2009 Strict Dress Code Survey

A Strict, Formal Dress Code Survey

Cen Zhou Jeffrey Blanco Yuhao Bai Justine Zayhowski

Introduction to the Dress Code A strict, formal dress code at Cushing Academy is something that people have wondered about. Many prestigious prep schools, especially in New England, have a formal dress code in place. Some think that a formal dress code presents the school well. Others feel that it adds nothing to the atmosphere of the school. Many students seem to be against the idea of a formal dress code, however, some feel they would rather have it. We decided to ask the students themselves whether they would be in favor of a formal dress code to see what they really think about this issue. In our ballots we also required them to tell us their gender as well so that we could see if there was a difference in how boys and girls felt about a formal dress code. The question we asked was: Are you in favor of a strict, formal dress code? A formal dress code at Cushing Academy would be similar to how other prep schools in New England enforce their dress codes. Brooks, for example, has a formal dress code and they state that the dress code at Brooks “is designed to promote a seriousness of purpose and to teach fluency in dressing, thus preparing students for various professional and social settings.” Brooks feels that a formal dress code is an extension of the learning experience and teaches students how to dress appropriately in order to prepare them for the adult world they will enter. They also state that faculty at Brooks are the, “final judges of what constitutes ‘appropriate dress.’” Any students at Brooks must change immediately if ever they are out of dress code and cannot continue class or any activity they are in until they are appropriately dressed. The dress code for boys includes, “blazer or sport coat, collared dress shirt (tucked in) with tie, or turtleneck. Dress slacks, trousers, corduroys or Bermuda shorts. Dress shoes, boots, leather sandals, Birkenstocks (no beach wear); hiking boots (winter only).” For girls the dress code is, “Dress or skirt with blouse or turtleneck (tucked in). Slacks or trousers with blouse or turtleneck (tucked in) and ladies’ blazer/jacket, khakis or corduroys or Bermuda shorts. Dress shoes, boots, leather sandals, Birkenstocks (no beachwear); hiking boots (winter only).” The clothing should also be free of any holes or tears. Here is a copy of the ballot: Circle one response for each question: 1. What is your gender? Male

Female

2. Should Cushing Academy adopt a strict, formal dress code? Yes

No

Introduction to Math Concepts

A good way to plot two distributions in relation to each other is through the use of two way tables. In a two way table, the explanatory variable is usually, but not always, put in terms of columns and the response variable as the rows. Two way tables are a good way to quickly extrapolate the data from a study. There are three different uses for the chi squared distributions. The first is to test for association between two categorical variables, the second is the goodness of fit test (seeing how a population distribution relates to a specified distribution), and the test for homogeneity of distributions of three or more categories. The first use is the one that will be focused on. As stated before, chi squared distributions are used to assess whether or not there is an association between two categorical variables. This test is the equivalent of a significance test but is used for categorical data. The null hypothesis would be a statement of no association between the two variables. The alternative hypothesis is a statement of association between the two categorical variables. It is also important to note that using chi squared distribution there are no one sided or two sided alternative hypotheses. The alternative is merely the opposite of the null. The test statistic for chi squared distribution is X^2 = ∑ (observed – expected) ^2/expected. The expected cell count is calculated by (row total*column total)/ n. N is the overall total. Also, if using a chi squared table instead of a graphing calculator, the degrees of freedom may be calculated by (number of rows – 1)*(number of columns – 1). Usually if the p-value corresponding to the test statistic is less than 0.05, it is said to be statistically significant. The graph of the chi squared distribution is skewed to the right as seen below:

The chi squared test is the best way to figure out if there is, or whether it is likely there could be, and association between two categorical variables. Procedure

In order to figure out if there is an association between gender and preference to a formal dress code, we randomly select 65 people (30 males and 35 females) and run a chi-squared test based on their answers. To get a sample that can represent the Cushing population, we decided to ask for different groups’ opinions. Considering that usually friends, people with similar ideas, sit together at one table in the dining hall we randomly choose several people from each table to answer the question during D lunch period one day. In this way, we get a simple random sample that can best represent the opinions of the Cushing community. Thus, we propose our null and alternative hypotheses: Null hypothesis: There is no association between “preference to dress code” and “gender”. Alternative hypothesis: There is an association between “preference to dress code” and “gender”. After we collect data, we create the following table that tells our survey result. Two – way-table for the favor of a formal dress-code and gender:

 

Yes 

No 

Total 

Male 

12 

18 

30 

Female 

13 

22 

35 

Total 

25 

40 

65 

Calculations 1. Find the degrees of freedom. df = (r-1)*(c-1) = (2-1)*(2-1) = 1 2. Calculate the expected cell counts by doing (row total*column total)/overall total 3. Put the observed values in matrix A and the expected in matrix B and use the chi squared calculator. Or do X^2 = ∑ (observed – expected) ^2/expected and use the distribution table. (Expected is bold.) Male Female

Yes No Total 12 18 30 11.5 18.5 13 22 35 13.5 21.5

Total

25

40

65

χ² = 0.0557 p = .813 df = 1 P-value = 0.813 > 0.05 therefore, the data is not statistically significant and one cannot say there is a difference in association between gender and response to a question on dress code. Females and males share similar opinions on this subject. Tables and Figures Joint Proportion Table: The proportion of each gender who agree with the formal dress-code: Population  n   X  Male 

30 

12 

Female 

35 

13 

Total 

65 

25 

Marginal Distribution Tables: Marginal distribution of gender:  

Male 

Female 

Proportion 

46% 

54% 

Marginal distribution of supporting a formal dress-code:  

Yes 

No 

Proportion 

38% 

62% 

Conditional Distribution Tables: Conditional distribution of in favor of dress-code for female:  

Yes 

No 

Proportion 

37% 

63% 

Conditional distribution of in favor of dress-code for male:  

Yes 

No 

Proportion 

40% 

60% 

Conclusion In conclusion, the p-value = 0.813 > 0.05, so it does not show us a strong association between the response on dress –code and gender. Therefore, the data is not significant at the 0.05 significance level and we cannot reject the null hypothesis (there is no association between gender and preference for a strict dress code) in favor of any alternative hypothesis. However, the study did show that the majority of students, regardless of gender, do not want a strict, formal dress code. Any attempt to formalize the Cushing Academy dress code would not be supported by the general student body. The sample size of this study was only 65, whereas one would prefer to have a larger SRS so outliers could not impact the results as greatly. In order to make it more accurate, the sample size of this report should be greater. Also, despite the goal not to, there is a tendency for people to ask their friends. His or her opinion can have a significant effect on his or her friends, so it can cause a failure of the report. There was probably a better way to randomize the sample. Peer pressure could also have caused a difference in the way people answered the question. Lack of information about dresscode can also confuse people’s idea, so collecting more information and making the subjects more aware of the question’s meaning can also improve the accuracy of the study.