Descriptive Statistics

Purpose:

Descriptive statistics summarize and describe the basic features of a dataset. Unlike inferential statistics, they do not test hypotheses, but instead they describe what the data look like.

Key Terms:

Central Tendency

  • Mean: The arithmetic average. Sensitive to outliers.
  • Median: The middle value when data are ordered. More robust to outliers than the mean.
  • Mode: The most frequently occurring value. A dataset can have more than one mode.

Variability

  • Range: The difference between the highest and lowest values. A small range indicates data are tightly clustered; a large range indicates greater spread.
  • Standard Deviation (SD): The average distance of each score from the mean. A small SD means scores cluster near the mean; a large SD means scores are spread out.
  • Variance: The square of the standard deviation. Less intuitive to interpret on its own, but used in many statistical formulas.

Jamovi Walkthrough:

  1. Click "Exploration"
  2. Click "Descriptives"
  3. Move the variable(s) of interest into the "Variables" box
  4. Under "Statistics," check: Mean, Median, Mode, Std. deviation, Variance, Range, Minimum, Maximum
  5. Under "Plots," check "Histogram" to visualize the distribution

R Walkthrough:

describe(df)   # psych package: mean, sd, median, min, max, range, skew, kurtosis
summary(df)    # base R: min, Q1, median, mean, Q3, max

mean(df$variable, na.rm = TRUE)
median(df$variable, na.rm = TRUE)
sd(df$variable, na.rm = TRUE)
range(df$variable, na.rm = TRUE)
var(df$variable, na.rm = TRUE)

Output Interpretation:

Mean: The average score. Sensitive to extreme values (outliers).

Median: The middle value. Use alongside or instead of the mean when data are skewed.

SD: How spread out scores are around the mean. Smaller SD = scores clustered near mean. Larger SD = scores spread out.

Range: The span of the data. Smaller range = data are more tightly clustered. Larger range = data are more widely spread.

Variance: SD squared. Harder to interpret directly; used in other statistical calculations.

APA Format:

Descriptive statistics are typically reported in text as M and SD in parentheses after the group name.

Participants reported moderate levels of perceived stress (M = 18.42, SD = 4.67).

For tables, see: APA sample tables

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