Contents

# Analysis of Variance (ANOVA)

Produces the analysis of variance (ANOVA) of a given data set

To access this command...

#### From the menu bar:

Choose Data - Statistics - Analysis of Variance (ANOVA)

#### From the tabbed interface:

Choose Data - Statistics - Analysis of Variance (ANOVA).

On the Data menu of the Data tab, choose Statistics - Analysis of Variance (ANOVA).

ANOVA is the acronym for ANalysis Of VAriance. This tool produces the analysis of variance of a given data set

For more information on ANOVA, refer to the corresponding Wikipedia article.

### Data

Input Range: The reference of the range of the data to analyze.

Results to: The reference of the top left cell of the range where the results will be displayed.

#### Grouped By

Select whether the input data has columns or rows layout.

## Type

Select if the analysis is for a single factor or for two factor ANOVA.

## Parameters

Alpha: the level of significance of the test.

Rows per sample: Define how many rows a sample has.

#### Example

The following data will be used as example

| A | B | C
--- | --- | --- | ---
1 | Maths | Physics | Biology
2 | 47 | 67 | 33
3 | 36 | 68 | 42
4 | 40 | 65 | 44
5 | 39 | 64 | 60
6 |  | 38 | 43
7 | 47 | 84 | 62
8 | 29 | 80 | 51
9 | 27 | 49 | 40
10 | 57 | 49 | 12
11 | 56 | 33 | 60
12 | 57 |  |
13 | 26 |  |

The following table displays the results of the analysis of variance (ANOVA) of the sample data above.

ANOVA - Single Factor
Alpha | 0.05 |
Groups | Count | Sum | Mean | Variance |
Column 1 | 11 | 461 | 41.9090909091 | 139.4909090909 |
Column 2 | 10 | 597 | 59.7 | 287.1222222222 |
Column 3 | 10 | 447 | 44.7 | 227.3444444444 |
Source of Variation | SS | df | MS | F | P-value | F-critical
Between Groups | 1876.5683284457 | 2 | 938.2841642229 | 4.3604117704 | 0.0224614952 | 3.340385558
Within Groups | 6025.1090909091 | 28 | 215.1824675325 |
Total | 7901.6774193548 | 30 |

Related Topics

Sampling

Descriptive Statistics

Analysis of Variance (ANOVA)

Correlation

Covariance

Exponential Smoothing

Moving Average

Regression Analysis

Paired t-test

F-test

Z-test

Chi-square test

Fourier Analysis