# OneSampleTTest.R # # The are two ways to calculate p-values in R for t-tests, # depending on whether you're working with raw data or # with summary statistics (mean and standard deviation) # # Load the survey data survey <-read.csv("http://www.courses.washington.edu/psy315/datasets/Psych315W19survey.csv") # If you have the mean and standard deviation of your sample (and degrees of freedom), then # you can use R's 'pt' function to calculate the p-value. 'pt' is a lot like the 'pnorm' function # for the z-distribution. # # Example 1 (from the t-test tutorial): # # Given sample of 25 systolic blood pressure scores with a mean of 131.66 and a standard # deviation of 22.2532 mm Hg, is this mean significantly greater than a normal value of # 120 mm HG? # # First, define our variables m <- 131.66 s <- 22.2532 H0 <- 120 n <- 25 # Next, calculate the t-statistic: sem <- s/sqrt(n) t<-(m-H0)/sem # Finally, calculate the p-value. We'll use the option 'lower.tail = FALSE' for # a one-tailed test in the positive direction. Use 'TRUE' when rejecting for # negative values of t: p <- pt(t,n-1,lower.tail = FALSE) p # Effect size: d <- abs(m-H0)/s d # Example 2: Are the heights of women with fathers 6 feet or taller significantly # different from 64 inches? H0 <- 64 # This example will conduct a t-test from the raw data instead of the summary statstics. # We'll use R's 't.test' function. # Load the survey data survey <-read.csv("http://www.courses.washington.edu/psy315/datasets/Psych315W19survey.csv") # Find the female students with fathers 6 feet (72 inches) or taller: female.students <- survey\$gender== "Female" & survey\$pheight >= 72 & !is.na(survey\$pheight) female.height <- survey\$height[female.students] # Use t.test out <- t.test(female.height, mu = H0, alternative = "two.sided") # The option 'mu = H0' defines the mean for the null hypothesis (64 in this example) # The option 'alternative = "two.sided" is for a two-sided test (of course) # Other options are "less" or "greater" for one sided tests. # Here's the t-statistic from the output: out\$statistic # Here are the degrees of freedom: out\$parameter # Here's the p-value out\$p.value # Calculate effect size: d <- abs(mean(female.height)-H0)/sd(female.height) d # Using R to print the result in APA format # # You can use R's 'sprintf' function to output the results of your hypothesis test # in APA format. This output can then be copied and pasted into your paper. # 'sprintf' is an old command from the C programming language that prints out a formatted # 'string', which is a list of characters. To stick a number into a string you can do this: sprintf('My favorite number is %g.',pi) # the '%g' tells sprintf to replace '%g' with the number supplied afterward. If there is # more than one '%g' then replace '%g' with numbers in the order supplied: sprintf('My favorite number is %g, and the square root of that number is %g',pi,sqrt(pi)) # If you want to put in characters instead of numbers, use '%s': sprintf('It is a %s day for statistics!','great') # If you want to control the number of decimal points, use '%a.bf' where a is the total # number of digits (including decimal points) and b is the number of digits to the right # of the decimal point. sprintf('pi to the nearest 2 digits is %3.2f',pi) # Putting this together, we can report the results of our last t-test in APA format: sprintf('t(%g) = %4.2f, p = %5.4f',out\$parameter,out\$statistic,out\$p.value) # Even if you don't understand 'sprintf' well, you can just cut and paste the line above # with 'out' as the output of the t-test and it'll give you what you want.