The Kruskal-Wallis test is equivalent to comparing medians in more than 2 groups.
T/F
True
Unlike the Pearson Correlation r, Spearman’s rank correlation coefficient lies within
the range 0 to 1.00 inclusive.
T/F
False
The Kruskal-Wallis test is less useful in finance or marketing, because normal
populations can usually be assumed in financial or marketing data.
T/F
False
Rejection of a hypothesis using a nonparametric test is more convincing than using an
equivalent parametric test when the data are badly skewed.
T/F
False
Non parametric tests can be used in small samples.
T/F
True
A researcher was interested in stress levels of lecturers during lectures. She took the
same group of 8 lecturers and measured their anxiety (out of 15) during a normal
lecture and again in a lecture in which she had paid students to be disruptive and
misbehave. The data were not normally distributed. Which test should she use to
compare her experimental conditions?
Wilcoxon Signed Rank test
Chi-square test utilizes the mean of each category in the 2-way table.
T/F
False
The Wilcoxon signed-rank test is useful to compare more than two sample medians.
T/F
False
Spearman’s rank correlation is used to measure agreement in rankings of paired (x, y)
data.
T/F
False
The Mann-Whitney test utilizes the ranks of two independent samples.
T/F
True
The Kruskal-Wallis test is analogous to the one-sample parametric t test for a mean.
T/F
False
The Spearman rank correlation test compares medians of two paired data sets.
T/F
False
The Mann-Whitney test can be used even if population variances are unequal.
T/F
True
Parametric tests require qualitative measurement on the sample data in the form of an
interval or ratio scale.
T/F
False
The null hypothesis for the Chi-Square test of independence should specify
that the two categorical variables are independent
The Kruskal-Wallis test is almost as powerful as one-factor ANOVA even when
normality can be assumed
T/F
False
The two populations are not identical’ is the alternative hypothesis in the MannWhitney U test.
T/F
True
As compared to the non-parametric tests, the availability and applicability of
parametric tests is limited.
T/F
False
The Wilcoxon signed-rank test is analogous to a parametric two-sample t test of means
from independent samples
T/F
False
The CEO of TOYZ Inc. wants to know if there is a difference in computer skills in
four departments (marketing, finance, operations, accounting). A 20-question skills test
is given to 8 randomly chosen employees of each department. Which nonparametric
test could be used to test if there is a difference in computer skills of employees in four
departments?
Kruskal Wallis Test
The Kruskal-Wallis test does not require normal populations, but it does require them
to be of similar shape.
T/F
False
test for normality
Shapiro Wilk Test
if p value < 0.05 for Shapiro Wilk, it means that the data is ___
not normal
how to normalize data
logarithmic
data-average/stdev
non parametric statistics is a ___ test
free distribution
The department of Trade and Industry claims that on the average the price pork in Metro Manila is 220 pesos per kilo. A group of consumers investiages the DTI’s recorded price of pork in 12 randomly selected supermarkets in Metro Manila.
What is the null and alternative hypothesis
Ho : The average price is 220
Ha: The average price is not 220
The department of Trade and Industry claims that on the average the price pork in Metro Manila is 220 pesos per kilo. A group of consumers investiages the DTI’s recorded price of pork in 12 randomly selected supermarkets in Metro Manila.
p value is 0.028
what is the decision
reject null hypotesis and conclude that the average price of pork of 220 in Metro Manila is not true
also called Mannn Whitney U test
Mann-Whitney Wilcoxon test
extension of the Wilcoxon Rank Sum test that is used whether 2 samples came from the same population
Mann Whitney U test
test for equality of variance
Levene’s test
p < 0.05 in Levene’s means
variances is not equal
test of goodness of fit
chi-square test
is used when we want to to test associations/relationship between independent variable and dependent variable which are bot categorical variables
chi-square test
null and alternative hypothesis of Chi square test
Ho = variable y is independent on variable x
Ha = variable y is dependent on variable x
chi square test assumptions
independent random sampling
data used is crosed tabulated frequency
nominal/ordinal level data
no more than 20% of the cells have an expected frequency less than 5
no empty cells
