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  3. Inferential Statistics
  • 1

    The Basics of R

    This lab is about teaching enough R to start using it for statistical analyses.

  • 2

    Introduction to R continued

    This lab continues with an introduction to R

  • 3

    Comparing two groups

    The current lab treats differences between two independent groups, paired groups and proportions

  • 4

    Categorical Association

    Investigating associations between categorical variables.

  • 5

    Simple Regression

    Predicting a response variable one predictor variable.

  • 6

    Multiple Regression

    Predicting a response variable with more than one predictor variable.

  • 7

    Quantitative associations: ANOVA

    This lab treats the statistical methodology of the analysis of variance

  • 8

    Nonparametric tests

    This lab will treat testing methods that can be employed when the assumptions of other methods are not met

Initializing

Exercise

Calculating the between group variance

Now that we've got our grand mean and the means of the different genres, we can calculate the between group variance. The formula for the between group variance is the following: $$\frac{n_1 * (\bar{y}_1 - \bar{y})^2 + n_2 * (\bar{y}_2 - \bar{y})^2 + ... + n_g * (\bar{y}_g - \bar{y})^2}{g - 1}$$

Okay, this formula looks really complicated so let's chop it up into parts. n here represents the sample size, so \(n_1\) represents the sample size of group 1 while \(n_g\) represents the sample size of gth group. In our current example, we only have three different genres and thus three different groups so this formula would go up \(n_3\). \(\bar{y}_1\) represents the average of group 1. \(\bar{y}\) would represent our overall average which is available in the variable grand_mean. g here represents the number of groups.

In the current exercise our overall average is stored in the console in the variable grand_mean while our group averages are stored in the variables classical_average, hiphop_average and pop_average. The dataframes classical_data, hiphop_data and pop_data contain our samples per genre.

Instructions

100 XP
  • Calculate the sample size of each group. Store the sample size of the classical genre in the variable called sample_classical, the sample size of hip hop genre in the variable called sample_hiphop and the sample size of the pop genre in the variable sample_pop. Because these are all dataframes, you can use the nrow() function on for instance the dataframes classical_data to calculate the sample size of this genre.
  • Calculate the between group variance and store it in a variable called between_group_variance.