Which statistics tool do I need?
Answer two or three questions in plain English and you'll get the right calculator or chart, with the reason why. No statistics knowledge needed.
Quick reference: which tool for which job
Already know what you want to do? Find it in the list.
| If you want to… | For example | Use |
|---|---|---|
| Find the average, median or mode | the typical test score | Mean, median and mode calculator |
| Measure how spread out numbers are | how consistent delivery times are | Standard deviation calculator |
| Find quartiles, the IQR or outliers | the five-number summary of quiz scores | Five-number summary calculator |
| Find the variance | from a list of scores or a frequency table | Variance calculator |
| See where one value stands | is 85 a high score in this class? | Z-score calculator |
| Compare a group with a fixed number | is the average fill really 500 ml? | One-sample t-test |
| Compare two separate groups | class A vs class B | Two-sample t-test |
| Compare before and after | scores before and after tutoring | Paired t-test |
| Compare three or more groups | scores for three teaching methods | ANOVA calculator |
| Measure how strongly two things are related | temperature and ice cream sales | Correlation coefficient calculator |
| Predict one variable from another | exam score from hours studied | Linear regression calculator |
| Find concentrations from a standard curve | protein in a sample from its absorbance | Standard curve calculator |
| Estimate a value with a margin of error | average spend, ± a few dollars | Confidence interval calculator |
| Compare two percentages (A/B test) | 12.0% vs 15.6% conversion | Two-proportion z-test |
| Test a percentage against a claim | is 58 of 100 more than half? | One-proportion z-test |
| Test whether two categories are related | study method by school year | Chi-square test calculator |
| Check whether counts fit what you expected | is this die fair? | Chi-square goodness of fit |
| Plan a survey | how many customers to ask | Sample size calculator |
| Find a probability on a bell curve | the share of people over 6 feet tall | Normal distribution calculator |
| Count combinations or permutations | how many 3-person committees from 10 people | Permutation and combination calculator |
| Find the chance of x successes in n tries | at least 6 right by guessing on 10 questions | Binomial distribution calculator |
| Get a p-value from a test statistic | t = 2.1 with 24 df | P-value calculator |
| Score a customer survey | Net Promoter Score from 0–10 answers | NPS Calculator (Net Promoter Score) |
| Chart amounts by category | sales by region | Bar graph maker |
| Show parts of a whole | how a budget is split | Pie chart maker |
| Show change over time | enrollment by year | Line graph maker |
| Chart the shape of one list of numbers | the spread of exam scores | Histogram maker |
| Compare groups in one chart, with outliers | scores for each class | Box plot maker |
| Chart two variables against each other | hours studied vs score | Scatter plot maker |
Choosing a test to compare groups
Most “which test?” questions are about comparing averages. Ask yourself two things: how many groups are there, and are they made of different people (or things), or the same ones measured twice?
- One group against a fixed number, such as a target or a published average: a one-sample t-test.
- Two separate groups, such as two classes or two versions of a web page: a two-sample t-test.
- The same people measured twice, such as before and after a course: a paired t-test. Using the two-sample test here throws away the pairing and makes real changes harder to detect.
- Three or more groups: a one-way ANOVA, followed by Tukey's comparisons. Plot the groups with a box plot first.
Every test gives a p-value: the chance of seeing a difference at least this big if there were really no difference. Below 0.05 is the usual cutoff for “statistically significant”. Also look at how big the difference is, because with large samples even tiny, unimportant differences can be significant.
Bar graph, histogram, box plot or scatter plot?
- Bar graph: one number per category (sales by region, votes per option).
- Histogram: the shape of one list of measurements, such as whether most scores bunch in the middle or trail off to one side.
- Box plot: compare several groups at once, with outliers marked.
- Scatter plot: two measurements on the same items, to see whether they move together.
All four chart makers take data pasted straight from Excel or Google Sheets and download a clean PNG for reports and slides.
Frequently asked questions
Which statistical test should I use to compare two groups?
If you are comparing averages, use a two-sample t-test for two separate groups, or a paired t-test when the same people or things were measured twice. Welch’s version of the two-sample test is the safe default because it doesn’t assume both groups are equally spread out. The t-test calculator does all three.
What is the difference between a t-test and a z-test?
Both compare averages. A z-test assumes you know the population standard deviation in advance, which is rare outside textbook exercises. A t-test uses the standard deviation of your sample instead, so it is the right choice for almost all real data. With large samples the two give nearly the same answer.
Should I use a bar graph or a histogram?
Which test do I use for three or more groups?
Use a one-way ANOVA, then a post hoc test such as Tukey’s to see which groups differ; the ANOVA calculator does both. Running a t-test for every pair of groups isn’t a good substitute: with three groups you’d run three tests, and the chance of at least one false alarm rises well above 5%. A box plot of the groups shows how they differ.
What is the difference between correlation and a scatter plot?
A scatter plot is the picture: one dot per pair of values. The correlation coefficient is a single number from −1 to 1 that summarizes how closely the dots follow a straight line, and linear regression gives the equation of that line so you can make predictions. Always look at the plot as well, because one outlier or a curved pattern can make the numbers misleading.