Stats Exam 1

Statistics

Numbers that summarize whole sets of data.

Data

Observations and measurements collected for analysis.

Statistical Literacy

The ability to understand, evaluate, and use data and statistics.

4 Questions for Evaluating Statistics

Who is the source? How much information is used? Are terms clearly defined? Do reliable sources support the claim?

Ethics

Accepted standards of right and wrong that guide behavior.

Stacking the Deck

Cherry-picking favorable evidence while ignoring contradictory evidence.

Conflict of Interest

Research conclusions influenced by personal or financial interests.

Inappropriate Outcome Data

Using the wrong measure to evaluate an outcome.

HARKing

Hypothesizing After Results Are Known

Population

The entire group a researcher wants to study.

Sample

A smaller group selected from the population.

Representative Sample

A sample that closely resembles the population.

Variable

A characteristic that can have different values.

Independent Variable (IV)

The variable manipulated by the researcher.

Dependent Variable (DV)

The outcome variable that is measured.

Hypothesis

A testable prediction.

Theory

A set of interconnected ideas that explain observations and predict future events.

Random Assignment

Randomly placing participants into groups.

Quasi-Experimental Design

A design where participants cannot be randomly assigned.

Quantitative Data

Numerical data.

Qualitative Data

Nonnumerical data.

Continuous Data

Data measured along a scale and can take many values.

Categorical Data

Data grouped into categories.

Nominal Scale

Categories only; no order.

Ordinal Scale

Data that can be ranked; intervals are not equal.

Interval Scale

Equal intervals between values but no true zero.

Ratio Scale

Equal intervals and a true zero point.

NOIR Measurement Scale Trick

Nominal = Name, Ordinal = Order, Interval = No true zero, Ratio = Real zero.

Descriptive Statistics

Summarize and organize data using graphs and numbers.

Inferential Statistics

Use probability to draw conclusions about populations from samples.

Frequency

Number of times a response occurs.

Relative Frequency

Frequency divided by total participants, expressed as a percentage.

Bar Graph

Used for categorical data

Histogram

Used for continuous data.

Line Graph

Shows the relationship between two continuous variables.

Scatterplot

As one variable decreases, the other increases.

Positive Relationship

As one variable increases, the other increases.

Negative Relationship

As one variable decreases, the other decreases.

No Relationship

No pattern exists between variables.

Violin Plot

A graph showing the distribution of a continuous variable.

Jitter Plot

Shows individual participant scores as dots.

Truncated Y-Axis

A graph where part of the Y-axis is omitted, making differences appear larger.

Normal Distribution

A symmetrical bell-shaped distribution.

Bell Curve

Another name for a normal distribution.

Positively Skewed Distribution

Data pile up on the left with a tail extending right.

Negatively Skewed Distribution

Data pile up on the right with a tail extending left.

Outlier

An extreme score far from the rest of the data.

Measures of Central Tendency

One-number summaries of the center of a dataset.

Mean

The average of a dataset.

Formula for Mean

M = ΣX ÷ n

Median

The middle score when data are arranged from lowest to highest.

Mode

The most common score or category.

Best Measure for Nominal Data

Mode.

Best Measures for Interval or Ratio Data

Mean and Median.

Effect of Outliers on Mean

The mean is pulled toward outliers.

Effect of Outliers on Median

The median is resistant to outliers.

Variability

Describes the spread or distribution of data.

Formula for Range

Largest Value − Smallest Value.

Standard Deviation (SD

The typical distance of scores from the mean.

Variance

The square of the standard deviation.

Relationship Between Variance and SD

Variance = SD²; SD = √Variance.

Small Standard Deviation

Scores are close together.

Large Standard Deviation

Scores are spread apart.

Z Score

The number of standard deviations a score is from the mean.

Formula for Z Score

z = (X − M) ÷ SD

Positive Z Score

Score is above the mean.

Negative Z Score

Score is below the mean.

Magnitude of a Z Score

Larger absolute values are farther from the mean.

Data Transformation

Converting data from one form to another.

Purpose of Z Scores

Provide context and allow comparison across different scales.

Normal Curve

A bell-shaped curve representing a normal distribution.

Key Fact About Normal Curve

The entire area under the curve equals 100%.

Empirical Rule

68%-95%-99.7% rule for normal distributions

Within 1 Standard Deviation

68% of data.

Within 2 Standard Deviations

95% of data.

Within 3 Standard Deviations

99.7% of data.

Percentile

The percentage of scores at or below a given score.

50th Percentile

The median.

Z Table

Used to determine areas and percentages under the normal curve.

Probability

The likelihood of an event occurring.

Equal Likelihood Model

All outcomes have the same probability.

Law of Large Numbers

Expected patterns emerge after many observations.

Absolute Risk

The actual probability an event occurs.

Relative Risk

The probability of an event compared to another group.

Sampling Error

The natural difference between a sample and the population.

Sampling Bias

Systematic error caused by how a sample is selected.

Convenience Sample

A sample selected because it is easy to access.

WEIRD

White, Educated, Industrialized, Rich, Democratic.

Distribution of Sample Means

The distribution formed by all possible sample means of a specific size.

Mu (μ)

Population mean.

Sigma (σ)

Population standard deviation.

Standard Error (SE)

The standard deviation of the distribution of sample means.

Formula for Standard Error

SE = σ ÷ √n

What Happens to SE When Sample Size Increases?

SE decreases.

Central Limit Theorem (CLT)

With large enough samples, distributions of sample means become approximately normal.

Null Hypothesis (H₀)

Predicts no effect, relationship, or difference.

Alternative Hypothesis (Hₐ)

Predicts an effect, relationship, or difference exists

Directional Hypothesis

Predicts the direction of the effect.

Non-Directional Hypothesis

Predicts a difference but not the direction.

Null Hypothesis Significance Testing (NHST)

Process used to determine whether data support a research hypothesis.