# GraphPad Prism Tutorial: t-Tests, ANOVA, Curve Fitting and Graphs for Biologists GraphPad Prism is a commercial statistics and graphing application built around a small set of data table types, and the fastest way to learn it is to match your table type to your experimental design before you open any analysis menu. A t test needs a Column table, a one-way ANOVA needs a Column table, and nonlinear regression needs an XY table, so that very first click decides almost everything that follows. Biologists gravitate to Prism because it sits at the junction of three jobs that are usually split across three programs. You enter data the way you actually collected it, run a validated test from a menu, and get a figure you can drop into a manuscript without rebuilding it in Illustrator. This guide walks through each of those jobs in order, with the assumptions and failure modes that matter most. ## What GraphPad Prism Does and Why Biologists Use It Prism is organized around six data table types rather than around a single spreadsheet grid. The table type is not cosmetic. It tells Prism which analyses are legitimate and which graph templates make sense. | Table type | How data are arranged | Analyses Prism runs on it | Graph Prism draws | |--|--|--|--| | XY | Each row is one X value, each subcolumn is a replicate | Linear and nonlinear regression, correlation, area under curve, interpolation | Scatter, fitted curve, dose-response | | Column | Each column is one group, each row is one subject | t tests, one-way ANOVA, nested t test, Mann-Whitney, Kruskal-Wallis | Scatter with mean and error bars, box plot, violin | | Grouped | Rows are one factor, columns are a second factor | Two-way ANOVA, mixed-effects models, multiple t tests | Grouped scatter, grouped bar | | Contingency | Rows and columns are categories, cells hold counts | Fisher's exact test, chi-square | Stacked bar, mosaic | | Survival | Time to event plus censoring status | Kaplan-Meier, log-rank, Cox regression | Step plot | | Parts of whole | Fractions of a total | Fraction comparison tests | Stacked bar, pie | Everything in Prism follows one chain: data table, then analysis, then results sheet, then graph, then layout. The links are live. Edit a number in the data table and the fitted parameters, the test statistics, the axis ranges, and the figure all update. A single project file holds every table, analysis, graph, and layout, which makes archiving straightforward. The results sheet also contains a plain-language description of the test you ran, including the null hypothesis and the assumptions. That text is designed to be adapted directly into a methods section, and it is one of the main reasons Prism is so common in biology labs that do not employ a statistician. ## How to Use GraphPad Prism: The Core Workflow ### Step 1: Pick the table type from the experimental design Ask two questions. How many factors did I manipulate, and how many groups do I have? One factor with two groups is a Column table and a t test. One factor with three or more groups is a Column table and a one-way ANOVA. Two crossed factors are a Grouped table and a two-way ANOVA. A continuous predictor such as concentration, time, or dose is an XY table and a regression. Choosing a table type and later changing your mind costs time, because Prism does not convert between some table types cleanly. Decide the design first. ### Step 2: Enter data with the right row meaning In a Column table, each column is a group and each row is one independent subject. Unequal group sizes are allowed, so you leave cells empty rather than inventing values. In an XY table, each row is one X value, and each subcolumn is a replicate at that X. This distinction matters more than any other single habit in Prism. If three measurements come from the same animal, they belong in a paired or nested analysis, not as three independent rows in a plain Column table. ### Step 3: Run the analysis and answer the dialog honestly The Analyze menu lists only the analyses valid for the current table. Prism asks specific questions before running: paired or unpaired, equal variances or Welch correction, one or two tails, which comparisons, which multiple comparison correction. These dialogs are where most bad analyses happen, because the defaults are reasonable but not always right for your design. ### Step 4: Read the results sheet, not just the p value A Prism results sheet reports the test statistic, degrees of freedom, p value, effect size, and where relevant a confidence interval for the effect. Effect size is the part most people skip. A difference of 2 units with a narrow confidence interval is a very different finding from the same difference with a wide one. ### Step 5: Build the graph, then the layout Prism generates a default graph from the analysis. Format Graph controls point shape, size, fill, and error bar type. Format Axes controls ranges, ticks, and log scaling. For multi-panel figures, the Layout tool places several graphs on one page with shared panel labels A, B, C. ## t Tests in Prism The t test asks whether two means differ by more than sampling noise would predict. It computes a ratio of the difference between means to the standard error of that difference, then compares that ratio against a [t distribution](/blog/data-analysis/students-t-distribution-definition-formula) with degrees of freedom determined by the sample sizes. Prism offers four t test variants on Column and XY tables. **Unpaired t test.** Two independent groups, such as treated versus untreated wells from different animals. This is the default for most experiments and assumes the two groups share a common standard deviation. **Welch's t test.** Still two independent groups, but it does not assume equal variances. Prism can report the standard and Welch results side by side. When group sizes or standard deviations differ substantially, the Welch correction is the safer choice, because the pooled-variance version can produce inflated false positive rates. **[Paired t test](/blog/guides/paired-vs-independent-t-tests-choosing-the-right-test-for-your-data).** The same subject measured twice, such as before and after a treatment, or left and right tissue from one animal. Prism pairs rows, so both columns must be in the same order. **Nested t test.** For designs where you have technical replicates within biological replicates, such as three fields of view per mouse. Running a plain unpaired t test on those numbers treats each field as independent and inflates the degrees of freedom, which is one of the most common causes of a spurious p value in [cell biology](/blog/careers/cell-biology). **One-sample t test.** Compares a single mean against a fixed theoretical value, such as a normalized control of 1.0. Every variant requires independence between observations and approximate normality within groups. Independence is a design property you cannot fix after the fact. Normality matters more as group size falls. With fewer than about ten subjects per group and visibly skewed data, the Mann-Whitney test or the Wilcoxon signed-rank test is a better fit, and Prism runs both from the same table. ## One-Way ANOVA in Prism A one-way ANOVA compares three or more group means in a single test. It partitions the total variance into a between-group component and a within-group component, then forms an F ratio of the two. A large F means the between-group spread is large relative to the noise inside groups. The reason to run one ANOVA instead of several t tests is the family-wise error rate. With four groups there are six possible pairwise comparisons. If each were tested independently at a 0.05 threshold, the chance of at least one false positive would climb well above 5% even when no group truly differs. ANOVA holds that rate at 5% overall, then hands the comparison job to a procedure designed for multiple tests. Prism's one-way ANOVA dialog offers several follow-up plans. - **Compare all pairs (Tukey).** The standard choice when you have no pre-planned single contrast. - **Compare each group to a control (Dunnett).** More powerful than Tukey when one group is the reference. - **Test for a linear trend.** Useful when groups are ordered, such as increasing doses. - **Compare selected pairs only.** Legitimate when the pairs were pre-specified, not when they were chosen after seeing the data. The same dialog offers Brown-Forsythe and Welch versions for unequal variances, plus the nonparametric Kruskal-Wallis test with Dunn's post hoc comparisons. For repeated measures designs, a repeated measures one-way ANOVA is available, with corrections for violations of sphericity. Prism also includes the ROUT method for outlier detection. It fits a model and removes points that deviate far beyond the expected scatter, which is defensible for gross errors such as a spilled well. Use it to identify suspicious points, then report what you removed and why. Removing points because they weaken a result is a different activity entirely. ### When the design has two factors If every level of one factor appears at every level of another, you need a two-way ANOVA on a Grouped table. This is common in nutrition and pharmacology, where doses are crossed with diets or genotypes. A published example shows the structure clearly. A fully randomized factorial study in Japanese quail allocated 900 chicks across 15 dietary treatments formed from three crude protein levels (22%, 24%, and 26%) crossed with five lysine levels (0.95%, 1.1%, 1.25%, 1.4%, and 1.55%) [1]. Crude protein and lysine both affected growth parameters at p < 0.01, and the two factors interacted at p < 0.05, which means the effect of lysine depended on the protein level [1]. In a Prism Grouped table, that study would produce three rows of output: a main effect for protein, a main effect for lysine, and an interaction row. Reading only the two main effects would misrepresent the result entirely. ## Nonlinear Regression in Prism Nonlinear regression, which Prism labels as curve fitting under the Analyze menu, fits a mathematical model whose parameters enter in a non-additive way. A straight line has the form y = intercept + slope times x. A dose-response curve has the form y = bottom + (top minus bottom) divided by (1 plus 10 raised to the power of ((logEC50 minus x) times Hill slope)). You cannot fit the second by transforming the data and running linear regression without distorting the error structure, so the fit is iterative. Prism starts from initial estimates, adjusts the parameters step by step to minimize the sum of squared residuals, and stops when further adjustment no longer improves the fit. ### Choosing the equation Prism ships with organized equation families: dose-response (Hill, logEC50, and the Emax style asymptote models), binding (one site, two sites, cooperative), enzyme kinetics (Michaelis-Menten, allosteric sigmoidal), exponential decay and association, growth equations, Gaussian, and polynomial. The Hill model is the standard tool for activation or inhibition dose-effect data, and more complex forms handle biphasic effects that arise when activation and inhibition combine [2]. The Emax model is the workhorse of clinical pharmacology because it is bounded above and below, which a simple log-linear model is not, and its parameters can be estimated by weighted least squares from mean and dose pairs [3]. Model choice has consequences beyond aesthetics. In a study of clonogenic survival across nine human pancreatic cancer cell lines and immortalized ductal epithelial cells irradiated at 0 to 10 Gy, the conventional linear-quadratic model and a nonlinear log-logistic regression both approximated the data accurately, but the linear-quadratic interpretation breaks down when curves share an alpha/beta ratio yet differ in overall steepness [4]. The model is a lens. A lens that loses resolution in part of the range changes the biological conclusion. ### The three settings that decide whether the fit is valid **What counts as a replicate.** Prism asks whether your replicates belong to one experiment or to several independent experiments. If you have three biological replicates each run in technical duplicate, the technical duplicates are not independent data points. Enter each independent experiment as a separate data set and use global fitting to share the parameters across data sets. This increases the reliability of the shared parameters without pretending you have more independent observations than you do. **Weighting.** Ordinary least squares assumes the scatter is the same at every X value. In practice, counts and proportional data often have variance that grows with the mean, so a point near the top of the curve carries more absolute noise than a point near the bottom. Prism offers weighting options, including 1/Y squared, for that situation. Choosing the wrong weighting does not just widen your intervals, it can shift the best-fit values. **Initial values and constraints.** Nonlinear fits can converge on a local minimum or fail outright. If a fit returns a nonsensical parameter or a "can't reach convergence" message, the usual causes are bad initial estimates, too many parameters for the number of points, or a data range that does not actually contain the curve's asymptotes. Fix the design first. Constraining a parameter to a plausible range is a last resort, and any constraint must be reported. ### Reading the parameter table Prism reports each parameter's best-fit value with a standard error and a 95% confidence interval, along with R squared, adjusted R squared, the sum of squares, and a residuals plot. Two cautions apply to every nonlinear fit. First, a high R squared does not prove the model is right. A four-parameter curve will fit almost any monotonic data set. Judge the model by whether the residuals scatter randomly around zero, by whether the parameters are biologically plausible, and by whether the confidence intervals are narrow enough to be informative. Second, Wald-based standard errors and confidence intervals can be inaccurate in nonlinear models, particularly when the parameters are strongly correlated or the sample is small. A methodological review of nonlinear regression warns that commonly reported parameter p values and confidence intervals may be inaccurate, connects the failure of Wald approximations to model curvature, and argues for likelihood-based intervals and parameter profiling instead [5]. Prism shows a covariance matrix for the fit. If two parameters are correlated above roughly 0.95, their individual confidence intervals are close to meaningless and the fit is over-parameterized for the data at hand. ### Comparing competing models Prism's Compare Models function uses the extra sum-of-squares F test for nested models and AICc for models that are not nested. Nested means one model is a restricted version of the other, such as one-phase versus two-phase decay, or a shared-versus-separate set of parameters across data sets. The same logic applies outside Prism. When researchers estimated lysine requirements in starter-phase Japanese quail, they explicitly compared linear and quadratic broken-line models using nonlinear least squares rather than assuming a shape [1]. The chosen model determined the recommended requirement, and the optimum of 1.4% lysine maximized body weight at 73.93 g, weight gain at 66.50 g, and the protein efficiency ratio at 2.70 [1]. The threshold you report is a property of the model as much as of the animal. ### Where curve fitting ends and spline modeling begins Prism fits parametric curves. It does not fit restricted cubic splines, the flexible method epidemiologists use for dose-response shapes that are not assumed in advance. A cohort of 10,135 adults found a J-shaped relationship between body mass index and diabetes risk, with odds ratios of 1.67 for overweight and 1.76 for obesity and a nonlinearity p value below 0.001, using R version 4.3.1 [6]. No simple Hill curve would have captured that shape. If your question is about the shape of a dose-response relationship rather than the parameters of a known mechanism, spline modeling in R or Stata is the appropriate tool. ## Making a Prism Graph That Survives Peer Review A Prism graph is not decoration. It is the reader's only view of your data, and a few choices determine whether it informs or misleads. **Show the points.** A bar graph showing mean and standard error hides the distribution. Two groups with identical means and identical error bars can look completely different as scatter plots, one unimodal and one bimodal. Prism's Column table produces a scatter dot plot with a mean line in a couple of clicks, and reviewers increasingly expect it. **State which error bar you used.** Standard deviation describes the spread of the observations. Standard error of the mean describes the precision of the mean and is always smaller than the SD when n is above 1. A 95% confidence interval describes the range that would contain the true mean in 95% of repeated samples. All three are defensible, and all three must be named in the legend. Prism's default template is not a substitute for that decision. **Use a log axis for dose-response data.** Concentrations spanning three or more orders of magnitude belong on a log10 X axis. Prism switches the axis and refits the curve so that logEC50 becomes the reported parameter, which is the conventional form. **Do not break axes to exaggerate a difference.** A broken Y axis compresses a real gap and makes a small effect look dramatic. If the effect is small, show it as small. **Report exact p values.** Asterisks alone force readers to guess. Prism can display both the symbol and the exact value. **Export at the right resolution.** Vector formats (PDF, SVG, EMF) are best for line art and scale without loss. Raster formats need at least 300 dpi at final print size for photographs and dense scatter plots. ## GraphPad Prism Alternatives Prism is one option among several, and the right one depends on whether you need point-and-click output or reproducible scripted pipelines. | Tool | Licensing | Strongest use case | Trade-off | |--|--|--|--| | GraphPad Prism | Commercial, per seat | Small to medium data sets, publication figures, standard tests | Not built for large batch pipelines or version-controlled analysis code | | R | Free, open source | Flexible modeling, splines, reproducible workflows | Steep learning curve, figure styling takes work | | Stata | Commercial | Epidemiology, meta-analysis, dose-response synthesis | Less common in bench labs | | SAS | Commercial | Designed experiments, mixed models, nonlinear least squares | Cost and syntax overhead | | Excel add-ins | Free or low cost | Quick dose-response fits without new software | Limited statistical scope | The published literature shows how these divide in practice. Meta-analyses of night shift work and cardiovascular disease, chronic noise exposure and dementia, and coffee consumption and gastric cancer all used Stata, with restricted cubic splines or generalized least squares handling the dose-response shape [7][8][9]. A study of physical activity and gestational diabetes used SAS 9.4 and R 4.2.1 to derive restricted cubic spline cut-offs [10]. Analyses of threshold effects in maternal vitamin A and neonatal ponderal index used R with EmpowerStats for segmented regression [11]. R has become the default for methods that need custom models. The bkmr package was released specifically to make Bayesian kernel machine regression available for mixtures of exposures, with flexible exposure-response surfaces and variable selection that Prism's parametric curves cannot reproduce [12]. Large survey analyses, such as the NHANES examination of cardiovascular health scores and gout risk in 14,813 adults, are also routinely run in R [13]. Excel-based tools fill the gap for simple dose-response work. One program, eeFit, fits standard Hill models for activation and inhibition plus biphasic models inside an Excel spreadsheet, requires no knowledge of nonlinear least squares, and benchmarked equivalent to or better than the commercial package Origin in accuracy and convergence while being much easier to learn [2]. For a lab that fits a handful of concentration-response curves a year, that is a real alternative to a Prism license. ## Common Mistakes and Limitations **Counting technical replicates as independent n.** Three wells from one animal are one observation for the purpose of a t test. The fix is a nested t test or a mixed model, and the fix must happen before you run the test. **Running many t tests instead of one ANOVA.** Covered above, and still the single most frequent error in submitted manuscripts with three or more groups. **Treating R squared as proof of a correct model.** A flexible equation will fit nonsense. Check residuals, parameter plausibility, and whether the data range actually contains the asymptotes you are estimating. **Ignoring the parameter covariance matrix.** Highly correlated parameters mean the experiment cannot separate their effects, no matter how good the R squared looks. **Leaving default error bars.** Prism picks a default. You pick the meaning. **Running a Gaussian test on count data.** Small counts are skewed. Use a nonparametric test or a model built for counts. **Extrapolating past the data.** A curve fitted between 0.1 and 10 micromolar says nothing reliable about 100 micromolar. Prism will happily interpolate outside that range if you ask it to. **Reporting p values from a nonlinear fit as if they were ordinary hypothesis tests.** Parameter standard errors in nonlinear models rest on approximations that can fail, and a review of the method documents exactly where those approximations break down [5]. **Not archiving the project file and software version.** Prism files reference the version that created them. Save the project file, not just the exported figure, and note the version in your lab notebook. **Assuming the software enforces the assumptions.** Prism will run an ANOVA on data that violate independence without complaint. The assumptions live in your design, not in the dialog box. Individual projects still need a statistician or a supervisor to review the design before data collection. That review is far cheaper than discovering a pseudoreplication problem after the figures are made. ## Frequently Asked Questions ### Is GraphPad Prism free? No. Prism is commercial software sold as a per-seat license, with academic pricing available from the vendor. Free alternatives exist, including R for full scripted analyses and Excel-based fitting tools for simple dose-response curves. ### What is the difference between a t test and a one-way ANOVA in Prism? A t test compares exactly two means and can be run in either direction. A one-way ANOVA compares three or more means in a single test and controls the overall false positive rate across all the group comparisons. ### Which t test should I choose in Prism? Choose paired when the same subject is measured twice, unpaired when the groups are independent, and Welch's version when the two groups have clearly different standard deviations or very different sizes. Use a nested t test when you have technical replicates inside biological replicates. ### How do I run nonlinear regression in Prism? Put your data in an XY table with replicates in subcolumns, open the Analyze menu, and choose Nonlinear regression. Pick an equation family, confirm whether replicates are from one experiment or several, set weighting if needed, and inspect the residuals and parameter confidence intervals before accepting the fit. ### Can Prism fit dose-response curves and report an EC50? Yes. The dose-response equation family includes Hill models that report logEC50, EC50, top, bottom, and Hill slope, with confidence intervals for each. The X axis should be on a log10 scale for concentrations that span several orders of magnitude. ### What are good free GraphPad Prism alternatives? R is the most capable free option, covering regression, splines, meta-analysis, and publication graphics. Excel-embedded fitting programs handle standard Hill and biphasic dose-response models for users who do not want to write code. ### Why does my Prism curve fit fail to converge? The usual causes are poor initial parameter estimates, more parameters than the data can support, or a data range that never reaches the curve's plateaus. Entering sensible starting values and checking that the highest and lowest concentrations actually define the asymptotes resolves most failures. ### How do I export a Prism graph for publication? Use vector formats such as PDF, SVG, or EMF for line art and scatter plots. Use TIFF or PNG at 300 dpi or higher for raster output. Check the journal's figure specifications before final export, and keep the Prism project file alongside the exported image. ## Sources 1. [Lysine Requirements in Starter-Phase Japanese Quail (Coturnix japonica) Through Dose-Response Modelling: Interactions With Dietary Protein Level.](https://pubmed.ncbi.nlm.nih.gov/42806819/) 2. [eeFit: a Microsoft Excel-embedded program for interactive analysis and fitting of experimental dose-response data.](https://pubmed.ncbi.nlm.nih.gov/30987445/) 3. [Methods for meta-analysis of pharmacodynamic dose-response data with application to multi-arm studies of alogliptin.](https://pubmed.ncbi.nlm.nih.gov/26994216/) 4. [On the analysis of clonogenic survival data: Statistical alternatives to the linear-quadratic model.](https://pubmed.ncbi.nlm.nih.gov/26822015/) 5. [Nonlinear Regression Modelling: A Primer with Applications and Caveats.](https://pubmed.ncbi.nlm.nih.gov/38489047/) 6. [A Nonlinear Association of Body Mass Index and Fasting Blood Glucose: A Dose-Response Analysis From Fasa Adults Cohort Study (FACS).](https://pubmed.ncbi.nlm.nih.gov/40114753/) 7. [Association between night shift work and cardiovascular disease: a systematic review and dose-response meta-analysis.](https://pubmed.ncbi.nlm.nih.gov/41069800/) 8. [Chronic Noise Exposure and Risk of Dementia: A Systematic Review and Dose-Response Meta-Analysis.](https://pubmed.ncbi.nlm.nih.gov/35795699/) 9. [Long-Term Coffee Consumption and Risk of Gastric Cancer: A PRISMA-Compliant Dose-Response Meta-Analysis of Prospective Cohort Studies.](https://pubmed.ncbi.nlm.nih.gov/26402838/) 10. [The study of the relationship between physical activity and gestational diabetes mellitus in the second trimester of pregnancy: a dose-response analysis with the restricted cubic spline model.](https://pubmed.ncbi.nlm.nih.gov/40790574/) 11. [Threshold Effects of Third-Trimester Maternal Vitamin A on Neonatal Ponderal Index: A Segmented Regression Analysis of 442 Mother-Infant Pairs.](https://pubmed.ncbi.nlm.nih.gov/40552338/) 12. [Statistical software for analyzing the health effects of multiple concurrent exposures via Bayesian kernel machine regression.](https://pubmed.ncbi.nlm.nih.gov/30126431/) 13. [Inverse and nonlinear relationships between Life's Essential 8 metrics and gout risk: A cross-sectional study.](https://pubmed.ncbi.nlm.nih.gov/41088673/) ## Related Articles - [Two Sample t-Test: Formula, Calculation and Example](/blog/data-analysis/two-sample-t-test-formula-example) - [How to Calculate a One-Way ANOVA: Worked Example With Welch F and Tukey HSD](/blog/research-skills/how-to-calculate-one-way-anova) - [ANOVA Table Explained: Components, Formulas and Example](/blog/data-analysis/anova-table-explained) - [How to Use jamovi: A Free Statistics Guide for t-Tests, ANOVA and Regression](/blog/data-analysis/how-to-use-jamovi) - [JASP Tutorial: Free Statistics Software for t-Tests, ANOVA and Bayesian Analysis](/blog/data-analysis/jasp-statistics-tutorial)