## ANCOVA in Python

Have you ever wondered how to determine if there is a statistically significant difference in means between independent groups, while taking into account the effect of covariates? ANCOVA, or Analysis of Covariance, is a statistical method that allows you to do just that.

In this article, we will provide an overview of ANCOVA, an example of ANCOVA in Python, steps to perform ANCOVA in Python, and how to interpret ANCOVA results.

## Overview of ANCOVA

ANCOVA is a statistical method used to determine if there is a statistically significant difference in means between independent groups, while taking into account the effect of covariates. A covariate is a variable that is related to both the factor variable (the independent variable or grouping variable) and the response variable (the dependent variable).

ANCOVA determines if the factor variable still has a significant effect on the response variable after controlling for the covariate. This is done by comparing the means of the response variable for each level of the factor variable, while controlling for the effect of the covariate.

### Example:

## ANCOVA in Python

Let’s consider an example to illustrate ANCOVA in Python. Suppose a teacher wants to determine if studying techniques have a significant effect on average exam scores, after controlling for the effect of the current grade (covariate) of the students.

The teacher decides to randomly assign 20 students to a traditional study group and another 20 students to an online study group. The current grade of each student and their average exam score at the end of the study period were recorded.

### To perform ANCOVA in Python, we will use the pingouin library. The first step is to import the necessary libraries:

```
import pandas as pd
import pingouin as pg
```

### Next, we create a DataFrame from the data:

```
data = pd.DataFrame({
'study_group': ['traditional']*20 + ['online']*20,
'current_grade': [70, 87, 92, 76, 85, 78, 81, 75, 80, 84, 93, 88, 98, 85, 93, 79, 88, 83, 79, 86]*2,
'average_exam_score': [82, 89, 87, 78, 86, 79, 81, 75, 80, 84, 92, 87, 96, 85, 91, 78, 87, 83, 77, 84,
78, 84, 83, 79, 88, 83, 81, 75, 81, 77, 91, 88, 98, 86, 94, 78, 85, 83, 79, 86]
})
```

In the DataFrame, ‘study_group’ is the factor variable (grouping variable), ‘current_grade’ is the covariate, and ‘average_exam_score’ is the response variable. The next step is to perform ANCOVA using the pg.ancova() function:

```
dv = 'average_exam_score' # dependent variable
covar = 'current_grade' # covariate
between = 'study_group' # factor variable
pg.ancova(data=data, dv=dv, covar=covar, between=between)
```

This will output the ANCOVA results, including the p-value, which we will discuss in the next section.

## Interpretation of ANCOVA Results

The p-value in ANCOVA represents the probability that the null hypothesis is true, i.e., there is no difference in means between the groups after controlling for the covariate. A p-value less than 0.05 is generally considered statistically significant, which means that there is evidence to reject the null hypothesis and conclude that there is a significant difference in means between the groups after controlling for the covariate.

In our example, the ANCOVA results show a p-value of 0.02, which is less than 0.05, indicating that there is a statistically significant difference in average exam scores between the traditional study group and the online study group, after controlling for the effect of the current grade. Therefore, the teacher can conclude that the studying techniques have a significant effect on average exam scores, after controlling for the effect of the current grade.

## Data Entry

Data entry is an important step in data analysis, whether you are importing data or creating data. Let’s consider some common data entry tasks in Python.

### Data Import

To import data in Python, you can use the numpy or pandas libraries. For example, to import a CSV file using pandas:

```
import pandas as pd
data = pd.read_csv('filename.csv')
```

This will create a DataFrame from the CSV file.

### Data Creation

To create data in Python, you can use the DataFrame() function from pandas. For example, to create a DataFrame with repeated values:

```
import pandas as pd
data = pd.DataFrame({
'variable1': [1]*10 + [2]*10,
'variable2': ['a', 'b'] * 10
})
```

This will create a DataFrame with 20 rows, where ‘variable1’ has values of 1 and 2 repeated 10 times, and ‘variable2’ has values ‘a’ and ‘b’ repeated 10 times.

### Data View

To view data in Python, you can use the head() function from pandas. For example, to view the first 5 rows of a DataFrame:

```
import pandas as pd
data = pd.read_csv('filename.csv')
data.head()
```

This will display the first 5 rows of the DataFrame.

## Conclusion

In this article, we provided an overview of ANCOVA, an example of ANCOVA in Python, steps to perform ANCOVA in Python, and how to interpret ANCOVA results. We also discussed common data entry tasks in Python.

By understanding ANCOVA and data entry in Python, you can perform more advanced data analysis and make data-driven decisions.

## ANCOVA Function

ANCOVA, or Analysis of Covariance, is a statistical method that allows you to determine if there is a statistically significant difference in means between independent groups, while taking into account the effect of covariates. In Python, you can perform ANCOVA using the pg.ancova() function from the pingouin library.

In this article, we will provide an overview of the ANCOVA function in Python, its parameters, and output.

### Function Overview

The pg.ancova() function in Python performs ANCOVA on a DataFrame and returns an ANCOVA table. The ANCOVA table displays information on the sources of variation, degrees of freedom, sum of squares, mean squares, F-value, and p-value.

### Function Parameters

The pg.ancova() function takes the following parameters:

- data: a DataFrame containing the data
- dv: the dependent variable (response variable)
- covar: the covariate variable
- between: the between-subjects (factor) variable

For example, let’s consider a DataFrame with columns ‘study_technique’, ‘current_grade’, and ‘exam_score’. To perform ANCOVA on this DataFrame using the pg.ancova() function:

```
import pandas as pd
import pingouin as pg
data = pd.read_csv('data.csv')
pg.ancova(data=data, dv='exam_score', covar='current_grade', between='study_technique')
```

### Function Output

The pg.ancova() function outputs an ANCOVA table with the following columns:

- Source: the source of variation (covariate, factor, residual)
- SS: the sum of squares (SS) for each source
- DF: the degrees of freedom (DF) for each source
- MS: the mean square (MS) for each source (SS/DF)
- F: the F-value for the factor source
- p-unc: the uncorrected p-value for the factor source
- np2: the partial eta-squared effect size for the factor source
- Residual: the residual source of variation (error term)

## ANCOVA Result Interpretation

### Overview of Result Interpretation

After performing ANCOVA, the ANCOVA table provides information to help interpret the significance of the results. The ANCOVA table shows whether the factor variable has a significant effect on the dependent variable, after controlling for the effect of the covariate variable.

The p-value in the ANCOVA table indicates the probability of observing the data if the null hypothesis is true. A p-value less than 0.05 indicates that we can reject the null hypothesis and conclude there is a statistically significant difference between the factor levels for the dependent variable.

### ANCOVA Table Analysis

Let’s consider an example to better analyze the ANCOVA table. Suppose we are analyzing the influence of study technique (factor variable) on exam scores (dependent variable), after controlling for current grade (covariate variable).

The ANCOVA table for this example might be:

Source | SS | DF | MS | F | p-unc | np2 |
---|---|---|---|---|---|---|

covar | 1234 | 1 | 1234.00 | 13.46 | 0.001 | 0.39 |

between | 4653 | 1 | 4653.00 | 51.13 | <0.001 | 0.62 |

Resid | 2886 | 117 | 24.66 | |||

Total | 8773 | 119 |

The ANCOVA table for this example shows that the total sum of squares is 8773, with 119 degrees of freedom. The sum of squares for the covariate (current grade) is 1234, with 1 degree of freedom, indicating that the covariate has a significant effect on exam scores.

The sum of squares for the between-subjects factor (study technique) is 4653, with 1 degree of freedom, indicating that there is a significant difference between the study techniques after controlling for the effect of current grade. The residual sum of squares is 2886, with 117 degrees of freedom, and the mean square for the residual is 24.66.

### Rejecting Null Hypothesis

The p-value in the ANCOVA table indicates whether we can reject the null hypothesis. In this example, the p-unc for the between-subjects factor is less than 0.001, which is less than the significance level of 0.05.

Therefore, we can reject the null hypothesis. This means that there is a statistically significant difference in average exam scores between the different study techniques after controlling for the effect of current grade.

A researcher can interpret this result to mean that choosing one study technique will lead to students having a higher average exam score compared to students who use another technique.

## Conclusion

The pg.ancova() function in Python enables you to perform ANCOVA on a DataFrame and output an ANCOVA table that provides valuable information for result interpretation. By understanding how to use the ANCOVA function and interpret ANCOVA results, you can improve your ability to analyze your data and make data-driven decisions.

In this article, we have explored ANCOVA in Python from multiple angles. We have covered the overview of ANCOVA, demonstrated an example of ANCOVA in Python, outlined the steps to perform ANCOVA, and explained how to interpret ANCOVA results.

We have also provided an overview of common data entry tasks in Python. We have gone through the details of the ANCOVA function in Python, the parameters of this function and its output.

Finally, we explained how to interpret the ANCOVA table and its significance. By understanding ANCOVA, ANCOVA in Python functions, and data management techniques, you can conduct more sophisticated data analysis and make confident decisions.