Basic Stats for Exercise Science Exam 2

Descriptive Statistics

Numerical and graphical methods used to summarize and describe data, showing how values are similar (central tendency) or different (variance).

Central Tendency

A single value that best represents an entire dataset; describes the 'typical' value of a group.

Variance (Variability)

A measure of how much data values differ from the central tendency; shows the spread of the data.

Dispersion

Another term for variability; how spread out data points are.

Mean

The average value; sum of all data points divided by the number of data points. Used when data are normally distributed.

Median

The middle value when numbers are ordered from smallest to largest; used when data are skewed or have outliers.

Mode

The most frequently occurring value in a dataset; used with categorical or limited-choice data.

Range

The difference between the largest and smallest values in a dataset (max - min).

Standard Deviation (SD)

The average amount that data points differ from the mean; measures spread relative to the mean.

Excel Formula for AverageIF

=AVERAGEIF(C:D,"value",X:Y) (average of values meeting a condition)

Excel Dollar Sign ($)

Locks cells or ranges in formulas so they don't shift when copied.

Outlier

A data point far from the rest of the dataset; can be due to error or natural variation.

Influential Outlier

A real data point that heavily affects mean and standard deviation.

Error

A data point that is impossible or incorrect (e.g., HR = 1000); should be removed.

Transforming Data

Applying equations (like log transformation) to reduce skew and normalize data.

Log Transformation

A common data transformation that 'pulls in' extreme values on one side of a skewed dataset.

Normal Distribution

A bell-shaped curve where most values are near the mean and fewer are extreme; mean = median = mode.

68-95-99.7 Rule

In a normal distribution, 68% of data fall within 1 SD, 95% within 2 SDs, and 99.7% within 3 SDs.

Skewed Distribution

A distribution that is not symmetrical; mean, median, and mode are unequal.

Kurtosis

The sharpness or flatness of a data distribution compared to a normal curve.

Inferential Statistics

Statistical methods that test hypotheses and generalize from samples to populations.

Descriptive vs. Inferential Statistics

Descriptive = summarize; Inferential = test and predict.

Graphical Analysis

Using graphs to visualize data, check distribution, and identify relationships or differences.

Histogram

Graph showing the distribution of a single continuous variable; x-axis = data bins, y-axis = frequency.

Scatterplot

Graph showing relationship between two continuous variables; each point represents one individual.

Line Graph

Graph showing changes or relationships between two continuous variables over time; lines connect means.

Bar Graph

Graph showing differences in a continuous variable between categories; x-axis = categories, y-axis = means.

Box and Whisker Plot

Graph showing median, quartiles, range, and outliers for group comparisons.

Categorical Variable

A variable with distinct groups or categories (e.g., gender, state, treatment type).

Continuous Variable

A variable with numerical values that can be measured on a scale (e.g., height, weight, time).

Descriptive Table

A table summarizing data using measures like mean, median, SD, and range.

Error Bars

Lines on a graph representing variability (often 1 standard deviation from the mean).

Normal Data

Data that follow a bell-shaped pattern with symmetrical variance.

Non-Normal Data

Data that are skewed, have outliers, or do not follow the bell curve.

Graph Axis Labels

x-axis = independent variable, y-axis = dependent variable; both must be labeled clearly.

Individual-Level Data

Data that shows each participant's results separately.

Group-Level Data

Data summarized by averaging individuals within groups.

Clinically Significant

A change that is large enough to have practical or medical importance.

Statistically Significant

A change or difference unlikely to have occurred by chance.

Correlation

A relationship between two continuous variables; visualized with a scatterplot or line graph.

Variance vs. Central Tendency

Variance = differences; Central Tendency = similarities.

Descriptive Summary Example

"M = 35 ± 10" means the mean is 35 and SD is 10.

Normality Assumption

Many inferential tests require normal data distributions for results to be valid.

Bias

A systematic error that skews results away from the truth.

Outlier Rule Example

Discard if greater than 3 standard deviations from the next closest data point.

Anchor ($) in Excel

Keeps a row, column, or both fixed when copying a formula.

Sample

A smaller group used to represent a larger population.

Population

The entire group that the researcher wants to study or draw conclusions about.

Descriptive Formula Shortcut in Excel

=AVERAGE, =STDEV.S, =MIN, =MAX, =COUNT, =AVERAGEIF.

Graph Choice Rule

Type of variable → Type of graph → Type of statistic.

Normal Curve Peak

Represents the most common (mean) values; tails represent rarer values.

Variance and Sample Size

Smaller samples underestimate variability, weakening statistical power.

Data Cleaning

Reviewing data for errors or outliers before calculating descriptive statistics.