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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.