Our innovative ANOVA calculator helps to quickly get the one-way and two-way ANOVA tables for up to 10 groups. These tables include all the relevant information from the observed data including the sum of squares, mean squares, degree of freedom, and test statistics.
“ANOVA stands for Analysis of Variance used to compare the means of three or more groups”.
The one way ANOVA calculator functions by partitioning the total variance of sample data into two components: variance between groups and variance within groups.
It is distributed into parts:
“This is used to compare the means of three or more groups based on a single independent variable”.
Characteristics:
Example:
Comparing the mean height of men and women.
“This is used to compare the means of three or more groups based on two independent variables”.
Characteristics:
Example:
Comparing the mean test scores of students who received different types of instruction and different levels of tutoring.
The ANOVA test calculator uses the following formula to summarize the various components.
F = MSB / MSW
Where:
The analysis of variance formula table summarizes the components to evaluate the F-statistic. It typically consists of the following components:
Source | Sum of Squares | Mean Squares | Degrees of Freedom | F Statistics |
Between Groups | SSB = ∑i = 1k ni (X̄i - X̄)2 | MSG = SSG / (k - 1) | k - 1 | F = MSB/MSW |
Within Groups | SSW = ∑i = 1K (ni – 1) Si2 | MSE = SSE / (n - k) | n - k | |
Total | SST = SSB + SSW | Sample Variance = SS | n - 1 |
Variance Between Groups: The variance between groups is a measure of how different the means of the groups are.
Variance Within Groups: The variance within groups is a measure of how much the data points within each group vary around the group mean.
The innovative ANOVA table calculator utilizes the test to determine the influence of independent variables on the dependent variable. There are a couple of steps that are important to consider as follows:
A doctor wants to know to know the difference in mean effectiveness of three different drugs for treatment. The doctor assigned some random numbers to the patients to measure the mean effectiveness of three drugs.
Group # 1: 11, 3, 4, 7, 8
Group # 2: 0, 1, 12, 6, 3
Group # 3: 6, 13, 8, 7, 5
Group 1 | Group 2 | Group 3 |
---|---|---|
11 | 0 | 6 |
3 | 1 | 13 |
4 | 12 | 8 |
7 | 6 | 7 |
8 | 3 | 5 |
∑Group 1 = 33 | ∑Group 2 = 22 | ∑Group 3 = 39 |
(Group 1)² | (Group 2)² | (Group 3)² |
---|---|---|
121 | 0 | 36 |
9 | 1 | 169 |
16 | 144 | 64 |
49 | 36 | 49 |
64 | 9 | 25 |
∑(Group1)² = 259 | ∑(Group2)² = 190 | ∑(Group3)² = 343 |
Data Summary | ||||||
---|---|---|---|---|---|---|
Groups | N | ∑x | Mean | ∑x² | Std. Dev. | Std. Error |
Group 1 | 5 | 33 | 6.6 | 259 | 3.2094 | 1.4353 |
Group 2 | 5 | 22 | 4.4 | 190 | 4.827 | 2.1587 |
Group 3 | 5 | 39 | 7.8 | 343 | 3.1145 | 1.3928 |
Total | 15 | 94 | 6.2666666666667 | 792 |
ANOVA Summary | |||||
---|---|---|---|---|---|
Source | Degrees of Freedom (DF) | Sum of Squares (SS) | Mean Square (MS) | F-Stat | P-Value |
Between Groups | 2 | 29.7333 | 14.8667 | 1.03 | |
Within Groups | 12 | 173.2 | 14.4333 | ||
Total | 14 | 202.9333 |
$$ SS_B = \sum^k_{i=1} n_i(\bar x_i - \bar x)^2 $$
$$ SS_B = 5 * (6.6 - 6.2666666666667)^2 + 5 * (4.4 - 6.2666666666667)^2 + 5 * (7.8 - 6.2666666666667)^2 $$
$$ SS_B = 29.7333 $$
$$ SS_W = \sum^k_{i=1} (n_i − 1)S_i^{\space 2} $$
$$ SS_W = (5 - 1) * (3.2094)^2 + (5 - 1) * (5.7966)^2 + 5 * (7.8 - 6.2666666666667)^2 $$
$$ SS_W = 173.2 $$
$$ SS_T = SS_B + SS_W $$
$$ SS_T = 29.7333 + 173.2 $$
$$ SS_T = 202.9333 $$
$$ MS_B = \dfrac{SS_B}{k - 1} $$
$$ MS_B = \dfrac{29.7333}{3 - 1} $$
$$ MS_B = \dfrac{29.7333}{2} $$
$$ MS_B = 14.8667 $$
$$ MS_W = \dfrac{SS_W}{N - k} $$
$$ MS_W = \dfrac{173.2}{15 - 3} $$
$$ MS_W = \dfrac{173.2}{12} $$
$$ MS_W = 14.4333 $$
$$ F = \dfrac{MS_B}{MS_W} $$
$$ F = \dfrac{14.8667}{14.4333} $$
$$ F = 1.03 $$
Our online two way ANOVA calculator meets the data recovery where the hypothesis becomes insights so it functions well when you come with the below values:
Wikipedia: Analysis of variance, Classes of models, Assumptions, Example, For a single factor.
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