Quantitative Research in Education Sohee Kang Ph.D., lecturer Math and Statistics Learning Centre

Outline Analyzing Educational Research Data Collecting data Using R (R commander) for describing and testing hypotheses

Analyzing Research Data Example: a high school research team was interested in increasing student achievement by implementing a study skills program. The first thing this team did was develop a survey, which all students completed. Representing data made it quite easy to see what study skills students were already using and which ones they would like to learn more about.

Collecting Data Observational Data Ex) survey data Design of Experiments Ex) Classroom experiments

Let’s look at Survey questionnaire Census at School Canada Website link:

Census at School – Canada Questionnaire – Grades 9 to /201 (selected questions)

Random Data Selector Country: Canada School/institution: University of Toronto Scarborough Type the number on the screen

Select a sample size = 200

Which software to use to analyze data? R is a language and environment for statistical computing and graphics. R can be used for: data manipulation, data analysis, creating graphs, designing and running computer simulations.

Why R? R is FREE: As an open-source project, you can use R free of charge. R is POWERFUL: Leading academics and researches from around the world use R to develop the latest methods in statistics, machine learning, and predictive modeling.

Three windows in R ConsoleEditor Graphics

Writing in R is like writing in English Jump three times forward Action Modifiers

Generate a sequence from 5 to 20 with values spaced by 0.5 ActionModifiers Writing in R is like writing in English

seq(from=5, to=20, by=0.5) Action Modifiers Function Arguments Generate a sequence from 5 to 20 with values spaced by 0.5 Writing in R is like writing in English

seq(from = 5, to = 20, by = 0.5) Basic anatomy of an R command Function Open parenthesis Argument name Equal sign Other arguments Comma Close parenthesis Argument value

Writing R code: 1.Read a downloaded file 2.Choose the selected Variables: Province, Gender, Language, Height, Physical Days, Smoke, Favorite Subject, Pressure, Travel, Communication

Descriptive Statistics Categorical Variables: Province, Gender, Favorite Subject, Travel, Pressure, Communication Quantitative Variables: Language, Height, Physical Days, Smoke

Graphs For Categorical variables: Bar plot and Pie chart For Quantitative variables: Histogram and boxplot

Summary Statistics For Categorical variables: Frequency, relative frequency For Quantitative variables: Mean, Median, SD (Standard deviation)

Relationship between Two Variables Categorical vs Categorical: Contingency Tables Categorical vs Quantitative: Tables of Statistics (side by side boxplot) Quantitative vs Quantitative Correlation (Scatter plot)

Pre-Post Test: Paired T-test Research question type: Difference between two related (paired or matched) variables. What kind of variables? Quantitative (Continuous) Common Applications: Comparing the means of data from two related samples; say, observations before and after an intervention on the same participant.

Example: Research question: Is there a difference in mark following a teaching intervention? Student Before Mark After Mark Example Data

Hypotheses: Null hypothesis H 0 : There is no difference in mean pre-post marks Alternative hypothesis Ha: There is a difference in mean pre-post marks

Steps in R Create a data file, “pre-post.txt” Read data from R Statistics > Means > Paired t-test Paired t-test data: prepost$Aftermark and prepost$Beforemark t = , df = 19, p-value = alternative hypothesis: true difference in means is not equal to 0 95 percent confidence interval: sample estimates: mean of the differences 2.05

Results: t test statistic value is t= and p-value is ; there is very small probability to observe this t-test statistic value or more extreme values under the assumption that there is no mean difference. Conclusion: There is a statistically significant, strong evidence that teaching intervention improved marks.