Unit 1 AP Stats

Data Set

Includes information about individuals, which can be a person, place, object, or animal.

Individual

In a data set, it refers to the entity being measured, which may not always be a person.

Variable

Characteristics that are evaluated or collected in a data set.

Example of Variable

In a zoo, the individual is one tiger and the variable is the number of pounds of meat consumed in one day.

Categorical Variables

Labels or categories into which data are grouped, often displayed using pie charts and bar graphs.

Quantitative Variables

Variables that can be quantified, such as height, as opposed to subjective values.

Caution in Data Classification

Not all numerical data are quantitative; for example, area codes and social security numbers should not be averaged.

Statistical Data Displays

Organized visual representations of data to enhance understanding.

Pie Chart

Displays the distribution of a categorical variable as slices of a whole, sized by percentage.

Bar Graph

Displays each category of data as a bar, allowing for quick visual comparisons.

Limitations of Graphs

Too many categories can make pie charts and bar graphs confusing and unusable.

Two-Way Table

Also known as a 'contingency table', used to display categorical data that require a more complex graph.

Level of Concern Table Example

A two-way table showing the responses of 480 adolescents regarding their concern over privacy on social media.

Row Variable

In a two-way table, it represents one of the categorical variables, such as level of concern.

Column Variable

In a two-way table, it represents another categorical variable, such as gender.

Total Responses

In the level of concern table, the total number of adolescents surveyed is 480.

Not Concerned at All

In the table, 26 adolescents (11 females and 15 males) reported not being concerned at all.

A Little Concerned

In the table, 99 adolescents (45 females and 54 males) reported being a little concerned.

Moderately Concerned

In the table, 115 adolescents (65 females and 50 males) reported being moderately concerned.

Somewhat Concerned

In the table, 155 adolescents (90 females and 65 males) reported being somewhat concerned.

Very Concerned

In the table, 85 adolescents (44 females and 41 males) reported being very concerned.

Marginal Distribution

The distribution of a categorical variable shows how often each outcome occurred, represented in a two-way table.

Conditional Distributions

Distributions that include only members of a specified variable within a table, showing how the variables in a data set relate to one another.

Mosaic Plot

A modified segmented bar graph where the width of the bars is proportionate to the size of the group, allowing comparison of both percentages and sizes among groups.

Statistical Relationships

An association between variables when there appears to be a statistical relationship between the values of each.

Independent Variables

When the distribution of one variable is the same for all categories of another, indicating no association between these variables.

Frequency Distribution Table

A table that converts raw data to percentages or proportions to show how variables relate within a group.

Total Column

The column in a two-way table that shows the total for each row or column as part of the entire sample.

Sample Size

The number of respondents in a survey, which can affect the ability to make equal comparisons using raw data.

Percentage Calculation

The process of converting individual values to a percentage of the whole column to obtain conditional distributions.

No. of Females

The count of female respondents in a survey, used to calculate conditional distributions.

No. of Males

The count of male respondents in a survey, used to calculate conditional distributions.

Survey Results

Data collected from respondents regarding their privacy concerns about social media use.

Adolescents' Privacy Concerns

The focus of the survey, examining how adolescents feel about privacy in relation to social media.

Column Total

The total number of responses in a specific column of a two-way table.

Row Responses

The individual responses recorded in each row of a two-way table.

Group Comparison

The analysis of how individuals responded within their groups and between two groups.

Statistical Independence

A concept where the outcome of one variable does not affect the outcome of another variable.

Alternative hypothesis

the hypothesis that sample observations are influenced by some nonrandom cause

Association

a relationship between two variables where the values of one variable occur in combination with specific values of the other variable

Bias

overestimating or underestimating the desired response in a survey consistently

Binomial distribution

the probability distribution of a binomial random variable

Binomial random variable

the number of successes, x, in repeated trials of a binomial experiment

Bivariate data

quantitative data that has two variables; often represented using a scatterplot

Blinding

the practice of not telling subjects whether they are receiving a treatment or placebo

Blocking

method of dividing subjects into subgroups called blocks, such that the variability within blocks is less than the variability between blocks

Categorical variable

places an individual into a category or group

Causation

cause-and-effect relationship between or among variables

Census

a survey that collects information from every member of a population

Central limit theorem

when n is large, the sampling distribution of the sample mean is approximately Normal

Chi-square for homogeneity

a test to determine whether two or more categorical distributions are equal

Chi-square test for independence

a test to determine whether there is an association between two categorical variables

Conditional distribution

the distribution of values of a categorical variable among one specified group of individuals described in a two-way table; each group will have a separate conditional distribution

Confidence interval

range of values that describes the amount of uncertainty associated with a sample statistic of a population parameter

Confounding variables

variables that affect the response variable under consideration

Continuous random variables

random variables with outcomes that can take on any numeric value within the range of values

Convenience

choosing only those individuals for a survey who are easy to access

Critical value

a factor used to compute margin of error

Degrees of freedom

the number of independent observations in a sample less the number of population parameters that must be estimated from sample data

Density curve

a curve that is on or above the horizontal axis; the total area underneath = 1, representing 100% of observations

Discrete random variables

random variables with a countable number of outcomes

Dotplot display

a graphic display of data for visual comparison of frequency within categories

Event

any outcome or collection of outcomes that is a subset of the sample space

Expected value

the sum of the products of each possible value and the probability that it occurs

Extrapolation

the use of a regression line to predict values that are outside the original interval of the explanatory variable; these predictions are often inaccurate or unrealistic

Geometric random variable

the number of trials, Y, takes to get a success

Independent event

when the occurrence of one event does not change the probability that the other event will happen

Individuals

objects described by a set of data

Inferential statistics

statistical data from a sample that are used to draw conclusions about the entire population

Law of large numbers

as more and more repetitions of any chance process occur, the proportion of times a specific outcome will happen approaches a single value

Least-squares regression line

the line that makes the sum of the squared residuals as small as possible

Lurking variables

variables other than the independent variable and the dependent variable that may affect experimental outcomes

Margin of error

the maximum expected difference between the true population parameter and a sample estimate of that parameter

Matched pairs design

experimental method where subjects are grouped into pairs based on a blocking variable, then randomly assigned to treatment or control

Mode

the number that occurs most frequently in a set

Nonresponse

when an individual chosen for the sample can't be contacted or refuses to participate

Normal distribution

shown by a Normal density curve with the mean, median, and mode at the center of the curve and described in the format N(µ,σ)

Null hypothesis

the hypothesis that sample observations result purely from chance

Observational study

a study that observes individuals and measures variables of interest but does not attempt to influence the outcome

P-value

a value that measures the strength of the evidence in support of the null hypothesis

Percentile

the lowest score that is greater than a certain percentage of the scores; for example, the 30th percentile indicates that 30 percent of the data fall below that number

Placebo effect

a subject's positive response to receiving a placebo when no treatment has actually been applied

Point estimate

the statistic itself, such as the sample mean, sample median, or sample proportion given as an estimate of the population parameter of interest

Pooling

the name given to a technique used to obtain a more precise estimate of the standard deviation of a sample statistic by combining the estimates given by two (or more) independent samples

Population

the entire group of individuals about which we want information

Power of the test

the probability a test will reject the null hypothesis at a chosen significance level α when the specified alternative value of the parameter is true

Probability

the likelihood that an event will occur; the mathematics of chance

Quantitative variable

measures a specific numerical value that can be used for analysis

Random sample

a group or set chosen in a random manner that allows for each member of the population to have an equal chance of being selected

Regression line

a line that describes how the response variable changes as the explanatory variable changes; can be used to make predictions about a relationship

Representative sampling

a group or set chosen to replicate characteristics of a larger population

Residual

the difference between the observed value of the response variable and the value predicted by the regression line

Robust

procedures work even if there is a violation of the condition of Normality

Sample

part of the population from which information is collected; used to draw conclusions about the entire population

Sampling distribution

a distribution of all the proportions (or means, depending on what is being calculated) from all possible samples

Sampling variability

statistical information from a statistic that varies as random sampling is repeated

Simpson's Paradox

a paradox in statistics in which a trend appears in different groups of data but is reversed when those groups are combined

Simulation

a random process of numerous trials used to estimate probability and imitate chance behavior

Standard deviation

the average distance of a value from the mean of the data

Standard Normal table

a table of areas under the Standard Normal curve; the table entry for each value of z is the area under the curve to the left of that z-score