Descriptive Statistics & Normality Calculator with APA 7 Results
Paste your variables and get the APA descriptives table (M, SD, 95% CI, median, min, max), skewness and kurtosis with z-values, the Shapiro–Wilk and Kolmogorov–Smirnov tests, a histogram per variable, and two results sentences written in APA 7 style.
Paste one or more columns from Excel or SPSS. A first row with names becomes the variable labels. Or type one value per line for a single variable.
How to use this calculator
1. Paste your columns. Copy one or more columns from Excel or SPSS Data View. If the first row holds the variable names, they are picked up as labels. You can also type one value per line for a single variable.
2. Check the names. The labels appear in both tables and both APA sentences, so make them match your thesis.
3. Read the descriptives table. Mean with its 95% confidence interval, median, mode, SD, SE, range and quartiles, computed the way SPSS Descriptives and Explore report them.
4. Read the normality table. Skewness and kurtosis with their standard errors and z-values, Shapiro–Wilk W and p, Kolmogorov–Smirnov D with the Lilliefors correction, and a verdict that follows the rule most supervisors apply.
5. Copy the two APA sentences. One describes the variables, the other reports normality. They open the results chapter. The full chapter, every hypothesis with tables, is what the Chapter 4 Interpreter writes from your SPSS output.
What the descriptive statistics are
The mean (M) is the arithmetic average; its 95% confidence interval is M ± tcrit × SE, the range in which the population mean is likely to sit. The median (Mdn) is the middle value and the mode the most frequent one. The standard deviation (SD) is the typical distance of a score from the mean, computed with n − 1 as SPSS does; the standard error (SE) is SD/√n. Quartiles use SPSS’s default weighted-average definition, so Q1, Mdn and Q3 match the Explore output.
APA 7 reports M and SD to two decimals, with n, and adds the range or the median when the distribution is skewed. A descriptives table is the first table of most results chapters; the calculator’s first table has the columns it needs.
Skewness, kurtosis and their z-values
Skewness measures asymmetry: positive when the tail stretches to the right (income, reaction times), negative when it stretches left (ceiling effects, easy tests). Kurtosis measures how heavy the tails are relative to a normal curve; SPSS and this calculator report excess kurtosis, where 0 is normal. Both use the bias-corrected G1 and G2 formulas that SPSS prints.
Dividing each by its standard error gives a z-value. |z| < 1.96 is the usual limit for samples under 300, |z| < 3.29 for larger ones (Kim, 2013). Many methodologists also accept skewness between −2 and +2 and kurtosis between −7 and +7 as tolerable for a t-test or ANOVA (West, Finch & Curran, 1995). The calculator marks z-values beyond 1.96 in bold.
Shapiro–Wilk and Kolmogorov–Smirnov
The Shapiro–Wilk test compares the ordered data with the values expected under a normal distribution; W close to 1 with p ≥ .05 means no significant departure. It is the most powerful of the common normality tests and the one SPSS Explore reports. The calculator uses Royston’s 1995 algorithm, the same as SPSS, R and scipy, valid for 3 to 5,000 values.
The Kolmogorov–Smirnov test measures the largest distance D between the empirical and the normal cumulative distribution. When the mean and SD are estimated from the data, as here, the ordinary K–S p-value is wrong; SPSS applies the Lilliefors correction, and so does this calculator, using the Dallal–Wilkinson approximation.
Both tests reject trivial departures in large samples. With n ≥ 50 the calculator’s verdict therefore follows the z-values, and with n < 50 it follows Shapiro–Wilk; the sentence reports both so the reader can judge. Look at the histogram too: a bell that is slightly off is fine, a second hump or a long tail is not.
How to report descriptives and normality in APA 7
Descriptives: “Job satisfaction ranged from 3.20 to 4.70 (M = 3.97, SD = 0.38, n = 30).” Normality: “Job satisfaction did not deviate significantly from normality, Shapiro–Wilk W(30) = .978, p = .771 (z-skewness = −0.19, z-kurtosis = −0.61).” Put every variable in one APA table, name the test, and say what you did when a variable failed: a transformation, a non-parametric test, or nothing because the sample was large. The calculator writes both sentences; rename the variables so they read like your study.
A results chapter opens with exactly this. See a real descriptive section and a real assumption section in the Chapter 4 Interpreter demo.
Frequently asked questions
Shapiro–Wilk says p < .05 but my histogram looks fine. Which do I trust?
With more than about 50 values, Shapiro–Wilk detects departures too small to matter for a t-test or ANOVA. Report the test, then rely on the z-values and the histogram, and say so. That is what the calculator’s verdict does.
Which normality test should I report?
Shapiro–Wilk, unless your department asks for Kolmogorov–Smirnov. If you report K–S, say it is with the Lilliefors correction, because the uncorrected version is not valid when the mean and SD come from the sample.
My variable is a Likert total. Does normality even apply?
Scale totals from several items behave close enough to continuous scores that the checks above apply. A single Likert item does not; describe it with frequencies and a median instead.
Do these numbers match SPSS?
Yes: mean, SD, SE, skewness, kurtosis and their standard errors match Descriptives; quartiles match Explore’s default; Shapiro–Wilk and the Lilliefors-corrected K–S match the Tests of Normality table. All values are checked against scipy and statsmodels.