Data Table Format

The Multifactor ANOVA in Prism requires the input data to be entered into a Multiple Variables data table. This table format is different from the Column or Grouped tables used for one-way and two-way ANOVA.

To create a Multiple Variables table:

1.From the Welcome dialog (or New Table and Graph dialog), click the Multiple Variables tab

2.Choose "Enter or import data into a new table"

3.Click Create

4.Enter your data with each row representing one observation and each column representing a different variable

Structure of the Multiple Variables Table

The data in a multiple variables data table is typically organized in a standard "database" or "tidy" format. In a Multiple Variables table:

•Each row is one observation (one subject, one sample, one experimental unit)

•Each column is one variable

•One column contains your response variable (the outcome you measured)

•Other columns contain your grouping variables (the factors that define your experimental groups)

Example: Plant growth experiment

Suppose you're studying how fertilizer type and watering frequency affect plant height. Your table might look like this:

In this example:

•Response variable: Height (continuous measurement)

•Factor 1: Fertilizer (3 levels: None, Organic, Synthetic)

•Factor 2: Watering (2 levels: Daily, Weekly)

•PlantID is just an identifier (not used in analysis)

Response Variable (Y Variable)

The response variable is the outcome you want to analyze - the measurement that you think is affected by your experimental factors.

Requirements for response variables:

•Must be continuous (measured on an interval or ratio scale)

•Must be numeric

•Should be normally distributed within each group

•All values should be in the same units

Good examples of response variables:

•Height (cm)

•Weight (g)

•Blood pressure (mmHg)

•Gene expression level (normalized units)

•Enzyme activity (units/mL)

•Cell count (cells/μL)

•Absorbance (OD units)

•Temperature (°C)

•Concentration (ng/mL)

•Time to completion (seconds)

•Tumor volume (mm³)

Note about missing values:

•Multifactor ANOVA in Prism will automatically omit any rows with missing values in the response variable or any assigned grouping variable. Only complete rows are used for the analysis

•Make sure missing data are truly missing at random, not systematically related to treatment

•If you have many missing values, consider whether your experimental design or data collection needs improvement

Grouping Variables (Factors)

Grouping variables (also called factors or predictor variables) are the categorical variables that define your experimental groups.

Requirements for grouping variables:

•Must be categorical (even if numbers, they're treated as categories)

•Must have two or more levels (groups)

•Should have clear, meaningful labels

•Can be text or numeric, but will be treated as categories (must be assigned as categorical variables in the data table)

Good examples of grouping variables:

•Treatment (Control, Drug_A, Drug_B, Drug_C)

•Genotype (WT, Het, KO)

•Sex (Male, Female)

•Age_group (Young, Middle, Old)

•Diet (Standard, High_fat, High_protein, Low_carb)

•Cell_line (HeLa, HEK293, CHO, A549)

•Tissue (Liver, Kidney, Heart, Lung, Brain)

•Strain (C57BL6, BALB_c, 129S, FVB)

•Temperature (4C, 25C, 37C)

•pH_level (pH5, pH7, pH9)

Tips for naming levels:

•Use descriptive names rather than codes when possible

•Avoid spaces for level names (use underscores: Drug_A rather than "Drug A") - Prism will handle spaces just fine, but in some cases it may be hard to distinguish which parts of a label name belong to one label or another if placed side by side (compare: "Drug A B Treatment" vs "Drug_A B_Treatment")

•Be consistent with capitalization and spelling - if using letter assignments, try to apply the labels consistently both within variables and across variables. For example, avoid "Drug_A" and "B_Drug" in the same variable. Additionally, "Drug_A Treatment_B" is far easier to interpret than "Drug_B B_Treatment"

•For numeric categories, consider adding a prefix to make the categorical nature clear (pH5, pH7, pH9 rather than just 5, 7, 9)

About numeric grouping variables:

If you have a numeric variable like dose (0, 10, 25, 50 mg) or time (0, 2, 4, 8, 24 hours), you can treat it as a factor in ANOVA, but keep in mind:

•It must be specified as a categorical variable in the data table

•ANOVA will ignore the ordering and spacing of values

•ANOVA treats 0, 10, 25, 50 the same as it would treat A, B, C, D

•This may not be the most powerful analysis for ordered variables

How Many Factors Can You Include?

Theoretical limit: Multifactor ANOVA can handle any number of factors.

Practical limits: the sample size requirements of an experiment grows exponentially with increasing numbers of factors.

•2 factors with 3 levels each = 9 treatment combinations

•3 factors with 3 levels each = 27 combinations

•4 factors with 3 levels each = 81 combinations

•5 factors with 3 levels each = 243 combinations

With 5 replicates per combination and 4 factors (3 levels each), you need 405 observations!

Interpretation becomes challenging:

•2 factors: 2 main effects + 1 two-way interaction = 3 tests

•3 factors: 3 main effects + 3 two-way interactions + 1 three-way interaction = 7 tests

•4 factors: 4 main effects + 6 two-way interactions + 4 three-way interactions = 14 tests

•5 factors: 5 main effects + 10 two-way interactions + 10 three-way interactions = 25 tests

Organizing Your Data

General principles:

1.One row per observation: Each experimental unit (subject, sample, measurement) gets its own row

2.One column per variable: Don't split one variable across multiple columns

3.Consistent coding: Use the same labels for the same groups throughout

4.Complete data: Try to minimize missing values

Example of well-organized data (3 factors: Drug × Gender × Age):

Common mistakes to avoid:

❌ Don't use separate columns for levels of one factor:

✅ Do use one column for the factor:

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❌ Avoid mixing levels across different variables if possible:

✅ Do separate factors into distinct columns:

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❌ Don't use inconsistent labels:

Prism will do its best to identify which labels belong together, but uses spelling (ignoring capitalizations) to accomplish this. So in this example, there would be two different levels identified instead of one "Control" level

✅ Do use consistent labels:

 

Replication and Sample Size

What is a replicate?

A replicate is an independent observation - a separate experimental unit that received the treatment.

True biological replicates:

•Different animals

•Different cell cultures (from different passages or preparations)

•Different plants

•Different patients

•Different experiments run on different days

Not true replicates (pseudo-replication):

•Multiple measurements from the same animal

•Multiple wells from the same cell culture preparation

•Multiple readings from the same sample

•Technical replicates

How many replicates do you need?

Minimum: At least 2 observations per treatment combination (but this is rarely sufficient)

Recommended:

•3-5 replicates per group for pilot studies or when effects are expected to be large

•5-10 replicates per group for typical studies

•10-20 replicates per group when effects may be small or variability is high

•More replicates are needed as the number of factors increases

Power considerations:

•More replicates = more statistical power (better ability to detect true effects)

•More factors/levels = more treatment combinations = need more total observations

•Higher-order interactions are harder to detect (need more replicates)

•Unbalanced designs (different sample sizes per group) have less power

Practical tip: For a 2 × 2 × 2 design (8 treatment combinations) with 5 replicates per group, you need 40 total observations. For a 3 × 3 × 3 design (27 combinations) with 5 replicates, you need 135 observations. Plan your sample size accordingly!

Entering Data into Prism

Step-by-step instructions:

1.Open Prism and create a new project (or add to an existing project)

2.Click "New" to create a new table

3.In the Welcome dialog, select the "Multiple Variables" tab

4.Click "Create"

5.Enter your data:

oType or paste data into the table

oEach row is one observation

oEach column is one variable

oUse the column headers to name your variables

6.Name your columns with descriptive titles:

oClick on a column header to edit its name

oUse clear names like "Blood_Pressure", "Treatment", "Gender"

oAvoid special characters or spaces when possible

7.Check your data:

oResponse variable column contains numbers only

oGrouping variable columns contain consistent category labels

oNo typos in category names

oMissing values are truly blank (not zero or placeholder text)

Importing data from other programs:

Rather than typing your data manually or copy/pasting it into Prism, you can import data from Excel, CSV, or text files:

1.Create a new Multiple Variables table

2.Use File > Import and select your data file

3.Follow the import wizard to:

oConfirm Prism recognized column headers

oVerify variable types are detected correctly

oCheck for any import errors or warnings

Data Quality Checks

Before running your analysis, check your data:

1.Check for typos and inconsistencies

oLook through your grouping variables for inconsistent spelling

oExample: "Control", "control", "CONTROL", "Cont" will be treated as 4 different groups

oUse Prism's data tables to scan for unique values

2.Check for outliers

oLook for values that seem impossible or implausible

oInvestigate (don't automatically delete!) any extreme values - they might be real or might be data entry errors

3.Verify you have data for all factor combinations

oWith 3 factors having 3, 2, and 4 levels respectively, you should have 3 × 2 × 4 = 24 treatment combinations

oCheck that you have at least some observations for each combination

oIf certain combinations are missing (by design or by accident), consider whether your design is still appropriate

4.Check for balance

oCount how many observations you have in each treatment combination

oIdeally, all combinations have the same sample size (balanced design)

oUnbalanced designs are okay but may have less statistical power

5.Check for appropriate data types

oResponse variable: Should be continuous numeric data

oGrouping variables: Should be categorical (even if represented by numbers)

6.Check for missing values

oPrism will exclude any row with missing data in the response or grouping variables

oMake sure missing data are not systematic (e.g., all missing values in one treatment group)

Common Data Entry Errors

Error 1: Using multiple tables for one experiment

❌ Wrong: Creating separate tables for each level of a factor

•Table 1: Males

•Table 2: Females

✅ Correct: One table with Gender as a grouping variable

 

Error 2: Averaging before analysis

❌ Wrong: Calculating means for each group and entering only means

✅ Correct: Enter all individual observations; let ANOVA calculate means

Why? ANOVA needs the raw data to estimate within-group variability. If you only enter means, Prism cannot perform the analysis.

 

Error 3: Including technical replicates as if they were biological replicates

❌ Wrong: Treating 3 measurements from the same animal as 3 independent observations

✅ Correct: Average the 3 technical replicates first, then use that average as one observation

Why? Technical replicates are not independent; including them inflates your sample size artificially and violates the independence assumption.

 

Error 4: Mixing continuous and categorical treatment of a variable

❌ Wrong: Using dose as a continuous predictor in one part of analysis and as categories in another

✅ Correct: Decide whether dose should be treated as continuous (use regression) or categorical (use ANOVA) and stick with it

 

Example Datasets

Simple 2-factor design (Treatment × Gender):

This design has:

•2 factors: Treatment (2 levels), Gender (2 levels)

•2 × 2 = 4 treatment combinations

•3 replicates per combination

•12 total observations

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More complex 4-factor design:

This design has:

•4 factors: Fertilizer (3 levels), Watering (3 levels), Light (3 levels), pH (3 levels)

•3 × 3 × 3 × 3 = 81 treatment combinations

•2 replicates per combination shown

•162 total observations needed