Question

There are two variables: Favorite film genre and favorite literary genre. Calculate lambda

using literary genre to predict Film Genre.

Literary Genres

mystery sci fi classics

film action 22 42 24

genres comedy 58 52 18

drama 26 30 12

Answer 1

Lambda is defined as an asymmetrical measure of association that is suitable for use with nominal variables.Lambda provides us with an indication of the strength of the relationship between independent and dependent variables. As an asymmetrical measure of association, lambda’s value may vary depending on which variable is considered the dependent variable and which variables are considered the independent variable.

To calculate lambda, you need two numbers: E1 and E2.

1. E1 is the error of prediction made when the independent variable is ignored. To find E1, you first need to find the mode of the dependent variable and subtract its frequency from N. E1 = N – Modal frequency.
2. E2 is the errors made when the prediction is based on the independent variable. To find E2, you first need to find the modal frequency for each category of the independent variables, subtract it from the category total to find the number of errors, then add up all the errors.

The formula for calculating lambda is: Lambda = (E1 – E2) / E1.

Lambda may range in value from 0.0 to 1.0.

• Zero indicates that there is nothing to be gained by using the independent variable to predict the dependent variable. In other words, the independent variable does not, in any way, predict the dependent variable.
• A lambda of 1.0 indicates that the independent variable is a perfect predictor of the dependent variable. That is, by using the independent variable as a predictor, we can predict the dependent variable without any error.

Film Genre	Frequency
Film action	88
Genres comedy	128
Drama	68
Total	284

Let's say you want to guess what the rating of another 284 people would be. Your best guess would be to pick to modal category, which is "Genres comedy" . If you consistently pick "Genres comedy," you will make the fewest number of wrong guesses. Original error=128 right and (284-128)=156 wrong (out of 284 total guesses).

Now, let's say that you are given one additional piece of information. You now know what the frequency of literary genre: mystery,sci fi and classics.

	literary genre
Film Genre	Mystery	Sci fi	Classics	Total
Film action	22	42	24	88
Genres comedy	58	52	18	128
Drama	26	30	12	68
Total	106	124	54	284

Now, if you had to guess the lierary genre rating, you could qualify your best guess by knowing the literary genre. For each literary genre, you would guess the modal category.

literary genre	N	Modal category	Right Guess	Wrong guess
Mystery	106	Genres comedy	58	48
Sci fi	124	Genres comedy	52	72
Classics	54	Film action	24	30
Total			134	150

The total number of new errors (wrong guesses) is 150

To calculate Lambda, subtract the number of new errors from the number of original errors and divide by the number of original errors. In this case, [(156-150)/156]=0.038

By knowing literary genre, we can reduce the error in predicting Film Genre by 26.3%. This indicates a weak or negligible relationship between literary genre and Film Genre.

As the independent variable is measured on a nominal scale, there is no direction for the relationship (neither positive nor negative, just an association).