In this video, we'll study analysis of variance. Assume that we want to analyze a categorical variable and see the correlation among different categories. For example, consider the car dataset. The question we may ask is, how different categories that make feature as a categorical variable has impact on the price? The diagram shows the average price of different vehicle makes. We do see a trend of increasing prices as we move right along the graph. But which category in the make feature has the most and which one has the least impact on the car price prediction? To analyze categorical variables such as the make variable, we can use a method such as the ANOVA method. ANOVA is statistical test that stands for Analysis of Variance. ANOVA can be used to find the correlation between different groups of a categorical variable. According to the car dataset, we can use ANOVA to see if there is any difference in mean price for the different car makes such a Subaru and Honda. The ANOVA test returns two values, the F-test score and the p-value. The F-test calculates the ratio of variation between the groups mean, over the variation within each of the sample groups. The p-value shows whether the obtained result is statistically significant. Without going too deep into the details, the F-test calculates the ratio of variation between groups means over the variation within each of the sample group means. This diagram illustrates a case where the F test score would be small. Because as we can see, the variation of the prices in each group of data is way larger than the differences between the average values of each group. Looking at this diagram, assume that group one is Honda and group two is Subaru. Both are the make feature categories. Since the F-score is small, the correlation between price as the target variable and the groupings is weak. In the second diagram, we see a case where the F-test score would be large. The variation between the averages of the two groups is comparable to the variations within the two groups. Assume that group one is Jaguar and group two is Honda. Both are the make feature categories. Since the F-score is large, thus the correlation is strong in this case. Getting back to our example, the bar chart shows the average price for different categories that make feature. As we can see from the bar chart, we expect a small F-score between Hondas and Subaru because there is a small difference between the average prices. On the other hand, we can expect a large F-value between Hondas and Jaguars, because the differences between the prices is very significant. However, from this chart, we do not know the exact variances. So, let's perform an ANOVA test to see if our intuition is correct. In the first line we extract the make and price data, then, we'll group the data by different makes. The ANOVA test can be performed in Python using the f underscore oneway method, as the built-in function of the SI/PI package. We pass in the price data of the two car make groups that we want to compare and it calculates the ANOVA results. The results confirm what we guessed at first. The prices between Hondas and Subarus are not significantly different as the F-test score is less than one and p-value is larger than 0.05. We can do the same for Honda and Jaguar. The prices between Honda's and Jaguars are significantly different since the F-score is very large. F equals 401 and the p-value is larger than 0.05. All in all, we can say that there's a strong correlation between a categorical variable and other variables if the ANOVA test gives us a large F-test value and a small p-value.