Stats Vocab

Individual

Objects described by a set of data (people, animals, things, etc.)

Variable

Any characteristic of an individual; can take different values.

Categorical variable

Places an individual into a group or category.

Quantitative variable

Takes numerical values for which arithmetic operations make sense.

Distribution

Tells what values a variable takes and how often.

Frequency table

Displays counts for each category.

Relative frequency table

Displays proportions or percentages for each category.

Two-way table

Describes two categorical variables.

Marginal distribution

Distribution of one variable among all individuals.

Conditional distribution

Distribution of one variable given a specific value of another variable.

Association

When knowing one variable helps predict another.

Dotplot

Graph showing each data value as a dot above a number line.

Stemplot

Displays data to show shape and distribution while retaining actual values.

Histogram

Displays distribution of a quantitative variable using bars.

Shape

Describes symmetry, skewness, peaks, and gaps.

Center

Describes typical value (mean, median).

Spread

Describes variability (range, IQR, standard deviation).

Outlier

Value that falls outside the overall pattern.

Resistant measure

Statistic not strongly affected by extreme values (median, IQR).

Density curve

Curve above the horizontal axis with area 1; shows distribution.

Median of a density curve

Divides area into two equal halves.

Mean of a density curve

Balance point of the curve.

Normal distribution

Symmetric, bell-shaped curve defined by mean (μ) and SD (σ).

68–95–99.7 Rule

Describes data within 1, 2, and 3 SDs of the mean.

Standard normal distribution

Normal distribution with mean 0 and SD 1.

z-score

Standardized value showing distance from mean in SDs: z = (x−μ)/σ.

Normal probability plot

Graph to assess Normality of data.

Scatterplot

Graph showing relationship between two quantitative variables.

Explanatory variable

Helps explain or predict changes in the response variable.

Response variable

Measures the outcome of a study.

Form

Overall pattern (linear, curved).

Direction

Indicates positive or negative association.

Strength

Describes how closely points follow a pattern.

Correlation (r)

Measures direction and strength of linear relationship.

Least-squares regression line (LSRL)

Line minimizing squared residuals: ŷ = a + bx.

Slope (b)

Change in predicted y for each 1-unit increase in x.

y-intercept (a)

Predicted value when x = 0.

Residual

Observed − predicted value (y − ŷ).

Coefficient of determination (r²)

Proportion of variation in y explained by x.

Residual plot

Graph of residuals versus x; checks fit of regression.

Influential point

Point that greatly changes correlation or slope if removed.

Population

Entire group we want to study or describe.

Sample

Subset of individuals from the population.

Census

Collects data from every individual in the population.

Sample survey

Collects data from a sample to generalize to the population.

Bias

Systematic error producing unrepresentative samples.

Voluntary response sample

People choose to participate; often biased.

Convenience sample

Chooses individuals easiest to reach; biased

Simple random sample (SRS)

Every group of n individuals has equal chance of selection.

Stratified random sample

Divides population into strata; SRS taken from each.

Cluster sample

Divides population into clusters; randomly selects clusters.

Undercoverage

Some groups left out of the sampling frame.

Nonresponse

Selected individuals can’t be contacted or refuse participation.

Response bias

Pattern of inaccurate answers due to wording or interviewer.

Observational study

Observes individuals without imposing treatment.

Experiment

Deliberately imposes treatment to measure response.

Explanatory variable (factor)

Variable manipulated in an experiment

Treatment

Specific condition applied to subjects.

Experimental units (subjects)

Individuals on which experiment is done.

Control group

Used for comparison; may receive placebo.

Random assignment

Uses chance to assign treatments; balances variables.

Replication

Using enough subjects to reduce chance variation.

Double-blind experiment

Neither subjects nor those interacting know treatments.

Statistically significant

Effect too large to be due to chance

Block design

Subjects grouped by similarity; treatments assigned within blocks

Matched pairs design

Compares two treatments using similar or same subjects.

Standard Deviation

The context typically varies by SD from the mean of mean.

Percentile:

percentile % of context are less than or equal to value.

z-score:

Specific value with context is z-score standard deviations above/below the mean.

Describe a distribution:

Be sure to address shape, center, variability, and outliers (in context).

Correlation (r):

The linear association between x-context and y-context is weak/moderate/strong

(strength) and positive/negative (direction).

Residual:

The actual y-context was residual above/below the predicted value when x-context = #.

y-intercept:

The predicted y-context when x = 0 context is y-intercept.

Slope:

The predicted y-context increases/decreases by slope for each additional x-context.

Standard Deviation of Residuals (s):

The actual y-context is typically about s away from the value

predicted by the LSRL.

Coefficient of Determination (r2):

About r2% of the variation in y-context can be explained by the

linear relationship with x-context.

Describe the relationship:

Be sure to address strength, direction, form and unusual features (in context).

Probability P(A):

After many many context, the proportion of times that context A will occur is about P(A).

Conditional Probability P(A|B):

Given context B, there is a P(A|B) probability of context A.

Expected Value (Mean, μ):

If the random process of context is repeated for a very large number of, the average number of x-context we can expect is expected value. (decimals OK).

Binomial Mean (μX):

After many, many trials the average # of success context out of n is μ#.

Binomial Standard Deviation (σX):

The number of success context out of n typically varies by σ#

from the mean of μ#.

Standard Deviation of Sample Proportions (σp%):

The sample proportion of success context typically varies by σ&' from the true proportion of p.

The sample proportion of success context typically varies by σ&' from the true proportion of p.

The sample mean amount of x-context typically varies

by σ*̅from the true mean of μ#.

Confidence Interval (A, B):

We are % confident that the interval from A to B captures the true

parameter context.

Confidence Level:

If we take many, many samples of the same size and calculate a confidence interval for each, about confidence level % of them will capture the true parameter in context

p-value:

Assuming H0 in context (H0), there is a p-value probability of getting the observed result

or less/greater/more extreme, purely by chance.

Conclusion for a Significance Test:

Because p-value p-value < / > α we reject / fail to reject H0. We

do / do not have convincing evidence for Ha in context.

Type 1 Error:

The H0 context is true, but we find convincing evidence for Ha context.

Type II Error:

The Ha context is true, but we don’t find convincing evidence for Ha context.

Power:

If Ha context is true at a specific value there is a power probability the significance test will

correctly reject H-.

Standard Error of the Slope (SEb):

The slope of the sample LSRL for x-context and y-context

typically varies from the slope of the population LSRL by about SE2.