__ANOVA (Analysis of Variance)__

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ANOVA, or Analysis of Variance, is a statistical technique used to compare the means of different groups in a sample. It is used to see if there are any statistically significant variations in mean values between two or more groups. The process entails dividing the entire variability of the data into several sources of variance.This is done by **SAS** in Easy Manner.

To do a one-way ANOVA (Analysis of Variance) the conventional way, follow these steps:

Step 1:

First, create your hypothesis.

- The null hypothesis (H0) states that all groups’ means are equal.
- A distinct group mean exists, according to the alternative hypothesis (Ha).

Step 2:

Gather Data: Gather information from every group you intend to compare. ANOVA requires that the data be numerical and that the variances be independent, normal, and homogeneous.

Step 3:

Compute Group Statistics: Determine each group’s mean and variance. Calculate the overall mean as well as the total sum of squares (SST), which represents all of the data’s variability.

Step 4:

Calculate the between-group variability in step four.

Identify the diversity between the group averages and the overall mean by computing the sum of squares between groups (SSB). SSB is calculated using the formula (ni * (Xi – X))2, where ni is the sample size for each group, Xi is the mean for each group, and X is the overall mean.

Step 5:

Calculate the within-group variability:

Identify the variability within each group by computing the sum of squares within groups (SSW). SSW is equal to ((Xij – Xi)2), where Xij denotes each individual data point and Xi is the group mean.

Step 6:

Calculate the F-Statistic :

F = (SSB / (k – 1)) / (SSW / (N – k)), where k is the number of groups and N is the total number of observations, to get the F-statistic.

Step 7:

Determine the critical value or p-value:

To get the p-value associated with the F-statistic, compare the estimated F-statistic with the critical value from an F-distribution table or utilise statistical software.

Step 8:

Make a decision:

Reject the null hypothesis if the p-value is less than the selected significance level, which is typically 0.05. There is proof that the means of at least two groups differ significantly.

Reject the null hypothesis if the p-value is larger than or equal to the significance level. To infer that there is a substantial difference between the group means would require further data.

Step 9:

Post-hoc Analysis (if required)

Conduct post-hoc tests (such as Tukey’s HSD or Bonferroni) to identify which particular group means are substantially different if you reject the null hypothesis.