Anscombe's Four Datasets

Description

This dataset is used to illustrate the importance of statistical display as an adjunct to summary statistics. Anscombe (1973) fabricated four different bivariate datasets such that, for all datasets, the respective X and Y means, X and Y standard deviations, and correlations, slopes, intercepts, and standard errors of estimate are equal. Accordingly, without a visual representation of these four panels, one might assume that the data values for all four datasets are the same. Scatterplots illustrate, however, the extent to which these datasets are different from one another.

Usage

Anscombe

Format

A data frame with 11 rows and 8 variables:

x1

values of X for the first dataset

y1

values of Y for the first dataset

x2

values of X for the second dataset

y2

values of Y for the second dataset

x3

values of X for the third dataset

y3

values of Y for the third dataset

x4

values of X for the fourth dataset

y4

values of Y for the fourth dataset

Heights and Weights of U.S. Basketball Players

Description

The dataset consists of the heights and weights of the 24 scoring leaders, 12 each from the U.S. Women’s and Men’s National Basketball Association, for the 2014 – 2015 season. These data are taken from the ESPN website at espn.com.

Usage

Basketball

Format

A data frame with 20 rows and 6 variables:

player

name of player

gender

gender of player

heightin

height of player in inches

weightlb

weight of player in pounds

games

number of games played

points

average total points scored per game

Source

https://www.espn.com/

Blood Pressure Data of African-American Adult Males

Description

The data were collected to determine whether an increase in calcium intake reduces blood pressure among African-American adult males. The data are based on a sample of 21 African-American adult males selected randomly from the population of African-American adult males. Ten of the 21 men were randomly assigned to a treatment condition that required them to take a calcium supplement for 12 weeks. The remaining 11 men received a placebo for the 12 weeks. At both the beginning and the end of this time period, systolic blood pressure readings of all men were recorded. These data are adapted from the Data and Story Library (DASL) website.

Usage

Blood

Format

A data frame with 21 rows and 4 variables:

id

case number

treatmen

treatment condition

systolc1

initial blood pressure

systolc2

final blood pressure

Brain Size and IQ Data

Description

The data are based on a study by Willerman et al. (1991) of the relationships between brain size, gender, and intelligence. The research participants consisted of 40 right-handed introductory psychology students with no history of alcoholism, unconsciousness, brain damage, epilepsy, or heart disease who were selected from a larger pool of introductory psychology students with total Scholastic Aptitude Test Scores higher than 1350 or lower than 940. The students in the study took four subtests (Vocabulary, Similarities, Block Design, and Picture Completion) of the Wechsler (1981) Adult Intelligence Scale-Revised. Among the students with Wechsler full-scale IQ’s less than 103, 10 males and 10 females were randomly selected. Similarly, among the students with Wechsler full-scale IQ’s greater than 130, 10 males and 10 females were randomly selected, yielding a randomized blocks design. MRI scans were performed at the same facility for all 40 research participants to measure brain size. The scans consisted of 18 horizontal MRI images. The computer counted all pixels with non-zero gray scale in each of the 18 images, and the total count served as an index for brain size. The dataset and description are adapted from the Data and Story Library (DASL) website.

Usage

Brainsz

Format

A data frame with 40 rows and 7 variables:

ID

case number

GENDER

gender of student

FSIQ

full-scale IQ score based on WAIS-R

VIQ

verbal IQ score based on WAIS-R

PIQ

performance IQ score based on WAIS-R

MRI

pixel count from 18 MRI scans

IQDI

group membership based on FSIQ score

Exercise 14.1 Figures

Description

This dataset contains simulated data for the figures accompanying Exercise 14.1 of Chapter 14. The data represent the results of a fictional study to determine whether there is a relationship between gender, teaching method, and achievement in reading. Each set of scores reflects a scenario with a different relationship among the variables.

Usage

Chapter14_Figures

Format

A data frame with 12 rows and 7 variables:

sex

individual's sex

score1

reading achievement score for first scenario

method

teaching method

score2

reading achievement score for second scenario

score3

reading achievement score for third scenario

score4

reading achievement score for fourth scenario

score5

reading achievement score for fifth scenario

Value and Circulation of Currency

Description

This dataset contains, for the smaller bill denominations, the value of the bill and the total value in circulation. The source for these data is The World Almanac and Book of Facts 2014.

Usage

Currency

Format

A data frame with 5 rows and 3 variables:

BillValue

denomination

TotalCirculation

total currency in circulation in U.S. dollars

NumberCirculation

total number of bills in circulation

Exercise, Food Intake, and Weight Loss

Description

A fabricated dataset constructed by Darlington (1990) to demonstrate the importance of including all relevant variables in an analysis. This dataset contains information about exercise, food intake, and weight loss for a fictional set of dieters.

Usage

Exercise

Format

A data frame with 10 rows and 4 variables:

ID

case number

Exercise

average daily number of hours exercised in that week

FoodIntake

average daily number of calories consumed in one particular week that is more than a baseline of 1,000 calories, as measured in increments of 100 calories

WeightLoss

number of pounds lost in that week

References

"Regression and linear models." Darlington, R. B. (1990, ISBN:978-0070153721)

Exercise 14.5 Data

Description

This dataset contains simulated data for the figures accompanying Exercise 14.1 of Chapter 14. The data represent the results of a fictional study in which a college professor examines the effect of the grade level of the students and the time of the course on how well undergraduate students at her college do in her course.

Usage

Exercise14_5

Format

A data frame with 40 rows and 3 variables:

Time

time of day student takes the course

Year

year of college in which the student is enrolled

Score

final exam score

Figure 15.1 Data

Description

This dataset contains simulated data for Figure 15.1 of Chapter 15.

Usage

Figure15_1

Format

A list with 3 elements:

x

an integer-scaled independent variable

y

an integer-scaled outcome variable

f

frequency of value pair

Figure 15.12 Data

Description

This dataset contains simulated data for Figures 15.12 - 15.13 of Chapter 15.

Usage

Figure15_12

Format

A data frame with 9 rows and 4 variables:

x

a numeric independent variable for Figure 15.12

y

a numeric outcome variable for Figure 15.12

xpr

a numeric independent variable for Figure 15.13

ypr

a numeric outcome variable for Figure 15.13

Figure 15.9 Data

Description

This dataset contains simulated data for Figures 15.9 - 15.11 of Chapter 15.

Usage

Figure15_9

Format

A data frame with 24 rows and 4 variables:

x

a numeric independent variable for Figure 15.9

y

a numeric outcome variable for Figure 15.9

res

residual value for regression of y on x

log_y

log of the outcome variable y

Figure 2.4. Annual Number of Deaths in New York City: Tobacco vs. Other

Description

This dataset contains data on causes of death in New York City that were used for Figure 2.4 of Chapter 2.

Usage

Figure2_4

Format

A data frame with 591,200 rows and 1 variable:

causes

cause of death

Figure 3.2 Data

Description

This dataset contains simulated test scores of Spanish fluency used to generate Figure 3.2 of Chapter 3.

Usage

Figure3_2

Format

A data frame with 100 rows and 1 variable:

fluency

score on test of Spanish fluency

Figure 3.3 Data

Description

This dataset contains simulated scores used to generate Figure 3.3 of Chapter 3.

Usage

Figure3_3

Format

A data frame with 45 rows and 1 variable:

score

numeric score from rectangular distribution

Figure 3.5(A) Data

Description

This dataset contains simulated scores used to generate Figure 3.5(A) of Chapter 3.

Usage

Figure3_5a

Format

A data frame with 121 rows and 1 variable:

DistnA

numeric score from a symmetric distribution

Figure 3.5(B) Data

Description

This dataset contains simulated scores used to generate Figure 3.5(B) of Chapter 3.

Usage

Figure3_5b

Format

A data frame with 75 rows and 1 variable:

DistnB

numeric score from a symmetric distribution

Figures 3.6 and 3.7 Data

Description

This dataset contains simulated scores used to generate Figures 3.6 ad 3.7 of Chapter 3.

Usage

Figure3_6and7

Format

A data frame with 69 rows and 2 variables:

NegSkew

numeric score from a distribution with severe negative skew

PosSkew

numeric score from a distribution with severe positive skew

Figure 5.5 Data

Description

This dataset contains simulated scores used to generate Figures 5.5(A) - 5.5(I) of Chapter 5.

Usage

Figure5_5

Format

A data frame with 10 rows and 18 variables:

ax

days elapsed in a given year

ay

days remaining in that same year

bx

age of elementary school student

by

number of seconds to run a 100-yard dash

cx

introversion score of adolescent boy

cy

aggression score of adolescent boy

dx

moodiness score of college freshman

dy

English ability score of college freshman

ex

weight of male college student

ey

achievement score in statistics of male college student

fx

expected grade in course of college student

fy

course evaluation score given by college student

gx

IQ score of child in grades K – 3

gy

reading achievement score of child in grades K – 3

hx

arithmetic reasoning score of elementary school student

hy

arithmetic fundamentals score of elementary school student

ix

diameter of tree

iy

circumference of tree

Framingham Heart Study

Description

The Framingham Heart Study is a long term prospective study of the etiology of cardiovascular disease among a population of non-institutionalized people in the community of Framingham, Massachusetts. The Framingham Heart Study was a landmark study in epidemiology in that it was the first prospective study of cardiovascular disease and identified the concept of risk factors and their joint effects. The study began in 1956 and 5,209 subjects were initially enrolled in the study. In our dataset, we included variables from the first examination in 1956 and the third examination, in 1968. Clinic examination data has included cardiovascular disease risk factors and markers of disease such as blood pressure, blood chemistry, lung function, smoking history, health behaviors, ECG tracings, echocardiography, and medication use. Through regular surveillance of area hospitals, participant contact, and death certificates, the Framingham Heart Study reviews and adjudicates events for the occurrence of any of the following types of coronary heart disease(CHD): angina pectoris, myocardial infarction, heart failure, and cerebrovascular disease.

Usage

Framingham

Format

A data frame with 400 rows and 33 variables:

ID

case number

SEX

sex

TOTCHOL1

serum cholesterol (mg/dL) at initial examination

AGE1

age (years) at initial examination

SYSBP1

systolic blood pressure (mmHg) at initial examination

DIABP1

diastolic blood pressure (mmHg) at initial examination

CURSMOKE1

indicator that participant currently is a cigarette smoker at initial examination

CIGPDAY1

cigarettes smoked per day at initial examination

BMI1

Body Mass Index (kg/(M*M)) at initial examination

DIABETES1

indicator that participant is diabetic at initial examination

BPMEDS1

use of anti-hypertensive medication at initial examination

HEARTRTE1

ventricular rate (beats/min) at initial examination

GLUCOSE1

casual glucose (mg/dL) at initial examination

PREVCHD1

prevalent CHD (angina pectoris, myocardial infarction, or coronary insufficiency) at initial examination

TIME1

days since initial examination

TIMECHD1

days from initial examination to any CHD event

TOTCHOL3

serum cholesterol (mg/dL) at third examination

AGE3

age (years) at third examination

SYSBP3

systolic blood pressure (mmHg) at third examination

DIABP3

diastolic blood pressure (mmHg) at third examination

CURSMOKE3

indicator that participant currently is a cigarette smoker at third examination

CIGPDAY3

cigarettes smoked per day at third examination

BMI3

Body Mass Index (kg/(M*M) at third examination

DIABETES3

indicator that participant is diabetic at third examination

BPMEDS3

use of anti-hypertensive medication at third examination

HEARTRTE3

ventricular rate (beats/min) at third examination

GLUCOSE3

casual glucose (mg/dL) at third examination

PREVCHD3

prevalent CHD (angina pectoris, myocardial infarction, or coronary insufficiency) at third examination

TIME3

days since initial examination at third examination

HDLC3

HDL cholesterol (mg/dL) at third examination

LDLC3

LDL cholesterol (mg/dL) at third examination

TIMECHD3

days from initial examination to any CHD event at third examination

ANYCHD4

indicator of event of hospitalized myocardial infarction, angina pectoris, coronary insufficiency, or fatal CHD by the end of the study

Details

The associated dataset is a subset of the data collected as part of the Framingham study and includes laboratory, clinic, questionnaire, and adjudicated event data on 400 participants. These participants for the dataset have been chosen so that among all male participants, 100 smokers and 100 non-smokers were selected at random. A similar procedure resulted in 100 female smokers and 100 female non-smokers. This procedure resulted in an over-sampling of smokers. The data for each participant is on one row. People who had any type of CHD in the initial examination period are not included in the dataset.

McDonald's Hamburger Nutrition Information

Description

This dataset contains the fat grams and calories associated with the different types of hamburger sold by McDonald’s. The data are from McDonald’s Nutrition Information Center.

Usage

Hamburger

Format

A data frame with 5 rows and 4 variables:

name

type of burger

fat

grams of fat

calories

total calories

cheese

cheese added

Ice Cream Sales Data

Description

This dataset contains fabricated data for the temperature, relative humidity, and ice cream sales for 30 days randomly selected between May 15th and September 6th.

Usage

IceCream

Format

A data frame with 30 rows and 4 variables:

id

case number

temp

temperature in degrees Fahrenheit

barsold

number of ice cream bars sold

relhumid

relative humidity

Clinton Impeachment Votes

Description

On February 12, 1999, for only the second time in the nation’s history, the U.S. Senate voted on whether to remove a president, based on impeachment articles passed by the U.S. House. Professor Alan Reifman of Texas Tech University created the dataset consisting of descriptions of each senator that can be used to understand some of the reasons that the senators voted the way they did. The data are taken from the Journal of Statistics Education [online].

Usage

Impeach

Format

A data frame with 100 rows and 11 variables:

name

senator’s name

state

state the senator represents

region

geographic region of the U.S.

vote1

vote on perjury

vote2

vote on obstruction of justice

guilty

total number of guilty votes

party

political party of senator

conserva

conservatism score, defined as the senator’s degree of ideological conservatism, based on 1997 voting records as judged by the American Conservative Union, where the scores ranged from 0 to 100 and 100 is most conservative

supportc

state voter support for Clinton, defined as the percent of the vote Clinton received in the 1996 presidential election in the senator’s state

reelect

year the senator’s seat is up for reelection

newbie

indicator for whether the senator is in their first-term

Learning Disabilities in Elementary Students

Description

This dataset is a subset of data from a study by Susan Tomasi and Sharon L. Weinberg (1999), which profiled learning disabled students in an urban setting. According to Public Law 94.142, enacted in 1976, a team may determine that a child has a learning disability (LD) if a severe discrepancy exists between a child’s actual achievement in, for example, math or reading, and his or her intellectual ability. The dataset consists of six variables, described below, on 105 elementary school children from an urban area who were classified as LD and who, as a result, had been receiving special education services for at least three years. Of the 105 children, 42 are female and 63 are male. There are two main types of placements for these students: part-time resource room placements, in which the students get additional instruction to supplement regular classroom instruction, and self-contained classroom placements, in which students are segregated full time. In this dataset, 66 students are in resource room placements while 39 are in self-contained classroom placements. For inferential purposes, we consider the children in the dataset to be a random sample of all children attending public elementary school in a certain city who have been diagnosed with learning disabilities. Many students in the dataset have missing values for either math or reading comprehension, or both. Such omissions can lead to problems when generalizing results. There are statistical remedies for missing data that are beyond the scope of this text. In this case, we will assume that there is no pattern to the missing values, so that our sample is representative of the population.

Usage

Learndis

Format

A data frame with 105 rows and 6 variables:

grade

student’s grade level

gender

student’s gender

placemen

type of placement: “RR” for part time in resource room or “MIS” for full time in self-contained classroom

readcomp

reading comprehension score, with possible range of 0 to 200

mathcomp

math comprehension score, with possible range of 0 to 200

iq

student’a intellectual ability, as measured by IQ score with possible range of 0 to 200

References

"Classifying children as learning disabled: An analysis of current practice in an urban setting." Tomasi, S., & Weinberg, S. L. (1999) <doi:10.2307/1511150>

Likert-Scale Assertiveness Measure

Description

This dataset contains fabricated data for a single survey item measured on a Likert scale. It is given that a survey was administered to 30 individuals and included an item measuring assertiveness by having the individual indicate agreement with the statement: “I have the ability to stand up for my own rights without denying the rights of others.” The response options were: 1 = "strongly agree"; 2 = "agree"; 3 = "neutral"; 4 = "disagree"; 5 = "strongly disagree." Notice that on this scale, high scores are associated with low levels of assertiveness.

Usage

Likert

Format

A data frame with 30 rows and 1 variable:

Assertiveness

five-point Likert-scale score of assertiveness, with high scores associated with low levels of assertiveness

Manual Dexterity

Description

This fictional dataset contains the treatment group number and the manual dexterity scores for 30 individuals selected by the director of a drug rehabilitation center. There are three treatments, and the individuals are randomly assigned ten to a treatment. After five weeks of treatment, a manual dexterity test is administered for which a higher score indicates greater manual dexterity.

Usage

ManDext

Format

A data frame with 30 rows and 3 variables:

ManualDex

manual dexterity score

Sex

individual’s sex

Treatment

treatment group assignment

Manual Dexterity (Dataset #2)

Description

This is a second fictional dataset that expands on ManDext, adding predicted outcome variables from regression analyses under alternative scenarios.

Usage

ManDext2

Format

A data frame with 30 rows and 9 variables:

ManualDex

manual dexterity score

Sex

individual’s sex

Treatment

treatment group assignment

yhat

predicted outcome for disordinal interaction scenario

yhat2

predicted outcome for ordinal interaction scenario

yhat3

predicted outcome for first no-interaction scenario

yhat4

predicted outcome for second no-interaction scenario

yhat5

predicted outcome for third no-interaction scenario

yhat6

predicted outcome for fourth no-interaction scenario

Marijuana Use of Twelfth Graders

Description

The dataset contains the year and percentage of twelfth graders who have ever used marijuana for several recent years. The source for these data is The World Almanac and Book of Facts 2014.

Usage

Marijuana

Format

A data frame with 23 rows and 2 variables:

Year

year for which data was collected

MarijuanaUse

percentage of twelfth graders who reported that they have ever used marijuana

National Education Longitudinal Study (NELS) of 1988

Description

In response to pressure from federal and state agencies to monitor school effectiveness in the United States, the National Center of Education Statistics (NCES) of the U.S. Department of Education conducted a survey in the spring of 1988, the National Education Longitudinal Study (NELS). The participants consisted of a nationally representative sample of approximately 25,000 eighth graders to measure achievement outcomes in four core subject areas (English, history, mathematics, and science), in addition to personal, familial, social, institutional, and cultural factors that might relate to these outcomes. Details on the design and initial analysis of this survey may be referenced in Horn, Hafner, and Owings (1992). A follow-up of these students was conducted during tenth grade in the spring of 1990; a second follow-up was conducted during the twelfth grade in the spring of 1992; and, finally, a third follow-up was conducted in the spring of 1994.

Usage

NELS

Format

A data frame with 500 rows and 48 variables:

id

case number

advmath8

indicator for whether advanced math taken in eighth grade

urban

urbanicity, a measure of the type of environment in which the student lives

region

geographic region of school

gender

student's gender

famsize

student’s family size

parmarl8

parents' marital status in eighth grade

homelang

home language background

slfcnc08

self-concept in eighth grade

slfcnc10

self-concept in tenth grade

slfcnc12

self-concept in twelfth grade

schtyp8

school type in eighth grade

tcherint

likert-scale variable classifying student agreement with the statement, “My teachers are interested in students”

late12

number of times late for school in twelfth grade

cuts12

number of times skipped/cut classes in twelfth grade

absent12

number of times student missed school in twelfth grade

approg

indicator for whether advanced placement program taken

hwkin12

time spent on homework weekly in school per week in twelfth grade

hwkout12

time spent on homework out of school per week in twelfth grade

excurr12

time spent weekly on extracurricular activities in twelfth grade, in hours

computer

indicator for whether computer owned by family in eighth grade

hsprog

type of high school program

unitengl

units in English (NAEP), or number of years of English taken in high school

unitmath

units in mathematics (NAEP), or number of years of math taken in high school

unitcalc

units in calculus (NAEP), or number of years of calculus taken in high school

schattrt

school average daily attendance rate

apoffer

number of advanced placement courses offered by school

nursery

indicator for whether nursery school attended

algebra8

indicator for whether algebra taken in eighth grade

numinst

number of post-secondary institutions attended

edexpect

highest level of education expected

expinc30

expected income at age 30, in dollars

achrdg08

reading achievement in eighth grade

achmat08

math achievement in eighth grade

achsci08

science achievement in eighth grade

achsls08

social studies achievement in eighth grade

achrdg10

reading achievement in tenth grade

achmat10

math achievement in tenth grade

achsci10

science achievement in tenth grade

achsls10

social studies achievement in tenth grade

achrdg12

reading achievement in twelfth grade

achmat12

math achievement in twelfth grade

achsci12

science achievement in twelfth grade

achsls12

social studies achievement in twelfth grade

cigarett

indicator for whether smoked cigarettes ever

alcbinge

indicator for whether ever binged on alcohol

marijuan

indicator for whether smoked marijuana ever

ses

socioeconomic status score, ranging from 0 to 35, and given as a composite of father’s education level, mother’s education level, father’s occupation, mother’s education, and family income

Details

For this dataset, we have selected a sub-sample of 500 cases and 48 variables. The cases were sampled randomly from the approximately 5,000 students who responded to all four administrations of the survey, who were always at grade level (neither repeated nor skipped a grade), and who pursued some form of post-secondary education. The particular variables were selected to explore the relationships between student and home background variables, self-concept, educational and income aspirations, academic motivation, risk-taking behavior, and academic achievement.

References

"A profile of American eighth-grade mathematics and science instruction." Horn, L., Hafner, & Owings (1992) <https://nces.ed.gov/pubsearch/pubsinfo.asp?pubid=92486>

Gender and Political Party Affiliation

Description

This dataset contains data on a fabricated random sample of 200 individuals, 100 females and 100 males, drawn from a population of interest. There are only two variables, both of which are categorical: gender and political party affiliation.

Usage

Politics

Format

A data frame with 200 rows and 2 variables:

Gender

individual's gender

Party

individual's political party affiliation

Educational Measures of the 50 States and Washington, D.C.

Description

This dataset includes different educational measures of the 50 states and Washington, D.C. These data are from The 2014 World Almanac and Book of Facts.

Usage

States

Format

A data frame with 51 rows and 10 variables:

state

name of state

region

region of the country in which the state is located

enrollmt

total public school enrollment 2011 - 2012

stuteach

average number of pupils per teacher 2011 - 2012

teachpay

average annual salary for public school teachers 2011 - 2012

educexpe

average expenditure per pupil 2011 - 2012

satcr

average SAT Critical Reading score 2013

satm

average SAT Math score 2013

satw

average SAT Writing score 2013

pertak

percentage of eligible students taking the SAT 2012

Significant Statisticians

Description

This dataset includes data on 12 statisticians who each have contributed significantly to the field of modern statistics.

Usage

Statisticians

Format

A data frame with 12 rows and 5 variables:

Statistician

name of statistician

Gender

gender of statistician, where 1 = “Female” and 2 = “Male”

Birth

year of birth

Death

year of death

AmStat

number of references in The American Statistician, 1995-2005

Stepping and Heart Rate

Description

Students at Ohio State University conducted an experiment in the fall of 1993 to explore the nature of the relationship between a person's heart rate and the frequency at which that person stepped up and down on steps of various heights. The response variable, heart rate, was measured in beats per minute. For each person, the resting heart rate was measured before a trial (HRInit) and after stepping (HRFinal). There were two different step heights (Height): 5.75 inches (coded as 1 = Low), and 11.5 inches (coded as 2 = High). There were three rates of stepping (Freq): 14 steps/min. (coded as 1 = Slow), 21 steps/min. (coded as 2 = Medium), and 28 steps/min. (coded as 3 = Fast). This resulted in six possible height/frequency combinations. Each subject performed the activity for three minutes. Subjects were kept on pace by the beat of an electric metronome. One experimenter counted the subject's heart rate, in beats per minute, for 20 seconds before and after each trial. The subject always rested between trials until her or his heart rate returned to close to the beginning rate. Another experimenter kept track of the time spent stepping. Each subject was always measured and timed by the same pair of experimenters to reduce variability in the experiment. The dataset and description are adapted from the Data and Story Library (DASL) website.

Usage

Stepping

Format

A data frame with 30 rows and 6 variables:

Order

overall performance order of the trial

Block

subject and experimenters' block number

Height

step height

Freq

rate of stepping

HRInit

resting heart rate of the subject before a trial, in beats per minute

HRFinal

final heart rate of the subject after a trial, in beats per minute

Average Monthy Temperatures for Two Cities

Description

This dataset gives the average monthly temperatures (in degrees Fahrenheit) for Springfield, MO and San Francisco, CA. These data are from Burrill and Hopensperger (1993).

Usage

Temp

Format

A data frame with 24 rows and 2 variables:

City

city where temperature was measured

Temperature

average monthly temperature, in degrees Fahrenheit

References

"Exploring Statistics with the T1-81" Burrill, G., & Hopensperger, P. (1993, ISBN:9780201524321)

Upper Body Strength

Description

This simulated dataset consists of the number of hours eight individuals spend at the gym on a weekly basis along with measures of their upper body strength.

Usage

UpperBodyStrength

Format

A data frame with 8 rows and 3 variables:

gym

number of hours spent at the gym weekly

strength

upper body strength score

gender

individual's gender

Wage and Education Data from the 1985 Current Population Survey

Description

This is a subsample of 100 males and 100 females randomly selected from the 534 cases that comprised the 1985 Current Population Survey in a way that controls for highest education level attained. The sample of 200 contains 20 males and 20 females with less than a high school diploma, 20 males and 20 females with a high school diploma, 20 males and 20 females with some college training, 20 males and 20 females with a college diploma, and 20 males and 20 females with some graduate school training. The data include information about gender, highest education level attained, and hourly wage.

Usage

Wages

Format

A data frame with 400 rows and 9 variables:

id

case number

educ

number of years of education

south

indicator for whether individual lives in the South

sex

individual’s sex

exper

number of years of work experience

wage

wage (dollars per hour)

occup

occupation category

marr

marital status

ed

highest education level

Bootstrapped Mean

Description

Function to obtain a sampling distribution of means by bootstrapping.

Usage

boot.mean(x, B, n = length(x))

Arguments

Value

A list with components:

Examples

# using simple vector
a = 1:10
set.seed(1234)
boot.mean(a, B = 500)

# using variable from data frame
set.seed(1234)
boot.mean(Framingham$AGE3, B = 1000)

Cumulative Percentage Table

Description

Returns as a named vector the cumulative percentage frequency distribution of a variable x at each unique value.

Usage

cumulative.table(x)

Arguments

Details

If x contains NA values (missing data), the cumulative percentage table will not reach 100. The table will end with the cumulative percentage of non-missing data within the object; the value remaining after subtracting this value from 100 represents the percentage of NA values within the object.

Value

A named numeric vector containing cumulative percentage frequencies, named by unique values of x and ordered numerically or alphabetically by name.

See Also

percent.table, cumsum, table

Examples

# using variable without NA values
cumulative.table(NELS$famsize)

# using variable with NA values
cumulative.table(NELS$parmarl8)

Levene's Test for Homogeneity of Variance

Description

Function to test the homogeneity of variance for two populations, an assumption of the independent samples t-test. The null hypothesis tested is that the two population variances are equal; the alternative is that the two population variances are not equal.

Usage

levenes.test(y, group)

Arguments

Value

An anova table containing test results: two values for degrees of freedom, the F-value, and the p-value.

See Also

t.test

Examples

# using simple data frame
value = c(7,2,4,4,8,3,61,2,80,4)
grp = rep(c("A","B"), each = 5)
ex_data = data.frame(value = value, grp = grp)
levenes.test(ex_data$value, group = ex_data$grp)

# using variable without NA values
levenes.test(NELS$famsize, group = NELS$gender)

# using variable with NA values
levenes.test(NELS$achrdg12, group = NELS$gender)

Leverage

Description

Returns the leverage values for a linear regression model.

Usage

leverage(x)

Arguments

Value

A numeric vector of leverage values.

See Also

lm, rstudent(), cooks.distance()

Examples

mod = lm(Framingham$SYSBP1 ~ Framingham$TOTCHOL1 + Framingham$AGE1)
leverage(mod)

Line Graph

Description

Function to plot the estimated density values of a variable as a line.

Usage

line.graph(x, ...)

Arguments

Value

A line graph of the estimated density distribution of a variable.

See Also

plot()

Examples

line.graph(Temp$Temperature[Temp$City == "SanFrancisco"])
line.graph(IceCream$barsold)

Percentage Table

Description

For one variable, returns a frequency distribution table given in percentages. For two variables, returns a contingency table given in percentages.

Usage

percent.table(x, y = NULL)

Arguments

Value

A table of frequency percentages (for one variable) or a contingency table of percentages (for two variables).

See Also

cumulative.table, table

Examples

# frequency table for one variable
percent.table(NELS$region)

# cross-tabulation for two variables
percent.table(Wages$south,Wages$occup)

Standard Error of Skewness

Description

Function to obtain the standard error of the skewness of a distribution of values.

Usage

se.skew(x)

Arguments

Details

Standard error of skewness is computed on non-missing values using the following equation.

\sqrt( 6*N*(N-1) / ((N-2)*(N+1)*(N+3)) )

Value

Standard error of skewness for x.

See Also

skew, skew.ratio

Examples

se.skew(Temp$Temperature[Temp$City == "Springfield"])
se.skew(Temp$Temperature[Temp$City == "SanFrancisco"])

Skewness of a Distribution

Description

Function to obtain the skewness value of a distribution of values.

Usage

skew(x)

Arguments

Details

Skewness value computed on non-missing values using the ratio of \Sigma((x - m)^3) / N to \sqrt(\Sigma((x - m)^2) / N) ^3.

Value

Skewness value of x.

See Also

se.skew, skew.ratio

Examples

skew(IceCream$relhumid)
skew(IceCream$temp)

Skewness Ratio

Description

Returns the ratio of a distribution's skewness value to its standard error of skewness.

Usage

skew.ratio(x)

Arguments

Details

skew.ratio relies on the functions skew and se.skew to compute the skewness value and standard error of skewness, respectively.

Value

Skewness ratio of x.

See Also

skew, se.skew

Examples

# skew ratio computed two ways
skew.ratio(NELS$achmat12)
skew(NELS$achmat12) / se.skew(NELS$achmat12)

Mode

Description

Function to obtain the mode(s) of a distribution.

Usage

the.mode(x)

Arguments

Value

A numeric vector of the value(s) of the distribution that have the highest frequency of occurrence.

See Also

mean, median

Examples

# single mode for factor variable
the.mode(NELS$urban)
# bimodal numeric variable
a = c(14,24,62,12,12,12,36,17,11,99,99,99)
the.mode(a)