# How to Interpret ANOVA Results in Excel (3 Ways)

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ANOVA, or Analysis of Variance, is an amalgamation of multiple statistical models to find the differences in means within or between groups. Users can use multiple components of an ANOVA analysis to interpret the results in Excel.

Let’s say we have the ANOVA analysis results as depicted in the below screenshot. In this article, we interpret multiple types of ANOVA results obtained using Excel.

## How to Interpret ANOVA Results in Excel: 3 Easy Methods

In Excel, there are 3 types of ANOVA analysis available. They are

(i) ANOVA: Single Factor:  Single factor ANOVA  is performed when a single variable is in play. The result of the analysis is to find whether the data model has any significant differences in its means. Therefore, it carries two prominent hypotheses to solve.

(a) Null Hypothesis (H0): The factor causes no difference in means within or between groups. If means are symbolized with µ, then the Null Hypothesis concludes: µ1 = µ2 = µ3…. = µN.

(b) Alternative Hypothesis (H1): the factor causes significant differences in the means. Thus, the Alternative Hypothesis results in µ1 ≠ µ2 .

(ii) ANOVA Two-Factor with Replication: When data contains more than one iteration for each set of the factors or independent variables, users apply two factors with replication ANOVA Analysis. Similar to the single factor ANOVA analysis, two factors with replication analysis tests for two variants of Null Hypothesis (H0).

(a) The groups have no difference in their means for the first independent variable.

(b) The groups have no difference in their means for the second independent variable.

For Interaction, users can add another Null Hypothesis stating-

(c) One independent variable does not affect the impact of the other independent variable or vice versa.

(iii) ANOVA Two-Factor without Replication: When more than one task is conducted by different groups, users execute two factors without replication in ANOVA Analysis. As a result, there are two Null Hypotheses.

For Rows:

Null Hypothesis (H0): No significant difference between the means of the different job types.

For Columns:

Null Hypothesis (H0): No significant difference between the means of the different group types.

### Method 1: Interpreting ANOVA Results for Single Factor Analysis in Excel

Executing ANOVA: Single Factor Analysis from Data Analysis Toolpak helps users to find if there is a statistically significant difference between the means of 3 or more independent samples (or groups). The following image showcases the data available to perform the test. Suppose we execute the ANOVA: Single Factor Data Analysis in Excel by going through Data > Data Analysis (in the Analysis section) > Anova: Single Factor (under the Analysis Tools options). The results of the test are depicted in the image below. #### Result Interpretation

Parameters: Anova Analysis determines the Null Hypothesis’s applicability in the data. Different result values from the Anova Analysis outcome can pinpoint the Null Analysis status. Average and Variance: From the Summary, you can see the groups have the highest average (i.e., 89.625) for Group 3 and the highest variance is 28.125 obtained for Group 2. Test Statistic (F) vs. Critical Value (FCrit): Anova results showcase Statistic (F= 8.53) > Critical Statistic (FCrit=3.47). Therefore, the data model rejects the Null Hypothesis. P-Value vs. Significance Level (a): Again, from the ANOVA outcomes, the P Value (0.0019) < the Significance Level (a = 0.05). So, you can say that the means are different and reject the Null Hypothesis. ### Method 2: Decoding ANOVA Results for Two-factor with Replication Analysis in Excel

Alternatively, ANOVA: Two-Factor with Replication evaluates the difference between the means of more than two groups. Let’s assign the below data to perform this analysis. After performing the Anova: Two-factor With Replication Analysis, the outcome may look like the following. #### Result Interpretation

Parameters: P Value only acts as the parameter for the rejection or acceptance of Null Hypothesis. Variable 1 Significant Status: Variable 1 (i.e., Sample) has P Value (i.e., 0.730) greater than the Significance Level (i.e., 0.05). Thus, Variable 1 can’t reject the Null Hypothesis. Variable 2 Significant Status: Similar to Variable 1, Variable 2 (i.e., Columns) has a P Value (i.e., 0.112) which is greater than 0.05. In this case, Variable 2 also falls under the Null Hypothesis. Therefore, the means are the same. Interaction Status: Variables 1 and 2 don’t have any interaction as they have a P Value (i.e., 0.175) more than the Significance Level (i.e., 0.05). Overall, no variable exerts any significant effect on each other.

Mean Interaction: Among the means for Groups A, B, and C, Group A has the highest mean. But these mean values don’t tell whether this comparison is significant or not. In this case, we can look at the mean values for Groups 1, 2, and 3. The mean values of Groups 1, 2, and 3 have greater values for Group 3. However, as no variables have significant impact on each other. Also, there are no significant interaction effects as the entries seem to be random and repetitive within a range.

### Method 3: Translating ANOVA Results for Two-factor Without Replication Analysis in Excel

When both factors or variables influence dependent variables, users usually execute ANOVA: Two-factor Without Replication Analysis. Let’s say we use the latter data to perform such an analysis. The results of a two factor without replication analysis look similar to the following. #### Result Interpretation

Parameters: Two-factor ANOVA Analysis Without Replication has similar parameters as the single factor ANOVA. Test Statistic (F) vs Critical Value (FCrit): For both variables, the Statistic values (F= 1.064, 3.234) < Critical Statistic (FCrit=6.944, 6.944). As a result, the data model can’t reject the Null Hypothesis. So, the means are equivalent. P-Value vs Significance Level (a): Now, in the ANOVA outcomes, the P values (0.426, 0.146) > the Significance Level (a = 0.05). In that case, you can say that the means are the same and accept the Null Hypothesis. Read More: How to Do Two Way ANOVA in Excel

## Conclusion

In this article, we describe the types of ANOVA analysis and demonstrate the way to interpret ANOVA results in Excel. We hope this article helps you to understand the outcomes and gives you the upper hand to choose the respective ANOVA analyses that best fit your data. Comment if you have further inquiries or have anything to add.

Happy Excelling.

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