Statistics made easy
8th revised edition (March 2026) - many illustrative examples - only €8.99
User Manual
Here you can download the numiqo user manual as a PDF file.
Download User ManualFAQ
How do I calculate a t-test?
Click Hypothesis tests. Select a metric variable and a nominal variable with two categories.
How do I calculate a one-sample t-test?
Click Hypothesis tests. Select one metric variable and enter the test value. The test value is the value you want to compare the sample mean against.
How do I calculate an independent-samples t-test?
Click Hypothesis tests. Select two metric variables and choose the option "t-test independent samples" under "Calculate". Alternatively, select one metric variable and one nominal variable with two categories.
How do I calculate a paired-samples t-test?
Click Hypothesis tests. Select two metric variables whose values belong together pairwise. Choose the option "t-test dependent samples" under "Calculate".
How do I calculate an equivalence test or TOST test?
Click Equivalence and non-inferiority. Copy your data into the upper table, choose the relevant variables, select equivalence testing, and specify the lower and upper equivalence bounds.
How do I calculate a non-inferiority test?
Click Equivalence and non-inferiority. Copy your data into the upper table, choose the relevant variables, select non-inferiority testing, and specify the non-inferiority margin.
How do I calculate an ANOVA?
Click Hypothesis tests. Select the matching metric and categorical variables. Then select the displayed ANOVA.
How do I calculate a one-way ANOVA?
Click Hypothesis tests. Select one metric variable and one categorical variable with more than two categories.
How do I calculate a two-way ANOVA without repeated measures?
Click Hypothesis tests. Select one metric variable and two categorical variables.
How do I calculate a two-way ANOVA with repeated measures?
Click Hypothesis tests. Select more than two metric variables and one additional independent variable.
How do I calculate a three-way ANOVA?
Click Hypothesis tests. Select three nominal variables and one metric variable.
How do I calculate a Mann-Whitney U test?
Click Hypothesis tests. Select an ordinal or metric variable and a nominal variable with two categories. Then select "Nonparametric test".
How do I calculate a Wilcoxon test?
Click Hypothesis tests. Select two metric variables. Then select "Nonparametric test" and then "Wilcoxon test". Alternatively, you can select two ordinal variables.
How do I calculate a Kruskal-Wallis test?
Click Hypothesis tests. Select a metric or ordinal variable and a nominal variable with more than two categories. Then select "Nonparametric test".
How do I calculate a Friedman test?
Click Hypothesis tests. Select more than two metric variables and then select "Nonparametric test". Alternatively, you can select more than two ordinal variables.
How do I calculate a binomial test?
Click Hypothesis tests. Select a categorical variable with two categories. Then enter the success probability.
How do I calculate a chi-square test?
Click Hypothesis tests. Select two nominal variables. For a chi-square goodness-of-fit test, select one categorical variable.
How do I calculate a correlation?
Click Correlation. Select two or more matching variables.
How do I calculate a Pearson correlation?
Click Correlation. Select two or more metric variables.
How do I calculate a Spearman rank correlation?
Click Correlation. Select two ordinal or metric variables. If you select two metric variables, then click "Spearman correlation".
How do I calculate a regression?
Click Regression. Copy your data into the upper table. Then select the dependent variable and one or more independent variables.
How do I calculate a linear regression?
Click Regression. Copy your data into the upper table. Then select one metric dependent variable and one or more independent variables.
How do I calculate a logistic regression?
Click Regression. Copy your data into the upper table. Then select one categorical dependent variable and one or more independent variables.
How do I calculate an ANCOVA?
Click ANCOVA. Copy your data into the upper table. Then select your dependent variable as well as one or more factors and covariates.
How do I calculate a Kaplan-Meier survival analysis?
Click Survival Analysis. Copy your data into the upper table. Then select the time variable, the event/status variable that indicates whether the event occurred or was censored, and optionally a factor variable for the groups you want to compare.
How do I calculate a log-rank test?
Click Survival Analysis. Copy your data into the upper table. Then select the time variable, the event/status variable that indicates whether the event occurred or was censored, and the factor variable that contains the groups you want to compare.
How do I calculate a Cox regression?
Click Survival Analysis. Copy your data into the upper table. Then select the time variable, the event/status variable that indicates whether the event occurred or was censored, and one or more predictor variables for the Cox regression.
How do I calculate a competing risks analysis?
Click Competing Risks Analysis. Copy your data into the upper table. Select the time variable and a status variable coded 0 for censored, 1 for the event of interest, and 2 for the competing event. Optionally select a group for Gray's test or predictors for Fine-Gray regression.
How do I calculate an exploratory factor analysis?
Click EFA/PCA. Copy your data into the upper table. Then choose "Exploratory Factor Analysis". Select the variables you want to analyze and choose the number of factors.
How do I calculate a principal component analysis?
Click EFA/PCA. Copy your data into the upper table. Then choose "Principal Component Analysis". Select the variables you want to analyze and choose the number of components.
How do I calculate a reliability analysis?
Click Reliability. Copy your data into the upper table. Then select the variables you want to analyze. Depending on which variables you select, different reliability analyses are calculated.
How do I calculate Cronbach's alpha?
Click Reliability. Copy your data into the upper table. Then select the variables you want to analyze. You need to choose at least three metric variables. Then choose "Cronbach's alpha".
How do I calculate the intra-class correlation?
Click Reliability. Copy your data into the upper table. Then select the variables you want to analyze. You need to choose at least three metric variables. Then choose "Intra-Class-Correlation".
How do I calculate Cohen's kappa?
Click Reliability. Copy your data into the upper table. Then select two nominal variables to get the results.
How do I calculate Fleiss' kappa?
Click Reliability. Copy your data into the upper table. To calculate Fleiss' kappa, select more than two nominal variables that have the same number of values.
How do I calculate Kendall's tau?
Click Reliability. Copy your data into the upper table. Then select two ordinal variables.
How do I calculate Kendall's W?
Click Reliability. Copy your data into the upper table. Then select more than two ordinal variables.
How do I calculate a cluster analysis?
Click Cluster. Copy your data into the upper table. Then choose a clustering method and select more than one variable. Finally, you can select the number of clusters.
How do I calculate a k-means cluster analysis?
Click Cluster. Copy your data into the upper table. Then choose the clustering method "k-Means Cluster". Select more than one variable. Finally, you can select the number of clusters.
How do I calculate a hierarchical cluster analysis?
Click Cluster. Copy your data into the upper table. Then choose the clustering method "Hierarchical Clustering". Select the linkage method (Single, Complete, or Average linkage). Finally, select how the distance is calculated (Euclidean, Manhattan, or Maximum). You can also choose the number of clusters.
How do I calculate a DBSCAN cluster analysis?
Click Cluster. Copy your data into the upper table. Then choose the clustering method "DBSCAN". Select the variables you want to analyze. Finally, select how the distance is calculated (Euclidean or Manhattan) and whether you want to standardize your data.
How do I calculate measurement system analysis (MSA)?
Click Measurement Systems Analysis. Copy your data into the upper table. Depending on which variables you select (measurement, parts, operator), different measurement system analyses will be performed.
How do I calculate process capability?
Click Process Capability. Copy your data into the upper table. Then select your variables.
How do I calculate statistical process control?
Click Statistical Process Control. Copy your data into the upper table. Then choose whether your data is discrete or continuous and select the type of SPC analysis you need. Finally, choose your measurements, subgroups, and stages.
How do I perform a design of experiments (DOE)?
Click DoE. Copy your data into the upper table. Then choose which type of design you need. You can create the following designs: 2-level factorial design, full factorial design, fractional factorial design, Plackett-Burman design, Box-Behnken design, central composite design, and mixture design.
How do I run a Monte Carlo simulation?
Click Monte Carlo. Define the uncertain input variables with probability distributions, or fit a distribution to one of your data variables. Enter one or more output equations (later outputs can reuse earlier ones), optionally add specification limits, and then run the simulation to get percentiles, PPM, Ppk, a histogram, and a sensitivity analysis.
How do I calculate a ROC curve?
Click ROC. Copy your data into the upper table, select an actual outcome and one or more test values or scores, and choose the positive outcome. State whether high or low scores indicate that outcome. numiqo reports valid and excluded observations, the ROC curve, AUC with DeLong uncertainty, cutoff performance, and optional pointwise bootstrap confidence bands. Several tests measured on the same rows create paired curves; separate outcome–test pairs or a grouping variable create independent curves.
How do I choose a ROC cutoff?
Create the curve in ROC, then choose the cutoff purpose. Balanced analysis maximizes the Youden index. Screening requires a minimum sensitivity and then maximizes specificity. Confirmatory or rule-in testing requires a minimum specificity and then maximizes sensitivity. Existing-cutoff analysis evaluates the entered threshold without optimizing it on these data. See the ROC cutoff-selection guide for interpretation and validation cautions.
How do I compare ROC curves?
For tests measured on the same participants, select one actual outcome and several test values or scores; numiqo uses paired DeLong comparisons. For separate samples, select the same number of outcomes and tests; they are paired by left-to-right column order and compared independently. To compare groups, select one outcome, one test, and a grouping variable. When several curve pairs are tested, numiqo also reports Holm-adjusted p-values. See Compare ROC Curves.
How do I calculate a moderation and mediation analysis?
Click Mediation/Moderation. Copy your data into the upper table. Then select your variables. For moderation analysis, select a dependent variable, an independent variable, and the moderator variable. For mediation analysis, select a dependent variable, an independent variable, and the mediator variable.
How do I run a predictive analytics model?
In the Statistics Calculator, open Predictive Analytics. Choose between Decision Tree, Random Forest, Gradient Boosting, or Compare Models. For a Decision Tree, you can use CART or CHAID. Then select one dependent variable and one or more independent variables. The model and its results are calculated automatically.
How do I generate graphs or charts?
Click Descriptive/Charts. Copy your data into the upper table and select the variables you want to visualize. Depending on the selected variable types, numiqo can generate histograms, box plots, violin plots, raincloud plots, QQ plots, run charts, line charts, scatter plots, scatter plot matrices, correlation heatmaps, bar charts, pie charts, Sankey diagrams, Bland-Altman plots, multi-vari charts, beeswarm plots, ridgeline plots, and Pareto charts.
How do I import or open data in numiqo?
To get started you go to the website numiqo.com and open the Statistics Calculator. The Statistics Calculator is your data table, where you can import or paste your own data. In the data table, each case (e.g., each person) represents a row. Each column contains a variable that describes your data (e.g., age, gender). In the Statistics Calculator, you will find sample data. If you want to delete them, click "Enter new data" in the top left corner. If you now want to import your own data into numiqo, click "Import/Export", and a dialog window will open. In the dialog window, under the "Import" section, you will find a field where you can drag and drop your file. The file can be an Excel file (.xlsx), a CSV file, an SAV file, or a numiqo file. Alternatively, you can browse for the file on your computer by clicking "Select File."
How do I export data?
To export data, open the "Import/Export" window in the Statistics Calculator. There, you will find an Export section with several options. You can export your data as an Excel file ("Download Excel") or as a numiqo file ("Download .numiqo"). It is also possible to create a data link for smaller datasets. In this case, your data is stored within a URL that you can access again later. Your data is not stored on our server.
How do I change the scale level or level of measurement?
Numiqo automatically suggests a scale level (measurement level) for your variables (metric, ordinal or nominal). If you want to change the scale level, go to the top row of the table in the Statistics Calculator. There, click on the respective scale level, and a dialog window will open where you can make your adjustments.
How do I set a filter?
If you want to include only a part of your dataset in the analysis (e.g., only women, only older people, etc.), the filter function is the right tool. To do this, go to the Statistics Calculator and click on the scale level of the variable. In the right column, "Filter Data," you can check the boxes for the categories of your variable that you want to include. For example, if you check "Female," only the results for women in your dataset will be displayed, and only women will be included in all subsequent analyses. If you want to remove the filter, click on "Clear Filter" at the top right of the Statistics Calculator.
How do I recode/transform variables?
If you want to recode a variable in numiqo, go to "Prepare Data". Then select the first field, "Recoding". Next, select the variable you want to recode. In our example, we want to recode "Age" to create age groups. If you want to recode individual values into a different value, enter them in the "Single Value" column. If you want to recode a range of values, enter the values in "From Value" and "To Value", and then specify the new value in the "New Value" column on the far right.
How do I create a score or an index?
If you want to create a score or index (i.e., a combined measure from multiple individual questions or variables), go to "Prepare Data." Then select the first field, "Create Index." Next, first select the variables you want to combine into an index. This is useful, for example, with items using a Likert scale. Then choose whether you want to create a sum index or a mean index. When calculating an index, it is often specified how many valid values a person must have at minimum for an index value to be calculated. You can enter this under Options, but it is not required. Finally, give your new index a name ("Variable Name") and click "Add." The index will now appear as a new variable at the end of your data table in the Statistics Calculator.
How do I customize a chart?
On the left side of your chart, you can adjust various settings with a click (e.g., display percentages, adjust alignment and order). You can also customize the data labels and the size of the chart. If you want to change the order of the categories of your variable in the chart, do the following: First, set the scale level of the variable to "ordinal." In the Values section, you can now change the order. The way the values are arranged here determines how they are displayed in the chart.
Which general settings can I change in the Statistics Calculator?
In the Statistics Calculator, click "Settings" above the data table. There you can specify which entries should be treated as missing values, choose the decimal separator, and set the number of decimal places displayed.
How do I change the color of a chart?
In the Statistics Calculator, click "Settings" above the data table. Under "Colors for charts," paste the desired hex color codes into the text box and save them. You can also reset the colors to their defaults or select a greyscale color scheme.
How do I download a chart?
To download and insert a chart, hover your mouse directly over the chart. Then select "Download PNG or SVG," and the chart will appear in your downloads. You can then copy and paste the chart into your desired document as needed.
What is numiqo?
numiqo is modern, secure statistics software in the browser - easy to use, with no installation and no server-side storage. From descriptive statistics to hypothesis tests and regression, numiqo helps you analyze data quickly and clearly.
Statistics made easy
- many illustrative examples
- ideal for exams and theses
- statistics made easy on 464 pages
- 8th revised edition (March 2026)
Only €8.99
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