QuantitativeResearch in Education

Sohee KangPh.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: http://

www.censusatschool.ca/

Census at School – Canada Questionnaire – Grades 9 to 12 2010/201 (selected questions)

Random Data Selector

• http://rds.censusatschool.org.uk/• Country: Canada• Email: ex)spollanen@gmail.com• 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 RConsole Editor 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

Action Modifiers

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

Argumentname

Equal sign

Other arguments

CommaClose

parenthesis

Argumentvalue

Writing R code:

1. Read a downloaded file2. 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 1 18 22 2 21 25 3 16 17 4 22 24 5 19 16 6 24 29 7 17 20 8 21 23 9 23 19 10 18 20 11 14 15 12 16 15 13 16 18 14 19 26 15 18 18 16 20 24 17 12 18 18 22 25 19 15 19

20 17 16

Example Data

Hypotheses:

• Null hypothesis

H0: 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$Aftermark and prepost$Beforemarkt = 3.2313, df = 19, p-value = 0.004395alternative hypothesis: true difference in means is not equal to 095 percent confidence interval: 0.7221251 3.3778749sample estimates:mean of the differences 2.05

Results:

• t test statistic value is t=3.2313 and p-value is 0.0004; 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.