Descriptive statistics and distribution analysis
Summary statistics, histograms, box plots, Q-Q plots, normality tests, one-sample hypothesis tests, and frequency analysis — the starting point of every analysis.
Understand your data before you model it
Every analysis starts here. What does the distribution look like? Is it symmetric or skewed? Are there outliers pulling the mean away from the median? Is it normal enough for a parametric test, or should you use a non-parametric alternative? The answers determine which test or model is appropriate — and skipping this step is how wrong conclusions happen.
Descriptive statistics, distribution plots, normality assessment, and one-sample tests belong in the same workflow — not scattered across separate tools. Characterise a continuous variable from summary statistics through to a formal normality test and a one-sample hypothesis test, or describe a discrete variable with frequency tables, bar plots, and proportion tests. Both continuous and discrete analysis in one place.
I use Excel to analyze, validate, and sumarize volumes of data every day. Since Analyse-It is always right there on my Excel ribbon, I go to it regularly. I am not a professional statistician, but Analyse-It gives me all of the tools in an easy to use package that lets me focus on understanding my data.
Shawn W.
Analyst
What’s included
Summarise location, spread, and shape in one output
Mean, median, SD, CV%, skewness, kurtosis, quantiles, geometric and harmonic mean — all the measures you need to characterise a variable, reported together. See immediately whether the distribution is symmetric, how spread out it is, and whether the tails are heavier or lighter than normal.
See the distribution, not just the numbers
A histogram shows the shape. A Q-Q plot shows departures from normality. A box plot shows the median, quartiles, and outliers. A CDF plot shows the cumulative distribution with Kolmogorov-Smirnov confidence bands. Dot plots show every observation. Each plot answers a different question — use whichever combination the data requires.
Assess normality before choosing a test
The Q-Q plot with Lilliefors confidence band shows visually whether the data depart from normality. Shapiro-Wilk, Anderson-Darling, and Kolmogorov-Smirnov provide formal tests. If the distribution isn’t normal, transform the variable directly and reassess — or switch to a non-parametric test.
Test a single sample against a hypothesised value
Does the mean differ from a target? One-sample t-test when normality holds, Wilcoxon or Sign test when it doesn’t. Mean and median estimates with confidence intervals. Hodges-Lehmann pseudo-median with Tukey CI for a robust location estimate. χ² test and CI for variance when dispersion is the question.
Describe and test categorical data
Frequency tables with cumulative and relative frequencies. Bar plots with cumulative frequency overlay. Binomial exact and Score Z tests for a single proportion. Pearson χ² and likelihood ratio G² tests for multinomial proportions — test whether the observed distribution matches a hypothesised one. Proportion with Clopper-Pearson exact or Wilson score CI.
Example analyses
See descriptive statistics and distribution analysis in detail — summary statistics, histograms, Q-Q plots, normality tests, and one-sample tests.
Continuous distribution
Newcomb’s speed of light, 64 observations.
Descriptive statistics, histogram with normal overlay, box plot, CDF plot, Q-Q plot with Lilliefors band, Shapiro-Wilk normality test, and one-sample t-test.
Discrete distribution
Hair–eye colour frequencies, 592 observations.
Frequency table, bar plot with cumulative frequency, pie chart, and Pearson χ² test of multinomial proportions.
Validated, reliable, trusted for over 30 years
NIST-validated calculations
Every statistic tested against NIST Standard Reference Datasets, published datasets and thousands of internal test-cases. No reliance on Excel's shaky built-in functions. See how we
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Data stays on your PC
No cloud processing, no uploads, no third-party access. Your data never leaves your computer — essential when working with sensitive, confidential, or patient-identifiable data.
Standard Excel workbooks
Analyses are ordinary Excel workbooks that you can share with colleagues, archive for audit, and open on any machine with Excel — no Analyse-it licence required.
No formulas to break
Results contain no formulas, so they can't be accidentally edited or corrupted. The results you reported will be exactly what you find when you reopen the workbook.
Technical details
Continuous descriptive statistics
- Sum, Mean, Variance, SD, CV%, Skewness, Kurtosis
- Geometric Mean, Harmonic Mean new in v4.50
- Median, Minimum, Maximum, Range, IQR
- Quantiles
- Mode
- Transform variable new in v5.50
Normality tests
- Shapiro-Wilk test
- Anderson-Darling test
- Kolmogorov-Smirnov test
Plots
- Histogram with optional normal overlay
- Frequency polygon
- Dot plot — jittered, aligned, spread; vary symbol/colour
- Skeletal box plot, Tukey outlier box plot, Quantile box plot
- Mean error bar plot, Mean confidence diamond plot
- CDF plot with optional Kolmogorov-Smirnov confidence band
- Normal Q-Q plot with optional Lilliefors confidence band
One-sample location tests
- Z test for mean with known population SD
- Student’s one-sample t-test for mean
- Wilcoxon test for mean/median
- Sign test for median
Location estimators
- Mean with t-based or Z-based CI
- Median with Thompson-Savur CI
- Hodges-Lehmann pseudo-median with Tukey CI
Dispersion tests & estimators
- χ² test for variance
- Variance with χ²-based CI
Discrete
- Frequency table (frequency, cumulative, relative, cumulative relative)
- Frequency bar plot with optional cumulative line
- Frequency pie (whole-to-part) plot
- Binomial exact test for proportions
- Score Z test for binomial proportions
- Pearson χ² and G² test for multinomial proportions
- Proportion with Clopper-Pearson exact or Wilson score CI
