Transcript Province, Gender, Language, Height, Physical Days, Smoke

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:
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)[email protected]
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
Console
Editor
Graphics
Writing in R is like writing in
English
Jump three times forward
Action
Modifiers
Writing in R is like writing in
English
Generate a sequence from 5 to 20 with values spaced by 0.5
Action
Modifiers
Writing in R is like writing in
English
Action
Modifiers
Generate a sequence from 5 to 20 with values spaced by 0.5
seq(from=5, to=20, by=0.5)
Function
Arguments
Basic anatomy of an R command
Open
parenthesis Equal signComma
Close
parenthesis
seq(from = 5, to = 20, by = 0.5)
Other
Function ArgumentArgument
value arguments
name
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?
Example
Data
Student Before Mark
1
18
2
21
3
16
4
22
5
19
6
24
7
17
8
21
9
23
10
18
11
14
12
16
13
16
14
19
15
18
16
20
17
12
18
22
19
15
After Mark
22
25
17
24
16
29
20
23
19
20
15
15
18
26
18
24
18
25
19
20
16
17
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$Aftermark and prepost$Beforemark
t = 3.2313, df = 19, p-value = 0.004395
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
0.7221251 3.3778749
sample 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.