Compare Variables: Pros And Cons Of Calculation

Compare Variables
Student’s Name
Institutional Affiliation
Compare Variables
Address the following research questions:
1 What colleges have the highest and lowest average SAT scores and why?
Using the R Studio function summary(), it was easier to establish what schools had the highest and lowest average SAT scores.
> summary(na.omit(sub$SAT_AVG))
Min. 1st Qu. Median Mean 3rd Qu. Max.
10.0 473.0 473.0 450.4 473.0 473.0
> summary(na.omit(sab$SAT_AVG))
Min. 1st Qu. Median Mean 3rd Qu. Max.
2.0 468.0 473.0 418.3 473.0 473.0
The output results indicate that Pennsylvania schools had a lower SAT score of 2 than California schools, which had a minimum score of 10. The maximum SAT score for both states was 473. Additionally, PA schools had the lowest average/mean SAT scores of 418.3, while California colleges had the highest average score of 473.
2 What are the differences between the standard errors of both states?
The standard errors of both California and Pennsylvania states differ significantly. The difference between the two states is 0.2113758 because the SEM for the State of PA is higher than that of CA.
3 Are there differences between California and Pennsylvania schools?
Yes, California has 795 schools, while Pennsylvania has only 405. Arguably, this elucidates that there are more educational institutions than those in Pennsylvania. The 390 difference may be as a result of location factors where pioneers and students prefer California for its popularity and city life to Pennsylvania State. Notably, California schools are different from those in Pennsylvania since their SAT scores differ in mean, standard deviation, and standard error means.
Then address the following in a research paper with an introduction, method, and results section:
Identify the dataset and variables and provide context to the research used to collect the data (in an introduction section).
Among the viable elements listed on college scorecard, SAT average scores are equally important. Various organizations, such as Common App, ACT, and College Board strongly urge students to make use of the College Scorecard and FASFA to search for schools, which have good values before they submit their exam scores and college applications. Prospective scholars sit for a combination of mathematics and evidence-based reading/writing section. Out of 1600, students are urged to attempt the 1000 average score to be considered for admission. Schools post their required SAT admission scores such that if a student score lies within or above these ranges, they are legible for admission into their dream colleges. For schools that do not list SAT scores, test-optional policies/procedures allow them to use high school records such as GPA or class rank criterion. However, these procedures have limitations where students sit for ACT or SAT tests in case they failed GPA or class rank criteria.
In California State, Stanford and Caltech Universities are the most selective colleges, while UCLA and Berkley are the most prestigious and selective public universities in the USA. Pitzer College is one of the numerous test-optional colleges in the country. Apart from the average SAT scores above, admissions to California State schools require a strong academic record, winning essay, great recommendation letters, and excellence in meaningful extracurricular activities. As for schools in Pennsylvania, the measures of admission using SAT scores are the same as those in California. Pennsylvania’s Dickinson, Gettysburg, Juniata are among the numerous test-optional scores and do not require to post their SAT scores to the Department of Education. However, top schools in Pennsylvania have holistic admissions criteria because a candidate is evaluated based on various tests, for example, essays, extracurricular activities, and exceptional recommendation letters. Notably, these tests compensate for less appealing SAT scores.
While still working with the main dataset ‘Most Recent Cohorts Scorecard Elements,’ the SAT_AVG variable was used in making inferences after comparing SAT scores between California and Pennsylvania colleges. In this paper, the R Studio software helped in the exploration of the variable SAT_AVG of the Most Recent Cohorts Scorecard Elements dataset by computing its descriptive statistics i.e. mean, standard deviation, standard error mean for each subset. Various columns, for instance, INSTNM and SAV_ATG were categorical and numerical variables respectively with traces of missing values (Ko, Hung, Chang, & Lin, 2014, p. 27). The dataset was subdivided into two sub-datasets; one for California schools and another for those in Pennsylvania State.
Identify the analysis performed, pros and cons of calculation, and why they are used for each research question (in a method section).
In statistics, descriptive and inferential statistics form the foundation for more complex computations and analyses. By definition, descriptive statistics define, indicate or finalize data, thus making its patterns emerge. Measures of central tendency, dispersion and those used to describe the shape of distribution are examples of descriptive statistics. Conversely, inferential statistics are statistical techniques that permit us to use samples for generalizations about their population. Remember that samples are subsets of a population and inferences drawn from them may not provide accurate information about the entire population due to observational and non-observational errors (Harding, Tremblay, & Cousineau, 2014, p. 108). Estimation of parameters (such as standard deviation) and testing of a statistical hypothesis are methods of inferential statistics. A sample drawn from a dataset can be a composite of a particular variable whether categorical or numerical (Ko et al., 2014, p. 28). The numerous subset datasets, which consist of variables are then compared against each other to draw meaningful inferences, thus helping to answer various research questions.
Sub-setting datasets in statistics using R Studio is quite common as R Studio possesses powerful indexing features for locating variables and elements present in the datasets. With such features, it is easy to include/omit/select certain required variables and particular elements or observations. The functions needed in the execution of these commands are available in the software and ready for use. For instance, the subset function is subset() and enables in the selection of variables/observations. The function sample() takes sample sizes of size n from the dataset. Moreover, there are two more other ways of sub-setting a dataset in R. One of them is the use of the tapply() function in analysis across a number of subgroups or subsets in a data frame. Therefore, with these functions, comparisons can be made across subgroups in a dataset and results analyzed to draw meaningful conclusions about a certain variable or observation in the dataset.
Understanding standard scores is important in the comparison of subgrou...