The file contains all summaries from the Statistics course from weeks 1-7. The information is taken from the lecture slides and the book. These summaries help studying for the exam.
Descriptive Inferential
- Summarise the data - Asses relationships in data
- Describes data without conclusions - Link findings based on sample to
- Measures of central tendency and population
spread - Comparing 2 groups (or 1 group with a
value)
Example: Mean english grade Example: Men vs women – association
Range of English grades -> visualisation between 2 variables
- barplot showing number of participants Example: Are gender and grade related –
per study internal (consistency of Qs in a survey)
Example: Does a group of Qs measure a
single construct?
● Requirement of the data is that it is variable. There must be variation
● R Studio basic functions:
- a <- 5 (a is 5)
- b <- a * a (b is 25)
- (d <- NA ) means not available
- b <- c ( 2, 4, 6, 7, 8) (storing multiple values in a variable)
- mn<- mean (b) (finding the mean and store it in “mn”)
- head (dat) (shows the first six rows of the data)
- dat [a, b] (view parts of a table, a gives selected rows of data, b gives
selected columns of data)
- dat[c(1, 3, 5), c(“participant”, “study”)] (rows 1,3,5
and 2 named columns)
- dat$gender (you get the column gender of dataset data)
- How can you view the value in the 3rd column and in the 4th row of
dataframe ‘dat’? Answer: dat[4,3]
● Basic options to visualise data in R:
- barplot - plot() - boxplot() - hist() - qqnorm en qqline()
● (count <- table(dat$gender))
, - first create frequency table, then display: barplot(counts)
● Descriptive statistics: Central tendency:
- mean(dat$english_score) (mean of all people for English score)
- median(dat$english_score)
- mean(dat[dat$gender==”F”, ]$english_score (mean of
women for English score)
● Descriptive statistics: Spread:
- min(dat$en_score) #min value
- max(dat$en_score) #max value
- var(dat$en_score) #variance : average squared deviation from mean
- sd(dat$en_score) #squared root of variance (standard deviation)
● Descriptive statistics: frequency tables:
- table(dat$gender)
- table(dat$study)
- table(dat\$gender, dat\($study) # a cross table of study and
gender
- table(dat$gender, dat$study)
● Inferential statistics:
- t.test() #single, sample, paired, independent
- wilcox.test() #for non-parametric alternatives to the t-test (Mann
Whitney U test, Wilcoxon signed-rank test)
- binom.test() #sign test
- chisq.test() #x2 -> chi-square test
- cor.test() #correlation
- alpha() #from package psych (for Cronbach’s α)
● Examples (t.test & correlation):
- t.test(english_grade ~ bl_edu, data=dat) #assessing
average group differences for a numerical variable
- cor(dat$english_score, dat$english_grade)#assessing
strength of the relationship between two numerical variables
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