Descriptive Statistics vs Inferential Statistics
Descriptive statistics help us to summarize and understand the data we have, inferential statistics help us to make predictions and inferences about larger populations based on that data.
Descriptive statistics primarily describe, summarize, and present data in a meaningful way. They provide a snapshot or summary of the data. This could include measures of central tendency like the mean, median, and mode, or measures of dispersion or variation like range, variance, and standard deviation. Graphical representations like pie charts, histograms, and box plots are also part of descriptive statistics. Descriptive statistics does not draw conclusions or make predictions beyond the data at hand.
Example: In a class of 30 students, the average score on a math exam might be 80% with a standard deviation of 5%.
Inferential statistics go a step further. Using the data gathered from a small group (a sample), they infer and make predictions about the larger group (the population). Inferential statistics involve hypothesis testing, correlations, regressions, confidence intervals, chi-square tests, t-tests, ANOVA (Analysis of Variance), etc.
Inferential statistics allows us to take risks and make educated guesses. It helps us to decide whether an observed result is due to chance or whether there are other factors at play.
Example: From a sample of 100 voters, we might infer that a particular candidate will win the election in a city of 1 million voters.
Difference between Descriptive Statistics and Inferential Statistics
|Descriptive Statistics||Inferential Statistics|
|Purpose||Summarizes and organizes data so it can be easily understood.||Makes predictions or inferences about a population based on observations and analyses of a sample of that population.|
|Methods||Measures of central tendency (mean, median, mode), measures of dispersion (range, variance, standard deviation), frequency distributions, and graphical representations.||Hypothesis testing, regression analysis, ANOVA, chi-square tests, t-tests, confidence intervals, etc.|
|Use of Data||Used to describe the data that are directly available from observations.||Uses sample data to make estimates, decisions, predictions, or other generalizations about a larger, unseen set of data (the population).|
|Scope||Provides a snapshot of the data at hand.||Makes educated guesses about the larger population based on a sample.|
|Conclusion||Does not draw conclusions beyond what is observed.||Uses statistical tests to determine whether a hypothesis is likely to be true.|
|Example||The average score of a class on a math test is 85%.||From a sample of students, we might infer that the average score for all students in the school district is between 80% and 90%.|