Descriptive and Inferential Statistics: Key Concepts and Measures

Small standard deviation

The data points are close to the mean.

Descriptive statistics

To summarize and describe data sets so they're easier to understand.

Measures of central tendency

Mode, median, and mean.

Mode

The most frequently occurring value in a data set.

Median

The middle value when all data points are ordered from high to low.

Bar graph usage

For categorical data (e.g., comparing two groups like "No Pesticide" vs "Pesticide").

Line graph usage

For continuous data (e.g., showing changes over time).

Overlap in error bars

The groups are likely not significantly different.

p-value

The probability that your results happened by random chance.

When to use the mode

When you want to know the most common value in a data set.

High p-value

The difference is probably due to random variation.

Mean

The mathematical average, found by adding all values and dividing by the total number.

Measure of central tendency affected by outliers

The mean.

Measure of central tendency least affected by outliers

The median.

When to use the median

When your data has extreme values or outliers.

Range of a data set

The difference between the highest and lowest values.

Variance

A measure of how far each data point is from the mean (in squared units).

Standard deviation (SD)

The average distance of data points from the mean.

Mean and standard deviation notation

Mean (±SD), for example: 79.8 (±10.8).

Large standard deviation

The data points are very spread out from the mean.

Percent of data within one standard deviation

68%.

Percent of data within two standard deviations

95%.

Percent of data within three standard deviations

99%.

Components of a table

A number (Table 1), a descriptive title, labeled columns/rows, and units.

Scatter plot usage

To show the relationship between two continuous variables.

Error bars on a graph

The standard deviation (spread) of the data.

Little or no overlap in error bars

The groups are likely significantly different.

Inferential statistics

To make conclusions or inferences about populations from sample data.

Null hypothesis (Ho)

The statement that there is no difference between groups or treatments.

Rejecting the null hypothesis

When your results are unlikely due to random chance (p ≤ 0.05).

Failing to reject the null hypothesis

When your results could reasonably be due to chance (p > 0.05).

Rule for statistical significance

If p ≤ 0.05, the result is statistically significant.

p = 0.01

There is a 1% chance the result is due to randomness → reject Ho.

p = 0.56

There's a 56% chance the result is random → do not reject Ho.

t-test usage

To compare the means of two groups to see if they are significantly different.

t-test comparison

The difference between group means relative to the variability in the data.

Low p-value

The difference between groups is real and not likely due to chance.

Assumptions of a t-test

(1) Equal variances between groups, (2) Normally distributed data.

Difference between descriptive and inferential statistics

Descriptive = summarize what happened; Inferential = test if differences are real or random.

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