Collect data from 20 (10 males and 10 females) adolescents on approxim

Question

Collect data from 20 (10 males and 10 females) adolescents on approximate duration of time (in hours) they spend on social media in a single day. Compute Mann- Whitney U test to study the effect of gender on the duration of time spend on social media. Ensure that you tabulate the raw data and show the calculations with the help of formulae discussed in the course material of BPCC108.

13 Jul 2023

Answer :

Word Count : 1211

Let's assume we have the following hypothetical data for the duration of time spent on social media in a single day for 10 males and 10 females:

Males: 1, 2, 2, 3, 3, 4, 4, 5, 6, 7 Females: 2, 3, 3, 4, 4, 5, 5, 6, 7, 8

Step 1: Rank the data Rank the combined data (both males and females) in ascending order and assign ranks. In case of ties, assign the average rank.

Sorted data: 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 7, 7, 8

Ranks: 1, 2.5, 2.5, 2.5, 5, 5, 5, 8, 8, 8, 11, 11, 11, 14.5, 14.5, 17, 17, 18

Step 2: Calculate the U statistic for each group The U statistic for each group (males and females) can be calculated using the following formulas:

U_male = n1 * n2 + (n1 * (n1 + 1)) / 2 - R_male U_female = n1 * n2 + (n2 * (n2 + 1)) / 2 - R_female

where:

n1 is the number of observations in group 1 (males)
n2 is the number of observations in group 2 (females)
R_male is the sum of ranks for group 1 (males)
R_female is the sum of ranks for group 2 (females)

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