Organization

Organization Name

I began by attempting to complete a simple ANOVA of the Visual Motor Composite Score and Organization Name, but some of the sample sizes were too small; therefore, I moved organizations with fewer than 30 participants to the other category: zzz retiredJohnBapt xxx

Bayside Neurorehab

County Physical Training

Deer Isle Stonginton HS

Mayo Regional Hospital

Orthopaedic Associates

Retired Lakes Regional HS

Dexter Regional HS

Sumner Memorial HS

Monmoth HS

Searsport HS

Then after ensuring the the variances are approximately equal across all groups, the ANOVA was completed. It had the following results: F = 21.44, p- value < 0.000. This indicates that at least one mean visual motor composite score is different than the rest.

I then completed a Bonferroni Unplanned T-Test to try to find the point of divergence in the mean Visual Motor Composite Score. See results of Bonferroni Unplanned T-Test in analysis-output.txt. This was also hard to understand and find the importance of the significant differences because there were so many organizations that were compared.

I then completed a Chi-Squared Test for Association using the categorical variable LowVM that indicates whether the data point has a Visual Motor Composite Score less than or equal to 17. Since the expected counts for the Low VM score group were too low for a normal Chi-Squared test and a Fisher's exact test is computationally intractable with this many categories, a randomization based chi-squared test was used. It found a chi-squared value of 324.378 and a p-value < 0.000 (Chi-square Test for Association - wo small groups.htm). This is the break-down of the proportion of participants who fall into the Low VM group in each organization (in %):

The schools with >=2% LowVM are:

(other)

Hebron Academy

Portland High School

Lewiston High School

Deering High School

North Yarmouth Academy

Edward Little High School

Central Aroostook High School

Maranacook Regional HS

Messalonskee HS

W S Cohen School

Easton HS

Freeport High School

Gould Academy RSU 24 Ellsworth HS and Sumner HS

Penquis Valley HS

Wisdom Middle and High School MSAD 33

Carrabassett Valley Academy

Lee Academy

KKAYFA

At this point it had become clear that the low VM scores were in some way related to the organization. It was less clear, however, what about these organizations was associated with the low vm scores.

Therefore, I broke the organizations into three categories: type, county and region. The type has 3 categories: public school, private school, and other. There are 17 counties included: Unknown, Waldo, Kennebec, Androscoggin, Oxford, York, Cumberland, Sagadahoc, Knox, Aroostook, Penobscot, Franklin, Somerset, Hancock, Lincoln, Piscataquis, Washington. There are 6 regions included: Unknown, Midcoast, Southern, Western, Northern, Eastern (based on the MaineDOT regions of service).

Organization Type

I started by completing a chi-squared test of the Organization Type and the Low VM. The expected counts were greater than 5, so the conditions are satisfied. The results of the chi squared test showed a chi squared value of 3.9958 and a p-value of 0.1356. There is not enough evidence to suggest that there is an association between having a low visual motor composite score and what type of organization the testing occurs at.

I also completed an ANOVA of organization type and visual motor composite score. There are at least 30 participants in each group and the variances are approximately equal. The results (F =47.38, p-value<2x10-16 ) shows that at least one mean visual motor composite score differs from the rest. This is interesting since there was not an association between organization type and low VM score.

Organization Region

Eastern Midcoast Northern Southern Unknown Western

Not 5429 6444 2802 21590 289 4838 LowVM LowVM 66 71 30 284 6 88 Proportion 0.01201092 0.01089793 0.01059322 0.01298345 0.02033898 0.01786439 I then investigated the relationship between organization region and low VM status. I tried to complete a chi squared test on the region of the organization and the Low VM, but there was an expected less than 5, so it could not be used. Therefore, I used a Fisher’s Exact Test, which should a p-value of 0.016, which indicates that there is an association between having a low VM Composite score and region of the organization.

Residuals from Chi-squared test:

Eastern Midcoast Northern Southern Unknown Western Low VM 0.0734779 0.1704326 0.1286897 0.0018211 -0.1269529 -0.3439549 3 1 4 7 Not Low -0.6403492 -1.4852947 -1.1215119 -0.0158712 1.1063757 2.9975156 VM 6 0

I then tried an ANOVA to determine if there is an overall association between the visual motor composite score and the region where the organization is located. First checking the conditions, the variance in the regions are similar and there are at least 30 participants in each category. Therefore, the conditions for the ANOVA hold. The results show an F-value of 12.44 and the p-value is 4.34x10-12. There is enough evidence to claim that at least one mean visual motor composite score varies from the rest.

To determine where the significant differences exist, a Bonferroni T-Test is used. It finds a significant difference between the mean visual motor composite score in Eastern and Midcoast (p-value = 9.1 x10-6), Eastern and Southern (p-value = 1.6 x 10-7), Southern and Northern (p-value = 0.0350), Midcoast and Unknown (p-value = .0013), Unknown and Southern (p-value = 0.0014), Midcoast and Western (p-value = 0.0082), and Southern and Western (p- value = 0.0020).

Mean VM Composite 33.6978 34.3417 33.8782 34.3066 32.6913 33.8815 Score 5 6 5 6 6 9

Summary:

ANOVAs: Organization Name and Visual Motor Composite Score: p-value < 0.000 Organization Type and Visual Motor Composite Score: p-value < 2x10-16 Organization Region and Visual Motor Composite Score: p-value = 4.34x10-12

Chi-Squared: Organization Name and LowVM: p-value <0.000 Organization Type and LowVM: 0.1356 Organization Region and LowVM: 0.016