What can you do with a two-year degree from a community...

What can you do with a two-year degree from a community college? Consider the information taken from the September $2,2009,$ USA Today article titled "Health care, energy among 'hot' jobs.". a. Rank the percentage growth and median incomes in ascending order (high to low). b. Compute the Spearman rank correlation coefficient for the two rankings. c. At the 0.05 level of significance, determine whether there is a significant relationship between a job's growth and its corresponding median income. d. Discuss the relationship between a job's growth and its corresponding income.

Key Concepts

Ranking Data

Ranking data involves ordering values from lowest to highest (or vice versa) based on a specific criterion. In statistical analyses, this is particularly useful when dealing with ordinal data or when you want to compare the relative performance of different items. Ranking simplifies comparisons by converting raw numbers into positions, allowing researchers to assess patterns in data without being affected by the actual numerical scale.

Spearman Rank Correlation Coefficient

The Spearman rank correlation coefficient is a non-parametric measure of the strength and direction of the association between two ranked variables. Unlike Pearson’s correlation which requires interval data and assumes a linear relationship, Spearman’s method evaluates monotonic relationships by comparing the rank orders of the data points. It is especially useful when the data do not meet the assumptions of normality or when dealing with ordinal measures.

Hypothesis Testing and Significance Level

Hypothesis testing is a statistical method used to decide whether there is enough evidence in a sample of data to infer that a certain condition holds for the entire population. When using a significance level, such as 0.05, researchers set a threshold probability for rejecting the null hypothesis, which typically represents no effect or no relationship. This process involves comparing the test statistic to a critical value and determining whether the observed relationship is statistically significant.

Interpreting Correlation Relationships

Interpreting a correlation relationship involves assessing both the magnitude and direction of association between variables. A positive correlation indicates that as one variable increases, the other tends to increase as well, whereas a negative correlation suggests an inverse relationship. Understanding these relationships is fundamental in determining how two factors, such as job growth and median income, are related, and helps in making informed decisions based on the data.

Transcript

00:01 In problem 58, we have information about 10 community college jobs.

00:06 This information consists of two columns.

00:10 One column is on the percentage growth, and the other column is on the median income.

00:16 So in the first part of the question, we're going to rank the percentage growth and the median incomes in ascending order, which is from high to low.

00:26 So the highest income would be the first rank and the highest percentage growth would be the first rank.

00:34 After that we're going to compute the spearmandran correlation coefficient for the two rankings.

00:41 Then from there we're going to check whether there's a significant relationship between a job's growth and its corresponding median income.

00:54 So the first thing we need to do here is to introduce two columns.

00:58 The columns for the ranking so we can talk about the ranking for the growth so the first title would be growth ranking and then we have another one for income ranking median income ranking so you can find out you can just order them from the the largest the largest growth to the smallest growth and then you put the assign the different numbers so then the top percentage is for physical therapists assistant jobs and this is the far it's going to get the first ranking 30 30 % percent is the second then we have 28 as a third this is the fourth and and this is the fifth one.

02:12 We have a tie.

02:14 So we're going to have an average of six and seven, which is 6 .5.

02:22 6 .5.

02:25 Then the next one is 8, 9 and 10, because there are no ties.

02:34 So for the median income, you would have to arrange this in order then get the best.

02:41 So the topmost income is for computer specialists, that's number one.

02:49 Second is for radiation therapists.

02:57 Third is for dental hygienists.

03:02 Fourth is for the registered nurses.

03:08 Fifth is the court reporters.

03:15 Sixth is the cardiovascular technicians.

03:20 7th is the occupational therapists assistance 8th in physical therapists assistance and the 9th is the environmental engineering technicians and lastly the 10 is the environmental technicians so now we have both rankings.

03:54 Next, we're going to, in part b of the question, we're going to calculate the spearmann rang correlation coefficient for the two rankings.

04:06 So that is given by the formula below.

04:10 And we have to first of all get the differences in the rankings and then we square the differences.

04:16 So let's call the differences d .i and the squares of the differences d .i.

04:23 Squared.

04:26 Okay, so 1 minus 8 is the first ranking, the first difference in the ranking...

Please give Ace some feedback