# One way ANOVA

## What is one way ANOVA?

The one-way analysis of variance (ANOVA) is a statistical technique used to determine if there are significant differences between the means of three or more independent groups. It involves one independent variable and compares group means to assess factor impacts. The test checks the null hypothesis that all group means are equal against the alternative that at least one is different. One-way ANOVA is widely used in fields like psychology, education, and medicine, with results presented in an ANOVA table.

## When to use one way ANOVA?

This test is appropriate when you have a continuous dependent variable and a categorical independent variable with three or more levels.

• Comparing Multiple Groups: When you need to compare the means of three or more independent groups to determine if there is a significant difference among them.
• Single Factor Influence: When the study focuses on the effect of a single factor (independent variable) on a dependent variable.
• Experimental Design: When you have an experimental design where subjects are randomly assigned to different groups representing different levels of the independent variable.
• Normal Distribution: When the data for the dependent variable in each group is approximately normally distributed.
• Homogeneity of Variances: When the variances of the populations are assumed to be equal (homoscedasticity).
• Independent Observations: When the observations within each group are independent of each other.

Some common examples of when one way ANOVA might be used include:

• Comparing the average scores of students who took different types of classes (e.g., online vs. in-person vs. hybrid).
• Analyzing the effectiveness of three or more different drugs in treating a disease.
• Comparing the average salaries of employees in three or more different departments within a company.

## Guidelines for correct usage of one way ANOVA

Guidelines for data collection, analysis, and result interpretation:

• Include only one categorical variable as a fixed factor, using appropriate models for multiple fixed or random factors.
• Ensure the response variable is continuous, using specific logistic models for categorical responses.
• Samples should be from a normal population or have sufficient size (>15 or 20) for accurate analysis.
• Each observation should be independent to ensure valid results.
• Collect data representing the population with precision and accuracy, recording in the order collected.
• Ensure the model fits the data well, using diagnostic and summary statistics for validation.

## Alternatives: When not to use one way ANOVA

• In case you have multiple categorical factors that are fixed, use the Fit General Linear Model if all of them are fixed factors.
• If there are random factors, use the Fit Mixed Effects Model instead.
• If you wish to visualize the connection between a continuous predictor and response, use the Fitted Line Plot.
• When you have more than one predictor, use the Fit Regression Model.

## Example of one way ANOVA?

The chemical engineer intends to evaluate the hardness of four different paint blends by applying six samples of each blend to a metal piece, curing them, and measuring their hardness. To test for the similarity of means and to examine the variations between pairs of means, the analyst employs one-way ANOVA with multiple comparisons. The following steps:

1. Gathered the necessary data.

1. Now analyses the data with the help of  https://qtools.zometric.com/ or https://intelliqs.zometric.com/.
2.  To find One way anova choose https://intelliqs.zometric.com/> Statistical module> Graphical analysis>One way anova.
3.  Inside the tool, feeds the data along with other inputs as follows:

5. After using the above mentioned tool, fetches the output as follows:

## How to do one way ANOVA

The guide is as follows:

1. Login in to QTools account with the help of https://qtools.zometric.com/ or https://intelliqs.zometric.com/
2. On the home page, choose Statistical Tool> Graphical analysis >one way ANOVA.
3. Click on one way ANOVA and reach the dashboard.
4. Next, update the data manually or can completely copy (Ctrl+C) the data from excel sheet and paste (Ctrl+V) it here.
5. Next, you need to put the value of confidence level.
6. Finally, click on calculate at the bottom of the page and you will get desired results.

On the dashboard of one way ANOVA, the window is separated into two parts.

On the left part, Data Pane is present. In the Data Pane, each row makes one subgroup. Data can be fed manually or the one can completely copy (Ctrl+C) the data from excel sheet and paste (Ctrl+V) it here.