# Statistics Impact Project

## Is there an association between wearing corrective eye-wear and ethnicity?

We got the idea for our survey from reading this document. We were reading the news and saw a scientific paper from Ohio State University that said that ethnicity played a role in research problems. Since we both wore glasses, we decided to create and take a survey in our school to test the hypothesis in our community.

## Bias

To find out, first we considered bias. The types of bias that could be found in the survey are nonresponse and undercoverage bias. There is a chance for undercoverage bias because it was an online survey and some may have not been able to respond due to lack of technology. There is also a chance for nonresponse bias because students surveyed could have chosen to not respond to the survey even though they were asked to do so. We minimized response bias by asking teachers to directly ask and force their students to take the survey.

## Confounding Variables

A possible confounding variable in this observation is if the students responding to the survey wear or use reading glasses. Since reading glasses are used on for reading and not for daily life, the students responding may be unsure whether to classify wearing reading glasses as yes or no. This confounding variable was minimized due to the addition of another response choice, for those who wore reading glasses. Although in none of the responses students picked reading glasses, the effect of reading glasses as a confounding variable was minimized for the Chi Squared Test.

## Subject Selection

Subjects were chosen with randomization. This was accomplished by asking each teacher who's classes were surveyed to choose two random classes out of their four to survey. Subjects were chosen from a large variety of classes, such as Orchestra, Chemistry, World History, and Statistics. A random number generator was used on a calculator to generate 2 random integers between 1 and 4, and these would be the periods we surveyed for each teacher. At the end, we ended up with 113 responses, as indicated by the charts below

## Chi Squared Test For Independence

Now that we gathered 113 responses, it was time to perform a Chi-square test of independence using the .05 significance level.

P- We are testing to see if there is an association between need for corrective eye-wear (glasses or contacts) and ethnicity at the alpha level a= .05.

H- H₀-There is no association between need for corrective eye-wear(glasses or contacts) and ethnicity

Ha-There is an association between need for corrective eye-wear(glasses or contacts) and ethnicity

A-Random- Samples were taken using random sampling by selecting 2 periods for teachers we got signatures from using random number generator, and we surveyed all students in those periods for the teachers. 10%: 113<10% of all students at Flower Mound High School. All expected counts are at least five.

N- Chi square test for independence with an alpha level of a= .05

T- x^2 = (24-25.12)^2/25.12 + (19-17.88)^2/17.88 +...+(21-24.54)^2/24.54

x^2= 3.8706

O- df=(5-1) * (2-1) = 4 * 1 =4, P(x2 > 3.8706) = .424

M- Since the P-value p=.424 is greater than the alpha level a= .05, we fail to reject the null hypothesis. There is not convincing evidence of an association between wearing corrective eyewear and ethnicity.