# PSYC122: Week 14 - Chi-square in R - Demo # Background ------------------------------------------------------------ # What we want to do is to run a chi-square analysis to determine whether there is a relationship # betweeen children's record for fighting in school and their preference for a violent or # non-violent TV programme. # Step 1: Set-up ------------------------------------------------------------------ # Run this code to empty the R environment rm(list=ls()) # Run this code to load relevant libraries library(lsr) library(tidyverse) # Run this code to read in data and have a look it fighting_data <- read_csv("fighting_TV.csv") # Read in the data file head(fighting_data) # Look at the table # It is a fairly simple data file that contains 3 variables for 155 participants: # 'ID': this variable indicates the participant ID number # 'TV': this variable indicates which TV programme children preferred (violent = 1, non-violent = 0) # 'Fight': this variable indicates whether children had been in a fight in school (yes = 1, 0 = no) # Step 2: Data-wrangling ------------------------------------------------------------------ # We need to do a little bit of wrangling to get our data into the format we need: # To make the output easier to read, we’re going to recode 'TV' and 'Fight' to have text labels # rather than numerical values. # TASK: # 1) Use mutate() and recode() to recode the values in TV' to make 1 = Violent and 0 = Non-violent # and the values in 'Fight' to 1 = Yes and 0 = No. # 2) Save the output to an object named fighting_recode. # # HINT: You can do this in two separate steps, or you can use pipes. Also, note that you will need to put # both sides of each recode argument (i.e., 1 and Violent) in quotation marks, even though 1 and 2 are numbers, # they actually represent categories rather than numerical data. # Run this code to recode the values fighting_recode <- fighting_data %>% mutate(TV = recode(TV, "1" = "Violent", "0" = "Non-violent"), Fight = recode(Fight, "1" = "Yes", "0" = "No")) head(fighting_recode) # Look at the new table # Step 3: Descriptive statistics ------------------------------------------------------------------ # Next you need to calculate descriptive statistics. For frequency data these are simply counts so we can use # the function count() rather than having to use the summarise() function. We want to know how many # participants are in each group (TV:Violent - Fight:Yes, TV:Violent - Fight:No, TV:Non-violent - # Fight:Yes, TV:Non-violent - Fight:No) so we will need to use group_by to display the results for all combinations of 'TV' and 'Fight'. # Run this code to do the counts and create the 'contingency' table fighting_counts <- fighting_recode %>% group_by(TV, Fight) %>% count() fighting_counts # QUESTION: How many children with a preference for non-violent TV programmes got into a fight in school? # ANSWER: 30 # QUESTION: How many children with a preference for non-violent TV programmes did not get into a fight in school? # ANSWER: 70 # QUESTION: How many children with a preference for violent TV programmes got into a fight in school? # ANSWER: 40 # QUESTION: How many children with a preference for violent TV programmes did not get into a fight in school? # ANSWER: 15 # You may also want to calculate the percentage of children who fought in each condition. # Run this code to calculate the percentages fighting_percent <- fighting_recode %>% group_by(TV, Fight) %>% count() %>% ungroup() %>% # ungroups the data group_by(TV) %>% # then groups it again but just by TV mutate(percent_TV = n/sum(n) * 100) fighting_percent # Step 4: Bar plot ------------------------------------------------------------------ # # We want to create a simple bar plot of our count data. # We'll use ggplot() for this in combination with the geom_bar() function. The different parts do the following # - The first line (or layer) sets up the base of the graph: the data to use and the aesthetics (what will go on the x # and y axis, how the plot will be grouped). # - The aes() function can take both an x and y argument, however, with a bar plot you are just asking R to count the number of data # points in each group so you don’t need to specify this. # - The 'fill' argument will separate the data into each level of the grouping variable and give it a different colour. # In this case, there is a different coloured bar for each level of 'actualdonate'. # - The next layer adds a geom or a shape, in this case we use geom_bar() as we want to draw a bar plot. # - position = "dodge" places the bars next to each other, rather than on top of each other. Try removing this # argument and just running the code with geom_bar() to see what happens. # # Run the code below code to create a bar plot ggplot(data = fighting_recode, aes(x = Fight, fill = TV)) + geom_bar(position = "dodge") # As you can see, the plot makes it much easier to visualise the data - children with # a preference for violent TV programmes were more likely to get into a fight in school. # Step 5: Chi-square ------------------------------------------------------------------ # So, let’s finally run that chi-square analysis to see whether our intuition from the plot holds up and there is a # significant association between the grouping variables. # Run this code to conduct the chi-square analysis results <- chisq.test(x = fighting_recode$TV, # the first grouping variable y = fighting_recode$Fight, # the second grouping variable correct = FALSE) # whether we want to apply the continuity correction (use if any of the expected cell frequencies < 10 in 2 x 2 table) results # Step 6: Checking assumptions --------------------------------------------------------- # The assumptions for chi-square are as follows: # 1) The data in the cells should be frequencies, or counts of cases rather than percentages. # 2) The levels (or categories) of the variables are mutually exclusive. That is, a particular participant fits into # one and only one group of each of the variables. # 3) Each participant may contribute data to one and only one cell. If, for example, the same participants are tested # over time such that the comparisons are of the same subjects at Time 1, Time 2, Time 3, etc., then Chi-square may # not be used. # 4) The study groups must be independent. This means that a different test must be used if the two groups are related. # For example, a different test must be used if the researcher’s data consists of paired samples, such as in studies # in which a parent is paired with his or her child. # 5) There are 2 variables, and both are measured as categories, usually at the nominal level. While Chi-square has no # rule about limiting the number of cells (by limiting the number of categories for each variable), a very large # number of cells (over 20) can make it difficult to meet assumption #6 below, and to interpret the meaning of the # results. # 6) The expected cell frequencies should be greater than 5. # Assumptions 1) to 5) should be evaluated by reviewing the design of the study. The only assumption that we need to # check with R is whether all expected frequencies are greater than 5. # Run this code to check the expected frequencies results$expected # Step 7: Effect size ------------------------------------------------------------------ # The last step before writing up the results is to calculate an effect size so that we have a standardised measure # of how large the association between our grouping variables is, the effect size measure for chi-square is Cramer’s V. # To calculate Cramer’s V we’re going to use the function cramersv() from the lsr package. # Run this code to calculate Cramer's V: eff_size <- cramersV(x = fighting_recode$TV, # the first grouping variable y = fighting_recode$Fight, # the second grouping variable correct = FALSE) # whether we want to apply the continuity correction (use if any of the expected cell frequencies < 10 in 2 x 2 table) eff_size # We can square the effect size (or multiple it by itself) to see how much variance in one # variable is accounted for by the other variable # Run this code to square the effect size percentageAccountedFor <- eff_size * eff_size percentageAccountedFor # Step 8: Interpreting relationships -------------------------------------- # To help with interpreting the relationships, it is useful to look at the standardised # residuals. These are z-scores that indicate how many standard deviations above or below # the expected count, an observed coutn is (thus indicating how much they differ). Remember: # +/- 1.96 p <.05, +/- 2.58 p <.01, +/-3.29 p < .001 # Run this code to check the standardised residuals results$residuals # Step 9: Write up ----------------------------------------------------------------- # # HINT: The Purdue writing lab website (https://owl.purdue.edu/owl/research_and_citation/apa6_style/apa_formatting_and_style_guide/statistics_in_apa.html) # is helpful for guidance on punctuating statistics. # Write up: # There was a significant association between school fighting and TV programme preference (violent # versus non-violent), Chi-square (1, N = 155) = 26.16, p < .001, Cramer's V = .41. Above # expectations, 73% (40 out of 55) of children who preferred violent TV programmes, had also # fought in school (z =3.00, p < .01), and significantly less than expected had not fought (z = # -2.76, p < .01). Conversely, 70% of children preferring non-violent TV programmes (70 out of 100), # had not engaged in fighting, more than expected (z = 2.05, p < .05) and those who had fought # were below expectations (z = -2.26, p < .05). Analysis showed 17% of the variance in school # fighting could be accounted for by TV programme preference.