Twenty ethnic, racial, or national groups were rated by a...

Name: Problem 13, Chapter 12: The Essentials of Statistics: A Tool for Social Research
Uploaded: 2020-09-18T18:41:27-08:00
Duration: 7 min 16 s
Channel: Harsh Gadhiya
Description: Twenty ethnic, racial, or national groups were rated by a random sample of white and black students on a Social Distance Scale. Lower scores represent less social distance and less prejudice. How similar are these rankings?

Twenty ethnic, racial, or national groups were rated by a random sample of white and black students on a Social Distance Scale. Lower scores represent less social distance and less prejudice. How similar are these rankings?

Key Concepts

Nonparametric Statistical Methods

Nonparametric statistical methods do not rely on assumptions about the probability distribution of the data, which makes them ideal for analyzing ordinal data. These methods, including the calculation of rank correlation coefficients, enable researchers to draw inferences from data that do not meet the strict criteria required by parametric tests.

Ordinal Data Analysis

Ordinal data analysis involves working with data that are categorized in a ranked order where the exact differences between the ranks are not necessarily equal. This type of analysis is common in social sciences, where responses are often collected on scales that reflect order without assuming precise numerical differences between ranks.

Rank Correlation Coefficients

Rank correlation coefficients, such as Spearman’s rho and Kendall’s tau, are statistical measures used to evaluate how closely two rankings are related. They assess the strength and direction of association between two sets of ordinal data, making them especially suitable for comparing the similarity of rankings derived from non-numeric scales.

Transcript

00:02 The proportions at two colleges are given.

00:06 In the first college, there are 2051 hispanic students out of 1, 2, 3 ,28.

00:13 And then second college, there are 321 out of 241.

00:18 The null hypothesis for this question will be that the proportion of these two colleges are equal, that there is no difference.

00:30 So this is let's say p c is equal to p l this is our null hypothesis and the alternative hypothesis is going to be both of these are not equal p c is not equal to p l what is going to be the random variable the random variable is going to be the difference of the proportion of these two colleges p c minus p l or right now let's find the z statistic we are going to use the normal distribution here this will follow a normal distribution so the z statistic what is the z statistic it is a difference of the sampled proportions let's look at the sample of proportions this is going to be 2051 divided by 1 2 3 to 8 so this is 0 .166 this is 0.

01:38 The other proportion is 321 divided by 2441 and this is 0 .1315.

01:50 The difference between these two is the 0 .166 minus 0 .1315.

02:02 This is around 0 .0345.

02:06 So this is 0 .0345 minus you know the hypothesized proportions difference over here the null hypothesis is that they both are equals the difference will be 0 upon pooled proportion what is pooled proportion the pooled proportion we have to find out using 2051 2 2051 plus 321 which is equal to 2372 so this is going to be 237 2 .3272 in the numerator divided by m plus n that is the sample size of both the cases that is 1 2 328 plus 2441 so this is 14769 in the denominator we have 147769 what is this division? 2372 divided by 14769.

03:18 This is 0 .16.

03:20 This is 0 .16 multiplied by 1 minus this value.

03:27 So this is going to be 0 .83 .839 around multiplied by 1 upon n plus 1 upon m.

03:45 Now what is 1 upon n? that is the first proportion...

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