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Perform one-way or two-way ANOVA tests by putting data values separated by commas.

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This ANOVA calculator performs both one-way and two-way ANOVA tests for analysis of variance. It provides step-wise calculations including mean, standard deviation, standard error, degrees of freedom, sum of squares, mean square, F-statistic, and p-value to support the analysis.

ANOVA is the short form of **“Analysis of Variance”**. It is the statistical method for evaluating and comparing the average of two or more values.

The analysis of variance helps us a lot in various fields including:

- Medical research
- Social sciences
- Manufacturing
- Agriculture
- Business

Source of Variation | Sum of Squares | Degrees of Freedom | Mean Squares | F Value |
---|---|---|---|---|

Between Groups | SSB = Σn(X - X̄)² | df₁ = k - 1 | MSB = SSB/(k-1) | f = MSB/MSE |

Error | SSE = ΣΣ(X - X̄)² | df₂ = N - k | MSE = SSE / (N-k) | |

Total | SST = SSB + SSE | df₃ = N - 1 |

The one-way ANOVA test helps to assess the difference in means among three or more groups. It uses one independent variable. This test is determined by the steps below:

- Find the mean of given groups
- Calculate the sum of squares between groups (SSB) and within groups (SSW)
- Calculate degrees of freedom between groups (dfB) and within groups (dfW)
- Calculate the mean square between (MSB) and the mean square within (MSW)
- Find the f-value by using the formula F = MSB / MSW
- Compare calculated F-statistic with critical F-value and make a decision

➥ If F-statistic > critical F-value, reject H0 (there is a significant difference).

Suppose a former needs to compare the crops of corn by using difference of fertilizers (A, B, C)

**Groups:**

- Group 1 = Corn fertilized with A
- Group 2 = Corn fertilized with B
- Group 3 = Corn fertilized with C

**Dependent Variable:**

- Corn yield

The former has a chance to use one-way ANOVA to find the difference in corn yields by using three different types of fertilizers. In addition to that the use of this online ANOVA calculator provides reliable results to determine the impact of various fertilizer types on corn yield.

Two-way ANOVA is a statistical approach that helps to evaluate the effects of two independent categorical variables on a quantitative dependent variable. Follow the steps to do two-way ANOVA.

- Find the sum of squares for every factor and integrate them into the dataset
- Calculate the degree of freedom
- Find the mean square of values for each factor
- Determine the f-value for factors and interaction
- Compute the p-value and compare these values

➥ Reject null hypotheses if F-statistics > critical F-values

Suppose, a researcher wants to analyze the impact of various teaching styles like online, traditional, or hybrid and the student's learning methods such as visual, auditory, or kinesthetic on final exam scores.

**Independent Variables:**

- Factor A = Teaching method
- Factor B = Learning style

**Dependent Variable: **

- Exam score

A two-way ANOVA will allow the researcher to determine if there is a significant interaction between teaching method and learning style on exam scores and the main effects of each factor on exam scores.

- Normality: The data available in each group should be distributed normally
- Homogeneity of variances: The variances of the groups should be equal
- Independence: There should be independent observations within and between various groups

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