basic stats for ex sci - rutgers

Statistics

An applied quantitative field that collects, describes, analyzes, and interprets data to reach valid conclusions about larger groups. Not about absolute truth, but estimating the likelihood findings are true.

Purpose of Statistics

Organized way to answer questions and test whether results are valid and reliable vs. due to chance.

Descriptive Statistics

Summarizes and describes data (e.g., averages, graphs, variance).

Inferential Statistics

Analyzes data to make generalizations from a sample to a population (e.g., t-tests, ANOVA, regression).

Good Question

Simple, specific, and sufficient to capture the entire construct.

Construct

Structured representation of an idea that can be measured (e.g., "exercise amount").

Item

A smaller piece of a construct, often used as a survey or measurement question (e.g., times per week, length, intensity).

Variable

Measurable item of data (categorical or continuous) that allows statistical testing.

Qualitative Data

Descriptive, non-numerical data (e.g., survey responses, favorite color).

Categorical Data

Groups or categories.

Nominal

No order (eye color).

Ordinal

Ordered (class rank, pain scale).

Binary

Only two options (yes/no).

Quantitative Data

Numerical, measurable data.

Discrete

Countable (courses taken).

Continuous

Measurable range (weight, VO₂max).

Cross-Sectional Study

Snapshot at one point in time; easier, but limited in studying change.

Longitudinal Study

Measures repeated over time; strong but resource-intensive.

Retrospective Study

Uses past/existing data; less reliable due to recall or record bias.

Prospective Study

Collects data forward in time; most reliable but more expensive.

Observational Protocol

Researcher only observes; no manipulation.

Experimental Protocol

Researcher actively manipulates variables; requires control or placebo group.

Objective Data

Collected by equipment or measurement (e.g., ECG, weight, HR).

Subjective Data

Self-reported information (e.g., stress surveys, happiness rating).

Validity

Relevance: Are you measuring what you think you're measuring?

Reliability

Consistency: Does the same input give the same output across time, raters, or versions?

Internal Validity

Whether results are "real" or due to errors, confounds, or poor design.

External Validity

Generalizability: whether findings apply to other populations/settings.

Face Validity

On the surface, measure seems appropriate (e.g., "perceived exertion scale" for exercise).

Content Validity

Measure covers all aspects of the construct (e.g., sleep diary + EEG + actigraph).

Convergent Validity

Different tools measuring the same construct agree (e.g., Apple Watch HR ≈ ECG).

Discriminant Validity

Tool measures only the intended construct, not something else (e.g., stress ≠ anxiety).

Correlation

Statistical test showing whether two continuous variables are related.

Correlation Coefficient (r)

Number from -1 to +1 showing strength and direction of relationship. Closer to ±1 = stronger; closer to 0 = weaker.

Test-Retest Reliability

Checking if the same test gives consistent results over time.

Inter-Rater Reliability

Consistency between different observers/researchers measuring the same thing.

Intra-Rater Reliability

Consistency when the same researcher measures multiple times.

Parallel Forms Reliability

Two different but equivalent versions of a test give consistent results.

Internal Consistency

Different survey questions that should measure the same idea give consistent responses.

Bias

Systematic error that distorts results (bad questions, poor equipment, flawed sampling).

Noise (Random Error)

Random variation in data that doesn't systematically bias results.

Data Cleaning

Process of correcting/removing errors to make raw data usable for analysis.

Missing Data

When values are absent; acceptable if random, but systematic missingness introduces bias.

Garbage In → Garbage Out

Bad data leads to meaningless statistical results.

VO₂max

Gold standard measure of cardiorespiratory fitness; maximal oxygen consumption during graded exercise.

Excel in Statistics

Used to organize, clean, and analyze data (correlations, graphs).

Sample

smaller group actually measured

Hypothesis Testing

Process of testing whether observed differences/patterns are likely real vs. chance.

Confounding Variable

Unmeasured factor that could explain observed results (e.g., smoking affecting HR differences).

Population

larger group you want to generalize to