# Tutorial:One Way ANOVA

### From Howto Wiki

## Contents |

## Summary

There are two main modes of datasets in Statistics - indexed and raw. When you perform an analysis, you do not need to use the whole dataset, so Origin provides several ways to select data. For example, you can use the interactive Regional Data Selector button to graphically select the data or you can use the **Column Browser** dialog to make your selection.

In this tutorial, you'll use the Analysis of Variance (ANOVA) statistical test, to learn how to use these two different modes of data to perform analysis and how to select data by using the **Column Browser** dialog.

ANOVA is a kind of parametric method for means comparison and is an extension of t-test. When there are more than two groups to be compared, pairwise t-test is not appropriate and ANOVA should be used. ANOVA requires normality and equal variance. Otherwise, non-parametric analysis should be used.

Minimum Origin Version Required: Origin 8.0 SR6

## What you will learn

This tutorial will show you how to:

- Use different input data mode on statistical analysis dialog
- Test normality for special part of dataset
- Perform one-way ANOVA
- Select data by Column Browser

## Steps

Origin can calculate ANOVA in indexed as well as raw data mode. For One-Way ANOVA, when using indexed mode, data should be organized in two columns : one for Factor and the other for data.

When using Raw data mode, the different levels are in different columns.

### Indexed data mode

Nitrogen content has been recorded in milligrams for 4 kinds of plant, and we are interested in whether different plants have different nitrogen content. We will perform One-Way ANOVA using index data mode for this example.

- Start with a new workbook and import the file \
*Samples*\*Statistics*\*nitrogen.txt*. Make sure you select*.txt*from the drop-down menu Files of type. First, we should perform a normality test on each group of data to determine if they are from a normal distribution. - Highlight the first column, right-click and select
**Sort Worksheet**from the Worksheet menu and choose**Ascending**. - Highlight the second column from row 1 to row 20 - which belongs to "PLANT1" - and open the
**Normality Test**dialog by choosing the menu item**Statistics: Descriptive Statistics: Normality Test**.

- Use the default setting of the dialog and click
**OK**. From the p-value of result,p-value=0.58545, we can see "PLANT1" follows a normal distribution. - In a similar way, you can highlight the range of data "PLANT2", "PLANT3" and "PLANT4" and test for Normality. Our sample data has normal distribution for all plants.
- With our nitrogen data worksheet active, open the
**ANOVAOneWay**dialog by using the menu item**Statistics: ANOVA: One-Way ANOVA**. Set the**Input Data**mode as**Indexed**, assign the "plant" and "nitrogen" column as**Factor**and**Data**respectively using the right-arrow buttons. Click the + to expand the**Means Comparison**node, set**Significance Level**as 0.05 and check the**Tukey**Means Comparison method. Check**Levene | |**from**Tests for Equal Variance**branch. Click the**OK**button to perform One-Way ANOVA.

**Explaining the result:**

- From the "Homogeneity of Variance Test" table of one-way ANOVA result, we can see that the four groups have equal variance, since the p-value is bigger than 0.05.

- From the result of Overall ANOVA we can conclude that at least two groups of the four have significant different means, since the p-value is smaller than 0.05.

- To research further, we expand the results of "Means Comparisons".

Here we see that PLANT4 has significantly different means when compared to each of the other three groups.

### raw data mode

- Select
**File : Open**and choose**WorkBooks**from**Files of type**drop-down list, and browse to \*Samples*\*Statistics*folder and open the file*Body.ogw* - Select menu item
**Statistics : ANOVA : One-Way ANOVA**to bring up the**ANOVAOneWay**dialog. Choose**Raw**as**Input Data**mode. Enter the**Level1 Name**and**Level2 Name**as "Male Weight" and "Female Weight" respectively. - Now we will use the
**Data Browser**to select data in the**Data**branch. Click the triangle icon beside**Male Weight**edit box, in the fly-out menu, select**Select Columns...**to open the**Column Browser**dialog.

In the Column Browser dialog, you can select**in Current Book**from**List Columns**drop-down list to see all available worksheet columns in the current book. Select*Weight*in the sheet*[Body]Male*and click**Add**and**OK**to add it to**Male Weight**edit box. Similarly, assign*Weight*from*[Body]Female*to**Female Weight**edit box.

- Accept other default settings in the ANOVAOneWay dialog and click
**OK**. From the output report footnote, we can conclude that at the 0.05 level, the population weight means between male and female are not significantly different.