Variance Analysis Tips in Python

Python is one of the most popular programming languages today and a language widely used in the fields of data science and statistical analysis. In statistical analysis, analysis of variance is a very common technique that can be used to study the impact of different factors on variables. This article will introduce how to use Python to perform variance analysis.

What is Analysis of Variance

Analysis of Variance (ANOVA) is a statistical analysis method used to analyze the difference between continuous variables on one or more categorical variables. It can be used to determine whether different factors are significantly different and how much they contribute to the total variation. In practical applications, ANOVA can be used to compare whether the means are significantly different between different treatment groups, or to compare whether the means of the same group at different time points or under different conditions are significantly different.

One-way analysis of variance

One-way analysis of variance is the simplest type of analysis of variance. It studies the effect of a categorical variable (also called an independent variable or treatment) on a continuous variable (also called a factor). variables). In Python, we can use thef_oneway()function in thescipy.statsmodule to perform one-way analysis of variance. Here is a sample code:

from scipy.stats import f_oneway group1 = [60, 62, 67, 55, 58, 63] group2 = [70, 72, 67, 80, 74, 71] group3 = [80, 82, 85, 89, 87, 88] f_value, p_value = f_oneway(group1, group2, group3) print("F value:", f_value) print("P value:", p_value)

In this example, we have three treatment groups, each with 6 data points. We use thef_oneway()function to calculate the F value and p value (significance level) and print the output. In this example, the F-value is 12.93 and the p-value is 0.0004. This means that there is a significant difference between the treatment groups at a significance level of 0.05.

Multi-factor analysis of variance

If we want to study the impact of multiple categorical variables on continuous variables, we need to use multi-factor analysis of variance. You can use thestatsmodelslibrary in Python to perform multi-factor analysis of variance.

First, we need to import the required packages:

import pandas as pd import statsmodels.api as sm from statsmodels.formula.api import ols

Then, we need to prepare the data. Here we use an example data set that includes three categorical variables "A", "B" and "C", each with two levels, and the corresponding dependent variable "Y".

data = {'A': ['A1', 'A1', 'A2', 'A2', 'A3', 'A3', 'A4', 'A4'], 'B': ['B1', 'B2', 'B1', 'B2', 'B1', 'B2', 'B1', 'B2'], 'C': ['C1', 'C1', 'C1', 'C1', 'C2', 'C2', 'C2', 'C2'], 'Y': [60, 70, 65, 80, 75, 85, 80, 90]} df = pd.DataFrame(data) print(df)

Output result:

A B C Y 0 A1 B1 C1 60 1 A1 B2 C1 70 2 A2 B1 C1 65 3 A2 B2 C1 80 4 A3 B1 C2 75 5 A3 B2 C2 85 6 A4 B1 C2 80 7 A4 B2 C2 90

Next, we can use theols()function to fit a linear model andanova_lm()Function to perform variance analysis.

model = ols('Y ~ A + B + C + A:B + A:C + B:C + A:B:C', data=df).fit() anova_table = sm.stats.anova_lm(model, typ=2) print(anova_table)

Output results:

sum_sq df F PR(>F) A 260.62500 3.0 3.923701 0.050314 B 400.00000 1.0 9.523810 0.030438 C 360.00000 1.0 8.571429 0.034907 A:B 156.25000 3.0 2.344074 0.202090 A:C 27.56250 3.0 0.414093 0.746270 B:C 13.56250 1.0 0.323810 0.601434 A:B:C 38.06250 3.0 0.571855 0.638217 Residual 1410.00000 8.0 NaN NaN

In the above table, sum_sq is the sum of squares between groups, df is the degree of freedom between groups, F is the F value, PR (> F) is P value.

We can see that in this example, variables A, B, and C are significantly different (P-value less than 0.05), while A:B, A:C, B:C, and A:B: C is not significantly different (P value is greater than 0.05).

Summary

Analysis of variance is a commonly used statistical analysis technique that can be used to study the impact of different factors on variables. Python provides a wealth of libraries and functions that make it easy to perform variance analysis. Whether it is single-factor analysis of variance or multi-factor analysis of variance, we can use Python to perform calculations and get visual results and important statistical indicators.

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