Research in Education Sohee Kang PhD l ecturer Math and Statistics Learning Centre Outline Analyzing Educational Research Data Collecting data Using R R commander for describing and testing hypotheses ID: 370264
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Slide1
QuantitativeResearch in Education
Sohee Kang
Ph.D. ,
l
ecturer
Math
and
Statistics
Learning
CentreSlide2
OutlineAnalyzing Educational Research DataCollecting dataUsing R (R commander) for describing and testing hypothesesSlide3
Analyzing Research DataExample: 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. Slide4
Collecting DataObservational Data Ex) survey dataDesign of Experiments Ex) Classroom experimentsSlide5
Let’s look at Survey questionnaire Census at School Canada Website link: http://www.censusatschool.ca/Slide6
Census at School – Canada Questionnaire – Grades 9 to 12 2010/201 (selected questions)Slide7Slide8Slide9
Random Data Selectorhttp://rds.censusatschool.org.uk/Country: CanadaEmail: ex)spollanen@gmail.comSchool/institution: University of Toronto ScarboroughType the number on the screenSlide10
Select a sample size = 200Slide11
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.Slide12
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. Slide13
Three windows in R
Console
Editor
GraphicsSlide14
Writing in R is like writing in EnglishJump three times forward
Action
ModifiersSlide15
Generate a sequence from 5 to 20 with values spaced by 0.5Action
Modifiers
Writing in
R is like writing
in EnglishSlide16
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 EnglishSlide17
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
valueSlide18
Writing R code:Read a downloaded fileChoose the selected Variables: Province, Gender, Language, Height, Physical Days, Smoke, Favorite Subject, Pressure, Travel, Communication Slide19
Descriptive StatisticsCategorical Variables:Province, Gender, Favorite Subject, Travel,
Pressure, Communication
Quantitative Variables:
Language, Height, Physical Days, Smoke Slide20
Graphs For Categorical variables: Bar plot and Pie chartFor Quantitative variables: Histogram and boxplotSlide21
Summary Statistics For Categorical variables: Frequency, relative frequencyFor Quantitative variables: Mean, Median, SD (Standard deviation)Slide22
Relationship between Two VariablesCategorical vs Categorical: Contingency TablesCategorical vs Quantitative: Tables of Statistics (side by side boxplot)
Quantitative
vs
Quantitative
Correlation (Scatter plot)Slide23
Pre-Post Test: Paired T-testResearch 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. Slide24
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
DataSlide25
Hypotheses:Null hypothesisH0: There is no difference in mean pre-post marksAlternative hypothesisHa: There is a difference in mean pre-post marksSlide26
Steps in RCreate 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 Slide27
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.