final
Nonparametric Tests
Chapter 15
Errors
TYPE I
-rejecting a true null hypothesis
TYPE II
-failing to reject a false hypothesis
Chi-Square is an important nonparametric test to be able to perform
Chapter 15 has more information than you may use in your program
You should read through Chapter 15 for exposure, but concentrate on Spearman’s Correlation of Ranked Data
Understand that we are covering information in a nontraditional order to highlight the purpose of the information and its importance to you
If you are completely lost and words are being used that you never heard, a short read may help
Sampling & Distribution of Samples – read over Chapter 8
Standard deviation – Chapter 4
Normally Distributed – Chapter 7 talks about distributions
Where are we??
Spearman’s rs
A descriptive “statistic”
Mathematical expression of degree to which two sets of ranked data are related
Referred to as a correlation coefficient but is specifically for two sets of ranked data
Most often used when the number of pairs is less than 20
Special case of the correlation coefficient we will work with in Chapter 6
Calculating Spearman’s rs
D is the difference in ranks of a pair of scores
N is the number of pairs of scores
means find the sum
Example
In the Gunther High School athletic department, does a person’s track performance give any indication to their academic performance?
| Name | Track Ranking | Class Standing | Class Rank |
| Joe | 1 | 47 | 3 |
| Amy | 2 | 80 | 5 |
| Nick | 3 | 76 | 4 |
| Susan | 4 | 8 | 2 |
| Andrea | 5 | 3 | 1 |
| Jacob | 6 | 85 | 6 |
Example
In the Gunther High School athletic department, does a person’s track performance give any indication to their academic performance?
| Name | Track Ranking | Class Standing | Class Rank | Difference | |
| Joe | 1 | 23 | 3 | ||
| Amy | 2 | 80 | 5 | ||
| Nick | 3 | 76 | 4 | ||
| Susan | 4 | 8 | 2 | ||
| Andrea | 5 | 3 | 1 | ||
| Jacob | 6 | 85 | 6 |
Example
In the Gunther High School athletic department, does a person’s track performance give any indication to their academic performance?
| Name | Track Ranking | Class Standing | Class Rank | Difference | |
| Joe | 1 | 23 | 3 | -2 | |
| Amy | 2 | 80 | 5 | ||
| Nick | 3 | 76 | 4 | ||
| Susan | 4 | 8 | 2 | ||
| Andrea | 5 | 3 | 1 | ||
| Jacob | 6 | 85 | 6 |
Example
In the Gunther High School athletic department, does a person’s track performance give any indication to their academic performance?
| Name | Track Ranking | Class Standing | Class Rank | Difference | |
| Joe | 1 | 23 | 3 | -2 | |
| Amy | 2 | 80 | 5 | -3 | |
| Nick | 3 | 76 | 4 | ||
| Susan | 4 | 8 | 2 | ||
| Andrea | 5 | 3 | 1 | ||
| Jacob | 6 | 85 | 6 |
Example
In the Gunther High School athletic department, does a person’s track performance give any indication to their academic performance?
| Name | Track Ranking | Class Standing | Class Rank | Difference | |
| Joe | 1 | 23 | 3 | -2 | |
| Amy | 2 | 80 | 5 | -3 | |
| Nick | 3 | 76 | 4 | -1 | |
| Susan | 4 | 8 | 2 | ||
| Andrea | 5 | 3 | 1 | ||
| Jacob | 6 | 85 | 6 |
Example
In the Gunther High School athletic department, does a person’s track performance give any indication to their academic performance?
| Name | Track Ranking | Class Standing | Class Rank | Difference | |
| Joe | 1 | 23 | 3 | -2 | |
| Amy | 2 | 80 | 5 | -3 | |
| Nick | 3 | 76 | 4 | -1 | |
| Susan | 4 | 8 | 2 | 2 | |
| Andrea | 5 | 3 | 1 | 4 | |
| Jacob | 6 | 85 | 6 | 0 |
Example
In the Gunther High School athletic department, does a person’s track performance give any indication to their academic performance?
| Name | Track Ranking | Class Standing | Class Rank | Difference | |
| Joe | 1 | 23 | 3 | -2 | 4 |
| Amy | 2 | 80 | 5 | -3 | |
| Nick | 3 | 76 | 4 | -1 | |
| Susan | 4 | 8 | 2 | 2 | |
| Andrea | 5 | 3 | 1 | 4 | |
| Jacob | 6 | 85 | 6 | 0 |
Example
In the Gunther High School athletic department, does a person’s track performance give any indication to their academic performance?
| Name | Track Ranking | Class Standing | Class Rank | Difference | |
| Joe | 1 | 23 | 3 | -2 | 4 |
| Amy | 2 | 80 | 5 | -3 | 9 |
| Nick | 3 | 76 | 4 | -1 | |
| Susan | 4 | 8 | 2 | 2 | |
| Andrea | 5 | 3 | 1 | 4 | |
| Jacob | 6 | 85 | 6 | 0 |
Example
In the Gunther High School athletic department, does a person’s track performance give any indication to their academic performance?
| Name | Track Ranking | Class Standing | Class Rank | Difference | |
| Joe | 1 | 23 | 3 | -2 | 4 |
| Amy | 2 | 80 | 5 | -3 | 9 |
| Nick | 3 | 76 | 4 | -1 | 1 |
| Susan | 4 | 8 | 2 | 2 | 4 |
| Andrea | 5 | 3 | 1 | 4 | 16 |
| Jacob | 6 | 85 | 6 | 0 | 0 |
Example
| Name | Track Ranking | Class Standing | Class Rank | Difference | |
| Joe | 1 | 23 | 3 | -2 | 4 |
| Amy | 2 | 80 | 5 | -3 | 9 |
| Nick | 3 | 76 | 4 | -1 | 1 |
| Susan | 4 | 8 | 2 | 2 | 4 |
| Andrea | 5 | 3 | 1 | 4 | 16 |
| Jacob | 6 | 85 | 6 | 0 | 0 |
Example
| Name | Track Ranking | Class Standing | Class Rank | Difference | |
| Joe | 1 | 23 | 3 | -2 | 4 |
| Amy | 2 | 80 | 5 | -3 | 9 |
| Nick | 3 | 76 | 4 | -1 | 1 |
| Susan | 4 | 8 | 2 | 2 | 4 |
| Andrea | 5 | 3 | 1 | 4 | 16 |
| Jacob | 6 | 85 | 6 | 0 | 0 |
Example
Using Table L in Appendix C, we look to the row for 6 subject:
| Number of Pairs | Two-Tailed .01 | Two-Tailed 0.05 |
| 6 | 1.00 | 0.886 |
We first ranked track performance, so a positive indicates that track performance could indicate a better academic performance…HOWEVER,
After looking at the table, our statistic is not greater than or equal to either value, so our assumed correlation is not reasonable.
At this point, you would do one of the following:
Gather more data
Change your hypothesis (or test)
Move on to other problems
Next Steps:
Read Chapter 15 if you have not already
Read places you need to refresh in memory