| Title: | Permutation Tests |
|---|---|
| Description: | Supplies permutation-test alternatives to traditional hypothesis-test procedures such as two-sample tests for means, medians, and standard deviations; correlation tests; tests for homogeneity and independence; and more. Suitable for general audiences, including individual and group users, introductory statistics courses, and more advanced statistics courses that desire an introduction to permutation tests. |
| Authors: | Neil A. Weiss |
| Maintainer: | Neil A. Weiss <[email protected]> |
| License: | GPL (>= 2) |
| Version: | 1.0.1 |
| Built: | 2024-11-01 11:16:23 UTC |
| Source: | CRAN |
Supplies permutation-test alternatives to traditional hypothesis-test procedures such as two-sample tests for means, medians, and standard deviations; correlation tests; tests for homogeneity and independence; and more. Suitable for general audiences, including individual and group users, introductory statistics courses, and more advanced statistics courses that desire an introduction to permutation tests.
| Package: | wPerm |
| Type: | Package |
| Version: | 1.0.1 |
| Date: | 2015-11-03 |
| License: | GPL (>= 2) |
Neil A. Weiss
Maintainer: Neil A. Weiss <[email protected]>
Body mass index for postmenopausal women with osteoporosis given six different treatments of Denosumab.
data("bmi")data("bmi")
A data frame with 236 observations on the following 2 variables.
BMIa numeric vector
TREATMENTa factor with levels 100-mg 14-mg 210-mg 60-mg Placebo
A clinical study was conducted to see whether an antibody called denosumab is effective in treatment of osteoporosis of postmenopausal women. In the article cited below, researchers reported on a study where women with osteoporosis were randomly assigned into groups that received either a placebo, or a six-month regimen of Denosumab at doses of 14 mg, 60 mg, 100 mg, or 210 mg. The bmi dataset provides data on the body-mass indexes (BMI) of the women in each treatment group.
McClung, M., et al. (2006) Denosumab in Postmenopausal Women with Low Bone Mineral Density. New England Journal of Medicine, 354, pp. 821-831.
data(bmi) str(bmi) attach(bmi) plot(BMI ~ TREATMENT) detach(bmi)data(bmi) str(bmi) attach(bmi) plot(BMI ~ TREATMENT) detach(bmi)
The final-exam scores (out of 40 possible) for a control group of 41 algebra students.
data("control")data("control")
The format is: num [1:41] 36 35 35 33 32 32 31 29 29 28 ...
One year at Arizona State University, the algebra course director decided to experiment with a new teaching method that might reduce variability in final-exam scores by eliminating lower scores. The director randomly divided the algebra students who were registered for class at 9:40 A.M. into two groups. One of the groups, called the control group, was taught the usual algebra course; the other group, called the experimental group, was taught by the new teaching method. Both classes covered the same material, took the same unit quizzes, and took the same final exam at the same time. The final-exam scores (out of 40 possible) for the students in the control group are provided in the control dataset.
data(control) str(control) boxplot(control) qqnorm(control)data(control) str(control) boxplot(control) qqnorm(control)
Elmendorf tear strengths, in grams, for independent samples of Brand A and Brand B vinyl floor coverings.
data("elmendorf")data("elmendorf")
A data frame with 20 observations on the following 2 variables.
BRANDa factor with levels BRAND.A BRAND.B
STRENGTHa numeric vector
Variation within a method used for testing a product is an essential factor in deciding whether the method should be employed. Indeed, when the variation of such a test is high, ascertaining the true quality of a product is difficult. The Elmendorf tear test is used to evaluate material strength for various manufactured products. In the article cited below, researchers investigated the variation of that test. For one aspect of the study, they randomly and independently obtained the data in "elmendorf" on Elmendorf tear strength, in grams, of two different brands of vinyl floor coverings.
Phillips, A., Jeffries, R., Schneider, J., and Frankoski, S. (1997) Using Repeatability and Reproducibility Studies to Evaluate a Destructive Test Method. Quality Engineering, 10, pp. 283-290.
data(elmendorf) str(elmendorf) plot(elmendorf) attach(elmendorf) detach(elmendorf)data(elmendorf) str(elmendorf) plot(elmendorf) attach(elmendorf) detach(elmendorf)
Last year's energy consumptions for independent random samples of households in the four U.S. regions.
data("energy")data("energy")
A data frame with 20 observations on the following 2 variables.
ENERGYa numeric vector
REGIONa factor with levels Midwest Northeast South West
The Energy Information Administration gathers data on residential energy consumption and expenditures and publishes its findings in Residential Energy Consumption Survey. Independent random samples of households in the four U.S. regions yielded the data on last year's energy consumptions presented in the energy dataset. The data are displayed to the nearest 10 million BTU.
data(energy) str(energy) attach(energy) plot(ENERGY ~ REGION) detach(energy)data(energy) str(energy) attach(energy) plot(ENERGY ~ REGION) detach(energy)
The final-exam scores (out of 40 possible) for an experimental group of 20 algebra students.
data("experimental")data("experimental")
The format is: num [1:20] 36 35 35 31 30 29 27 27 26 23 ...
One year at Arizona State University, the algebra course director decided to experiment with a new teaching method that might reduce variability in final-exam scores by eliminating lower scores. The director randomly divided the algebra students who were registered for class at 9:40 A.M. into two groups. One of the groups, called the control group, was taught the usual algebra course; the other group, called the experimental group, was taught by the new teaching method. Both classes covered the same material, took the same unit quizzes, and took the same final exam at the same time. The final-exam scores (out of 40 possible) for the students in the experimental group are provided in the experimental dataset.
data(experimental) str(experimental) boxplot(experimental) qqnorm(experimental)data(experimental) str(experimental) boxplot(experimental) qqnorm(experimental)
Contingency table of social class and nursery-rhyme knowledge for 66 children in kindergarten through second grade.
data("learning")data("learning")
A data frame with 2 observations on the following 4 variables.
SOCIAL_CLASSa factor with levels Middle Working
A_fewa numeric vector
Somea numeric vector
Lotsa numeric vector
M. Stuart et al. studied various aspects of grade-school children and their mothers. The researchers gave a questionnaire to parents of 66 children in kindergarten through second grade. Two social-class groups, middle and working, were identified based on the mother's occupation. One aspect of the study cross-classified social class (of the mother) and nursery-rhyme knowledge (of the child).
Stuart, M., Dixon, M., Masterson, J., and Quinlan, P. (1998) Learning to Read at Home and at School. British Journal of Educational Psychology, 68, pp. 3-14.
data(learning) str(learning) learningdata(learning) str(learning) learning
Performs a permutation (randomization) test for homogeneity of one variable on two or more populations, using chi-square as the test statistic.
perm.hom.test(x, type = c("cont", "flat", "raw"), variable = NULL, R = 9999)perm.hom.test(x, type = c("cont", "flat", "raw"), variable = NULL, R = 9999)
x |
a data frame (see details below). |
type |
a character string indicating the type of data frame; must be one of "cont" (default), "flat", or "raw". |
variable |
an optional character string that gives the name of the variable whose distributions are to be compared. |
R |
number of replications (default = 9999). |
The null hypothesis is that the populations are homogeneous with respect to the variable under consideration. The alternative hypothesis is that the populations are nonhomogeneous with respect to the variable under consideration.
Types of data frames permitted:
cont: In this type of data frame, the first variable gives either the possible values of the variable under consideration or the populations. The remaining variables give the observed frequencies.
flat: This type of data frame consists of three variables. The first two variables give the pairs of possible values of the variable under consideration and the populations; the third variable gives the frequencies of the pairs.
raw: This type of data frame consists of two variables, which give the raw data of the variable-values and populations.
A list with class "perm.cs.hom" containing the following components:
Perm.values |
the values of chi-square obtained from the permutations. |
Header |
the main title for the output. |
Variable |
the name of the variable whose distributions are to be compared or NULL. |
Statistic |
the statistic used for the permutation test; here, always chi.square. |
Observed |
the value of the chi-square statistic for the observed data. |
n |
the (total) sample size. |
Null |
the null hypothesis; here, always homogeneous. |
Alternative |
the alternative hypothesis; here, always nonhomogeneous. |
P.value |
the P-value or a statement like P < 0.001. |
p.value |
the P-value. |
Neil A. Weiss
# Self-concept for independent random samples of sighted and blind # Indian adolescents. data("self") str(self) self # Note that self is in the form of a contingency table ("cont"). # Permutation homogeneity test to decide whether a difference exists in # self-concept distributions between sighted and blind Indian adolescents, # using 999 replications. perm.hom.test(self, "cont", "Self-concept", 999) # Or, equivalently, since "cont" is the default "type": perm.hom.test(self, variable = "Self-concept", R = 999)# Self-concept for independent random samples of sighted and blind # Indian adolescents. data("self") str(self) self # Note that self is in the form of a contingency table ("cont"). # Permutation homogeneity test to decide whether a difference exists in # self-concept distributions between sighted and blind Indian adolescents, # using 999 replications. perm.hom.test(self, "cont", "Self-concept", 999) # Or, equivalently, since "cont" is the default "type": perm.hom.test(self, variable = "Self-concept", R = 999)
Performs a permutation (randomization) test for difference in location based on independent samples from two populations.
perm.ind.loc(x, y, parameter, stacked = TRUE, variable = NULL, alternative = c("two.sided", "less", "greater"), R = 9999)perm.ind.loc(x, y, parameter, stacked = TRUE, variable = NULL, alternative = c("two.sided", "less", "greater"), R = 9999)
x |
a numeric vector of observations of the variable (stacked case) or a numeric vector of data values representing the first of the two samples (unstacked case). |
y |
a vector of corresponding population identifiers (stacked case) or a numeric vector of data values representing the second of the two samples (unstacked case). |
parameter |
the location parameter under consideration (e.g., mean, trimmed mean). |
stacked |
a logical value (default TRUE) indicating whether the data are stacked. |
variable |
an optional character string that gives the name of the variable under consideration; ignored if stacked is TRUE. |
alternative |
a character string specifying the alternative hypothesis; must be one of "two.sided" (default), "less", or "greater". |
R |
number of replications (default = 9999) |
The null hypothesis is that the distributions of the variable on the two populations are identical—"identical".
The possible alternative hypotheses are:
Two tailed ("two.sided"): The distribution of the variable on the first population has either systematically smaller values or systematically larger values than that of the variable on the second population—"shifted".
Left tailed ("less"): The distribution of the variable on the first population has systematically smaller values than that of the variable on the second population—"shifted.left".
Right tailed ("greater"): The distribution of the variable on the first population has systematically larger values than that of the variable on the second population—"shifted.right".
A list with class "perm.ts.ind" containing the following components:
Stacked |
TRUE if the data are stacked, FALSE otherwise. |
Perm.values |
the values of the test statistic obtained from the permutations. |
Header |
the main title for the output. |
Variable |
the name of the variable under consideration or NULL. |
Pop.1 |
the first population. |
Pop.2 |
the second population. |
n.1 |
the sample size for the first population. |
n.2 |
the sample size for the second population. |
Statistic |
the test statistic. |
Observed |
the observed value of the test statistic. |
Null |
the null hypothesis; here, always identical. |
Alternative |
the alternative hypothesis. |
P.value |
the P-value or a statement like P < 0.001. |
p.value |
the P-value. |
For the permutation test, we need to assume that, under the null hypothesis, the two distributions are identical (i.e., the variable under consideration has the same distribution on both populations). If the two distributions have the same shape and spread, then a null hypothesis of equal population means or equal population medians implies that the two distributions are identical.
Neil A. Weiss
# Annual salaries, in thousands of dollars, for independent samples of # faculty in private and public institutions. data("salary") str(salary) attach(salary) # Note that the data are stacked. # Independent-samples permutation test to decide whether there is a # difference in location for salaries of faculty in private and public # institutions, using the mean as the location parameter. perm.ind.loc(SALARY, TYPE, mean) # Independent-samples permutation test to decide whether faculty in private # institutions have systematically larger salaries than those in public # institutions, using the 20% trimmed mean as the location parameter. tr20.mean <- function(x) mean(x, trim = 0.20) perm.ind.loc(SALARY, TYPE, tr20.mean, alternative = "greater") detach(salary) # clean up.# Annual salaries, in thousands of dollars, for independent samples of # faculty in private and public institutions. data("salary") str(salary) attach(salary) # Note that the data are stacked. # Independent-samples permutation test to decide whether there is a # difference in location for salaries of faculty in private and public # institutions, using the mean as the location parameter. perm.ind.loc(SALARY, TYPE, mean) # Independent-samples permutation test to decide whether faculty in private # institutions have systematically larger salaries than those in public # institutions, using the 20% trimmed mean as the location parameter. tr20.mean <- function(x) mean(x, trim = 0.20) perm.ind.loc(SALARY, TYPE, tr20.mean, alternative = "greater") detach(salary) # clean up.
Performs a permutation (randomization) test for difference in spread (variation) based on independent samples from two populations.
perm.ind.spread(x, y, parameter, stacked = TRUE, variable = NULL, alternative = c("two.sided", "less", "greater"), R = 9999)perm.ind.spread(x, y, parameter, stacked = TRUE, variable = NULL, alternative = c("two.sided", "less", "greater"), R = 9999)
x |
a numeric vector of observations of the variable (stacked case) or a numeric vector of data values representing the first of the two samples (unstacked case). |
y |
a vector of corresponding population identifiers (stacked case) or a numeric vector of data values representing the second of the two samples (unstacked case). |
parameter |
the spread parameter under consideration (e.g., sd, var). |
stacked |
a logical value (default TRUE) indicating whether the data are stacked. |
variable |
an optional character string that gives the name of the variable under consideration; ignored if stacked is TRUE. |
alternative |
a character string specifying the alternative hypothesis; must be one of "two.sided" (default), "less", or "greater". |
R |
number of replications (default = 9999). |
The null hypothesis is that the distributions of the variable on the two populations are identical—"identical".
The possible alternative hypotheses are:
Two tailed ("two.sided"): The distribution of the variable on the first population has a different spread than that of the variable on the second population—"different.spread".
Left tailed ("less"): The distribution of the variable on the first population has a smaller spread than that of the variable on the second population—"smaller.spread".
Right tailed ("greater"): The distribution of the variable on the first population has a larger spread than that of the variable on the second population—"larger.spread".
A list with class "perm.ts.ind" containing the following components:
Stacked |
TRUE if the data are stacked, FALSE otherwise. |
Perm.values |
the values of the test statistic obtained from the permutations. |
Header |
the main title for the output. |
Variable |
the name of the variable under consideration or NULL. |
Pop.1 |
the first population. |
Pop.2 |
the second population. |
n.1 |
the sample size for the first population. |
n.2 |
the sample size for the second population. |
Statistic |
the test statistic. |
Observed |
the observed value of the test statistic. |
Null |
the null hypothesis; here, always identical. |
Alternative |
the alternative hypothesis. |
P.value |
the P-value or a statement like P < 0.001. |
p.value |
the P-value. |
Neil A. Weiss
# Manufacturers use the Elmendorf tear test to evaluate material # strength for various manufactured products. # # Elmendorf tear strength, in grams, of two different vinyl floor # coverings, Brand A and Brand B. data("elmendorf") str(elmendorf) # Note that the data are stacked. # Permutation test to decide whether there is a difference in spread of # tear strength for Brand A and Brand B vinyl floor coverings, using the # standard deviation as the spread parameter. attach(elmendorf) perm.ind.spread(STRENGTH, BRAND, sd) detach(elmendorf) # clean up # Final-exam scores (out of 40 possible) for two groups of algebra # students. One group, called the control group, was taught the usual # algebra course; the other group, called the experimental group, was # taught by a new teaching method. data("control") str(control) data("experimental") str(experimental) # Permutation test to decide whether the new teaching method reduces # variation in final-exam scores, using the variance as the spread # parameter. perm.ind.spread(control, experimental, var, stacked = FALSE, variable = "Score", alternative = "greater")# Manufacturers use the Elmendorf tear test to evaluate material # strength for various manufactured products. # # Elmendorf tear strength, in grams, of two different vinyl floor # coverings, Brand A and Brand B. data("elmendorf") str(elmendorf) # Note that the data are stacked. # Permutation test to decide whether there is a difference in spread of # tear strength for Brand A and Brand B vinyl floor coverings, using the # standard deviation as the spread parameter. attach(elmendorf) perm.ind.spread(STRENGTH, BRAND, sd) detach(elmendorf) # clean up # Final-exam scores (out of 40 possible) for two groups of algebra # students. One group, called the control group, was taught the usual # algebra course; the other group, called the experimental group, was # taught by a new teaching method. data("control") str(control) data("experimental") str(experimental) # Permutation test to decide whether the new teaching method reduces # variation in final-exam scores, using the variance as the spread # parameter. perm.ind.spread(control, experimental, var, stacked = FALSE, variable = "Score", alternative = "greater")
Performs a permutation (randomization) test for independence of two variables, using chi-square as the test statistic.
perm.ind.test(x, type = c("cont", "flat", "raw"), var.names = NULL, R = 9999)perm.ind.test(x, type = c("cont", "flat", "raw"), var.names = NULL, R = 9999)
x |
a data frame (see details below). |
type |
a character string indicating the type of data frame; must be one of "cont" (default), "flat", or "raw". |
var.names |
an optional character string of length two that gives the names of the variables under consideration; if omitted Var.1 and Var.2 are used. |
R |
number of replications (default = 9999). |
The null hypothesis is that the two variables are not associated (i.e., are independent). The alternative hypothesis is that the two variables are associated (i.e., are dependent).
Types of data frames permitted:
cont: In this type of data frame, the first variable gives the possible values of one of the two variables under consideration. The remaining variables of the data frame give the observed frequencies.
flat: This type of data frame consists of three variables. The first two variables give the pairs of possible values of the two variables under consideration; the third variable of the data frame gives the frequencies of the pairs.
raw: This type of data frame consists of two variables, which give the raw data of the two variables under consideration.
A list with class "perm.two.var" containing the following components:
Perm.values |
the values of chi-square obtained from the permutations. |
Header |
the main title for the output. |
Variable.1 |
the name of the first variable or Var.1 |
Variable.2 |
the name of the second variable or Var.2 |
Statistic |
the statistic used for the permutation test; here, always chi.square. |
Observed |
the value of the chi-square statistic for the observed data. |
n |
the sample size. |
Null |
the null hypothesis; here, always nonassociated. |
Alternative |
the alternative hypothesis; here, always associated. |
P.value |
the P-value or a statement like P < 0.001. |
p.value |
the P-value. |
Neil A. Weiss
# Religious belief vs education for a sample of 509 people. data("relig.and.ed") str(relig.and.ed) relig.and.ed # Note that relig.and.ed is in the form of a flat contingency table ("flat"). # Permutation independence test to decide whether an association exists # between religiosity and education, using 999 replications. perm.ind.test(relig.and.ed, "flat", c("Religiosity", "Education"), 999) # Social class vs nursery-rhyme knowledge for a sample of 66 grade-school # children. data("learning") str(learning) learning # Note that the learning data is in the form of a contingency table ("cont"). # Permutation independence test to decide whether an association exists # between social class and nursery-rhyme knowledge, using 999 replications. perm.ind.test(learning, "cont", c("Social class", "Nursery-rhyme knowledge"), 999) # Or, equivalently, since "cont" is the default "type": perm.ind.test(learning, var.names = c("Social class", "Nursery-rhyme knowledge"), R = 999)# Religious belief vs education for a sample of 509 people. data("relig.and.ed") str(relig.and.ed) relig.and.ed # Note that relig.and.ed is in the form of a flat contingency table ("flat"). # Permutation independence test to decide whether an association exists # between religiosity and education, using 999 replications. perm.ind.test(relig.and.ed, "flat", c("Religiosity", "Education"), 999) # Social class vs nursery-rhyme knowledge for a sample of 66 grade-school # children. data("learning") str(learning) learning # Note that the learning data is in the form of a contingency table ("cont"). # Permutation independence test to decide whether an association exists # between social class and nursery-rhyme knowledge, using 999 replications. perm.ind.test(learning, "cont", c("Social class", "Nursery-rhyme knowledge"), 999) # Or, equivalently, since "cont" is the default "type": perm.ind.test(learning, var.names = c("Social class", "Nursery-rhyme knowledge"), R = 999)
Performs a permutation (randomization) test for location, using trimmed data (trim = 0 gives untrimmed data) on several independent samples.
perm.oneway.anova(x, y, trim = 0, ford = NULL, R = 9999)perm.oneway.anova(x, y, trim = 0, ford = NULL, R = 9999)
x |
a (non-empty) vector of observations of the (response) variable. |
y |
a vector of the corresponding populations (levels of the factor). |
trim |
the fraction (0 to 0.5) of observations to be trimmed from each sample; default is 0. |
ford |
an optional integer vector giving the change from alphabetical order of the populations to some other desired order. |
R |
number of replications (default = 9999). |
The null hypothesis is that the distributions of the variable are identical on all the populations. The alternative hypothesis is that the distributions of the variable have systematically larger values on some of the populations than on others.
A list with class "perm.oneway.anova" containing the following components:
Perm.values |
the values of the test statistic obtained from the permutations. |
Header |
the main title for the output. |
Response |
the name of the (response) variable. |
Factor |
the name of the factor. |
Levels |
the populations (levels of the factor). |
n |
the sample sizes. |
Mean |
the sample means. |
SD |
the sample standard deviations. |
Statistic |
the test statistic; here, always F.trim. |
Observed |
the observed value of the test statistic. |
P.value |
the P-value or a statement like P < 0.001. |
p.value |
the P-value. |
Trim |
the trim value. |
Neil A. Weiss
# Last year's energy consumptions, to the nearest 10 million BTU, for # independent random samples of households in the four U.S. regions. data("energy") str(energy) attach(energy) # Permutation one-way ANOVA to decide whether the energy distributions # have systematically larger values in some U.S. regions than in others. # Regions ordered to Northeast, Midwest, South, and West; 999 replications. perm.oneway.anova(ENERGY, REGION, ford = c(2,1,3,4), R = 999) detach(energy) # clean up# Last year's energy consumptions, to the nearest 10 million BTU, for # independent random samples of households in the four U.S. regions. data("energy") str(energy) attach(energy) # Permutation one-way ANOVA to decide whether the energy distributions # have systematically larger values in some U.S. regions than in others. # Regions ordered to Northeast, Midwest, South, and West; 999 replications. perm.oneway.anova(ENERGY, REGION, ford = c(2,1,3,4), R = 999) detach(energy) # clean up
Performs a permutation (randomization) test for difference in location based on a paired sample.
perm.paired.loc(x, y, parameter, variable = NULL, alternative = c("two.sided", "less", "greater"), R = 9999)perm.paired.loc(x, y, parameter, variable = NULL, alternative = c("two.sided", "less", "greater"), R = 9999)
x |
a numeric vector of data values representing the first components of the pairs. |
y |
a numeric vector of data values representing the second components of the pairs. |
parameter |
the location parameter under consideration (e.g., mean, trimmed mean). |
variable |
an optional character string that gives the name of the variable under consideration. |
alternative |
a character string specifying the alternative hypothesis; must be one of "two.sided" (default), "less", or "greater". |
R |
number of replications (default = 9999). |
The null hypothesis is that the distributions of the variable on the two populations are identical—"identical".
The possible alternative hypotheses are:
Two tailed ("two.sided"): The distribution of the variable on the first population has either systematically smaller values or systematically larger values than that of the variable on the second population—"shifted".
Left tailed ("less"): The distribution of the variable on the first population has systematically smaller values than that of the variable on the second population—"shifted.left".
Right tailed ("greater"): The distribution of the variable on the first population has systematically larger values than that of the variable on the second population—"shifted.right".
A list with class "perm.paired.loc" containing the following components:
Perm.values |
the values of the test statistic obtained from the permutations. |
Header |
the main title for the output. |
Variable |
the name of the variable under consideration or NULL. |
Pop.1 |
the first population. |
Pop.2 |
the second population. |
n |
the sample size. |
Statistic |
the test statistic. |
Observed |
the observed value of the test statistic. |
Null |
the null hypothesis; here, always identical. |
Alternative |
the alternative hypothesis. |
P.value |
the P-value or a statement like P < 0.001. |
p.value |
the P-value. |
Neil A. Weiss
# Ages of a sample of 10 heterosexual spouses. data("spouse.ages") str(spouse.ages) attach(spouse.ages) # Paired-sample permutation test to decide whether there is a difference # in location for age distributions of married men and married women, # using the mean as the location parameter. Variable named "Age". perm.paired.loc(HUSBAND, WIFE, mean, "Age") # Paired-sample permutation test to decide whether married men have # systematically greater ages than married women, using the 10% trimmed # mean as the location parameter. tr10.mean <- function(x) mean(x, trim = 0.10) perm.paired.loc(HUSBAND, WIFE, tr10.mean, alternative = "greater") detach(spouse.ages) # clean up.# Ages of a sample of 10 heterosexual spouses. data("spouse.ages") str(spouse.ages) attach(spouse.ages) # Paired-sample permutation test to decide whether there is a difference # in location for age distributions of married men and married women, # using the mean as the location parameter. Variable named "Age". perm.paired.loc(HUSBAND, WIFE, mean, "Age") # Paired-sample permutation test to decide whether married men have # systematically greater ages than married women, using the 10% trimmed # mean as the location parameter. tr10.mean <- function(x) mean(x, trim = 0.10) perm.paired.loc(HUSBAND, WIFE, tr10.mean, alternative = "greater") detach(spouse.ages) # clean up.
Performs a permutation (randomization) test for a relationship (correlation, association) for two quantitative variables, using Pearson's r (product moment correlation coefficient), Spearman's rho (rank correlation coefficient), or Kendall's tau as the test statistic.
perm.relation(x, y, method = c("pearson", "kendall", "spearman"), alternative = c("two.sided", "less", "greater"), R = 9999)perm.relation(x, y, method = c("pearson", "kendall", "spearman"), alternative = c("two.sided", "less", "greater"), R = 9999)
x |
a numeric vector of data values representing the first variable. |
y |
a numeric vector of data values representing the second variable. |
method |
a character string indicating which method is to be used for the test; one of "pearson" (default), "kendall", or "spearman". |
alternative |
a character string specifying the alternative hypothesis; must be one of "two.sided" (default), "less", or "greater". |
R |
number of replications (default = 9999). |
The null hypothesis is that there is no relationship between the variables.
The possible alternative hypotheses are:
Two tailed ("two.sided"): There is a relationship between the variables—"relation".
Left tailed ("less"): There is a negative relationship between the variables—"neg.relation".
Right tailed ("greater"): There is a positive relationship between the variables—"pos.relation".
A list with class "perm.two.var" containing the following components:
Perm.values |
the values of the test statistic obtained from the permutations. |
Header |
the main title for the output. |
Variable.1 |
the name of the first variable. |
Variable.2 |
the name of the second variable. |
n |
the sample size. |
Statistic |
the test statistic. |
Observed |
the observed value of the test statistic. |
Null |
the null hypothesis; here, always no relation. |
Alternative |
the alternative hypothesis. |
P.value |
the P-value or a statement like P < 0.001. |
p.value |
the P-value. |
Neil A. Weiss
# Prices, in euros, of a 50cl bottle of water and distances, in meters, # of convenience stores from the Contemporary Art Museum in El Raval, # Barcelona. data("water") str(water) attach(water) # Permutation test to decide whether a negative relationship exists # between price and distance, using Pearson's r as the test statistic. perm.relation(PRICE, DISTANCE, alternative = "less") # Permutation test to decide whether a negative relationship exists # between price and distance, using Kendall's tau as the test statistic. perm.relation(PRICE, DISTANCE, "kendall", "less") # Permutation test to decide whether a negative relationship exists # between price and distance, using Spearman's rho as the test statistic. perm.relation(PRICE, DISTANCE, "spearman", "less") detach(water) # clean up.# Prices, in euros, of a 50cl bottle of water and distances, in meters, # of convenience stores from the Contemporary Art Museum in El Raval, # Barcelona. data("water") str(water) attach(water) # Permutation test to decide whether a negative relationship exists # between price and distance, using Pearson's r as the test statistic. perm.relation(PRICE, DISTANCE, alternative = "less") # Permutation test to decide whether a negative relationship exists # between price and distance, using Kendall's tau as the test statistic. perm.relation(PRICE, DISTANCE, "kendall", "less") # Permutation test to decide whether a negative relationship exists # between price and distance, using Spearman's rho as the test statistic. perm.relation(PRICE, DISTANCE, "spearman", "less") detach(water) # clean up.
perm.cs.hom"
This is a method for the function print() to print objects of class
"perm.cs.hom".
## S3 method for class 'perm.cs.hom' print(x, ...)## S3 method for class 'perm.cs.hom' print(x, ...)
x |
an object of class " |
... |
further arguments passed to or from other methods. |
This print method summarizes and formats for easy reading the results of
a permutation function with output list of class "perm.cs.hom".
The perm.cs.hom object is returned invisibly.
Neil A. Weiss
perm.oneway.anova"
This is a method for the function print() to print objects of class
"perm.oneway.anova".
## S3 method for class 'perm.oneway.anova' print(x, ...)## S3 method for class 'perm.oneway.anova' print(x, ...)
x |
an object of class " |
... |
further arguments passed to or from other methods. |
This print method summarizes and formats for easy reading the results of
a permutation function with output list of class "perm.oneway.anova".
The perm.oneway.anova object is returned invisibly.
Neil A. Weiss
perm.paired.loc"
This is a method for the function print() to print objects of class
"perm.paired.loc".
## S3 method for class 'perm.paired.loc' print(x, ...)## S3 method for class 'perm.paired.loc' print(x, ...)
x |
an object of class " |
... |
further arguments passed to or from other methods. |
This print method summarizes and formats for easy reading the results of
a permutation function with output list of class "perm.paired.loc".
The perm.paired.loc object is returned invisibly.
Neil A. Weiss
perm.ts.ind"
This is a method for the function print() to print objects of class
"perm.ts.ind".
## S3 method for class 'perm.ts.ind' print(x, ...)## S3 method for class 'perm.ts.ind' print(x, ...)
x |
an object of class " |
... |
further arguments passed to or from other methods. |
This print method summarizes and formats for easy reading the results of
a permutation function with output list of class "perm.ts.ind".
The perm.ts.ind object is returned invisibly.
Neil A. Weiss
perm.two.var"
This is a method for the function print() to print objects of class
"perm.two.var".
## S3 method for class 'perm.two.var' print(x, ...)## S3 method for class 'perm.two.var' print(x, ...)
x |
an object of class " |
... |
further arguments passed to or from other methods. |
This print method summarizes and formats for easy reading the results of
a permutation function with output list of class "perm.two.var".
The perm.two.var object is returned invisibly.
Neil A. Weiss
Flat contingency table for religiosity and educational attainment for a sample of 509 people worldwide.
data("relig.and.ed")data("relig.and.ed")
A data frame with 12 observations on the following 3 variables.
RELIGIOUSITYa factor with levels Religious Not religious Atheist Do not know
EDUCATIONa factor with levels Basic Secondary Advanced
COUNTa numeric vector
A worldwide poll on religion was conducted by WIN-Gallup International and published as the document Global Index of Religiosity and Atheism. One question involved religious belief and educational attainment. The data in the relig.and.ed dataset are based on the answers to that question.
data(relig.and.ed) str(relig.and.ed) relig.and.eddata(relig.and.ed) str(relig.and.ed) relig.and.ed
Salaries, in thousands of dollars rounded to the nearest hundred, for independent random samples of 35 faculty members from private institutions and 30 faculty members from public institutions.
data("salary")data("salary")
A data frame with 65 observations on the following 2 variables.
TYPEa factor with levels PRIVATE PUBLIC
SALARYa numeric vector
The American Association of University Professors (AAUP) conducts salary studies of college professors and publishes its findings in AAUP Annual Report on the Economic Status of the Profession. Independent random samples of 35 faculty members in private institutions and 30 faculty members in public institutions yielded the salaries, in thousands of dollars rounded to the nearest hundred, provided in the salary dataset.
data(salary) str(salary) plot(salary) attach(salary) detach(salary)data(salary) str(salary) plot(salary) attach(salary) detach(salary)
Contingency table on self-concept for independent random samples of sighted and blind Indian adolescents.
data("self")data("self")
A data frame with 2 observations on the following 4 variables.
SIGHTEDNESSa factor with levels Blind Sighted
Higha numeric vector
Moderatea numeric vector
Lowa numeric vector
Self-concept can be defined as the general view of oneself in terms of personal value and capabilities. A study of whether visual impairment affects self-concept was reported in the article cited below. The researchers classified self-concept as high, moderate, or low. Independent random samples of sighted and blind Indian adolescents gave the data on self-concept presented in the self dataset.
Halder, S. and Datta, P. (2014) An Exploration into Self Concept: A Comparative Analysis between the Adolescents Who Are Sighted and Blind in India. British Journal of Visual Impairment, 30, pp. 31-41.
data(self) str(self) selfdata(self) str(self) self
Ages, in years, of a random sample of 10 heterosexual married couples.
data("spouse.ages")data("spouse.ages")
A data frame with 10 observations on the following 2 variables.
HUSBANDa numeric vector
WIFEa numeric vector
The U.S. Census Bureau publishes information on the ages of married people in Current Population Reports. A random sample of 10 heterosexual married couples gave the data on ages, in years, shown in the spouse.ages dataset.
data(spouse.ages) str(spouse.ages) attach(spouse.ages) detach(spouse.ages)data(spouse.ages) str(spouse.ages) attach(spouse.ages) detach(spouse.ages)
Prices, in euros, of a 50cl bottle of water and distances, in meters, of convenience stores from the Contemporary Art Museum in El Raval, Barcelona.
data("water")data("water")
A data frame with 10 observations on the following 2 variables.
DISTANCEa numeric vector
PRICEa numeric vector
Does the price of a convenience-store item, such as a bottle of water, decrease as distance from the Contemporary Art Museum in El Raval, Barcelona, increases? A sample of 10 convenience stores yielded the data presented in the water dataset on price, in euros, of a 50cl bottle of water and distance, in meters, of the convenience store from the Contemporary Art Museum.
Barcelona Field Studies Centre, http://geographyfieldwork.com/SpearmansRank.htm.
data(water) str(water) plot(water) attach(water) detach(water)data(water) str(water) plot(water) attach(water) detach(water)