AP Statistics Cram Vocabulary

Undercoverage

A sampling error that occurs when some members of the population are inadequately represented in the sample, leading to biased results.

Nonresponse

A type of sampling error that occurs when individuals selected for the sample do not respond, resulting in a bias if those who do not respond differ significantly from those who do.

Response Bias

A type of sampling error that occurs when respondents provide inaccurate answers or when the survey method influences the responses, leading to skewed results.

Sampling Variablity

The natural variation in the results obtained from different samples drawn from the same population. It affects the reliability of estimates and can lead to different conclusions.

Comparison

The process of evaluating two or more items to determine similarities and differences, often used in statistics to analyze groups or treatments.

Random Assignment

A technique used in experiments to assign participants to different groups randomly, minimizing differences between groups and establishing causation.

Control

A technique used in experiments to ensure that the treatment effect can be isolated. It involves keeping all other variables constant except for the treatment being tested.

Replication

The repeated application of an experimental treatment to multiple subjects or trials to ensure consistency and reliability of results.

Confounding

The situation in experiments where the effects of two or more variables are intertwined, making it difficult to determine the individual impact of each variable.

Why do we use random assignment in treatment groups?

Random assignment to treatment groups helps to reduce or eliminate bias in the results of an experiment.

2 Reasons for Controlling as much of the experiment as possible?

Helps prevent confounding and reduces variability in the response variable

Experimental Units/Subjects

The smallest collection of individuals to which treatments are applied.Ex

Explanatory Variable

The variable that is changed to measure a specific response

Normal CDF

Normal Distribution: Bound

Inverse Normal

Given a percentile

MadLib For Association

There is a [strength], [direction], [form], association between [x in context] and [y in context].

MadLib for Slope

For each additional [unit] increase in [x in context], the predicted/expected [increase/decrease] in [y in context] is [slope].

Coefficient of Determination MadLib

[r²%] of the variation in [y in context] is explained by [x in context] in our linear model.

variable: s

standard deviation of the residuals

Influential Points

Data points that significantly affect the slope of the regression line when included or excluded from analysis.

Sample Space

The set of all possible outcomes of a random experiment.

Conditions for a Binomial Setting

• Binary - outcomes can be classified as either “success” or “failure”

• Independent Trials - all trials are independent of one another

• Number of Trials - number of trials is set in advance

• Success Probability - probability of success is the same for each trial

Conditions for a Geometric Setting

• Binary - outcomes can be classified as either “success” or “failure”

• Independent Trials - all trials are independent of one another

• Success Probability - probability of success is the same for each trial

Type I Error

The error made when a true null hypothesis is rejected, also known as a false positive.

Type II Error

The error made when a false null hypothesis is not rejected, also known as a false negative.

Power

The probability of correctly rejecting a false null hypothesis in a statistical test.

Four Step Process for Sampling Distribution Problems

• State: State/define the distribution and values of interest and what we are trying to find

• Plan: Check that the conditions are satisfied, depending on which type of data you are investigating (proportion or mean)

• Do: Perform calculations - AND SHOW WORK

• Conclude: Answer the question/provide a conclusion - IN CONTEXT

4 Ways to Increase Power

• Increase the sample size

• Increase the significance level (alpha)

• Use good sampling techniques that will reduce variability in the data

• Increase the difference between the null and alternative parameter values, making it easier to detect a difference and in turn reject H_0