# PSYC412: Week 11 - Lab activity 2 # Step 1: Background and set up ------------------------------------------- # Empty R environment rm(list=ls()) # Load relevant libraries library(broom) library(car) library(tidyverse) # Read in the data acoustics <- read_csv("voice_acoustics.csv") ratings <- read_csv("voice_ratings.csv") # Have a look at the data acoustics ratings # QUESTION 1: How are the acoustics data and the ratings data organised (wide or long)? Are both data files 'tidy'? # # ANSWER: Recall the difference between wide and long data. In wide data, each row represents an individual # case, with observations for that case in separate columns; in long data, each row represents a single # observation, and the observations are grouped together into cases based on the value of a variable (for these # data, the VoiceID variable). The acoustics data file is tidy and in the long format. The ratings data is in # the wide format. # Step 2: Restructuring the ratings data ---------------------------------- # We are going to need to do some data-wrangling before we do any analysis! Specifically, we need the change # the ratings data to the long format. # # TASK: Use the pivot_longer() function to restructure the ratings data from wide to long and store the resulting table # as 'ratings_tidy'. ratings_tidy <- pivot_longer( data = ratings, # the data you want to restructure cols = P1:P28, # columns you want to apply th above to names_to = "participant", # variable name that captures whatever is across the columns you are restructuring, in this case P1 to P28 for the 28 different participants) values_to = "rating") # variable name that captures whatever is in the cells (in this case numbers for ratings) # Step 3: Calculate mean trustworthiness rating for each voice ------------ # TASK: Now that we’ve gotten the ratings data into a tidy format, the next step is to calculate the mean rating # for each voice. Remember that each voice is identified by the VoiceID variable. Store the resulting table in # a variable named ratings_mean. # # HINT: Use group_by() and summarise(). Are you using the tidy data? Also, remember that if there are any # missing values (NAs) then na.rm = TRUE would help. ratings_mean <- ratings_tidy %>% group_by(VoiceID) %>% summarise(mean_rating = mean(rating)) # Step 4: Join the data together ----------------------------------------- # Ok, before we get ahead of ourselves, in order to perform the regression analysis we need to combine the data # from ratings_mean (the mean ratings) with acoustics (the pitch and dispersion ratings). Also, as we said, we # only want to analyse male voices today. # # TASK: Join the two tables and keep only the data for the male voices, call the resulting table 'joined'. # # HINT: Use the inner_join() function (making use of the variable that is common across both tables) to join. Use # the filter() to only keep male voices. Remember that the Boolean operator for exactly equal is ==. joined <- ratings_mean %>% inner_join(acoustics, "VoiceID") %>% filter(sex == "M") # Step 5: Spreading the data ---------------------------------------------- # Ok so we are starting to get an understanding of our data and we want to start thinking about the regression. # However, the regression would be easier to work with if Pitch and Dispersion were in separate columns. This # can be achieved using the spread() function. It is a bit like the reverse of gather(). It takes the data and # you tell it which values you want spread and by which column (though in the order of data, column, value). # Run the code below to do this. joined_wide <- joined %>% pivot_wider( names_from = measures, # name of the categorical column to spread values_from = value) # name of the data to spread # QUESTION 2: Why do we not need to specify within the `pivot_wider()` function which data to use? # ANSWER: Because we use the function in a pipe. The data to be used is specified before the %>% sign. # For more info on pipes see here: https://r4ds.had.co.nz/pipes.html?q=pipes#pipes # Step 6: Visualising the data -------------------------------------------- # As always, it is a good idea to visualise your data. # # TASK: Now that we have all the variables in one place, make two scatterplots, one of mean trustworthiness # rating with dispersion and one for mean trustworthiness rating and pitch. # # HINT: For this you'll need the ggplot() function together with geom_point() and geom_smooth(). Make # sure to give your axes some sensible labels. ggplot(joined_wide, aes(x = Dispersion, y = mean_rating)) + geom_point() + geom_smooth(method = "lm") + theme_bw() + labs (y = "Mean Trustworthiness Rating") ggplot(joined_wide, aes(x = Pitch, y = mean_rating)) + geom_point() + geom_smooth(method = "lm") + theme_bw() + labs (y = "Mean Trustworthiness Rating") # QUESTION 3: According to the scatterplot, how would you decribe the relationships between trustworthiness # and dispersion and trustworthiness and pitch in terms of direction and strength? Which one of the two # seems stronger? # # ANSWER: According to the scatterplot, there appears to be a positive relationship between both pitch and # trustworthiness and dispersion and trustworthiness, but the relationship with pitch seems stronger (because # the data point fall slightly closer to the line of best fit). # Step 7: Conducting and interpreting simple regression ----------------------- # With all the variables in place, we're ready now to start building the regression models. # # TASK: Use the lm() function to run the following two regression models and use the summary() function to # look at the output of each model: # 1. Run the simple linear regression of predicting trustworthiness mean ratings from Pitch, and store the model in mod_pitch. # 2. Run the simple linear regression of predicting trustworthiness mean ratings from Dispersion, and store the model in mod_disp. # # HINT: lm(dv ~ iv, data = my_data) mod_disp <- lm(mean_rating ~ Dispersion, joined_wide) mod_disp_sum <- summary(mod_disp) mod_pitch <- lm(mean_rating ~ Pitch, joined_wide) mod_pitch_sum <- summary(mod_pitch) # QUESTION 4: What do you conclude from the output of these models? Which model is significant? Which predictors # are significant? How much variance does each model describe? # # ANSWER: Overall, the Pitch only model is significant (F(1,30) = 14.83, p < .001) and describes 30.9% of the variance. # In contrast, the Dispersion only model is not actually significant (F(1,30) = 1.98, p = .17) meaning that it # is not actually any use as a model. This is backed up by it only explaining 3.1% of the variance. # Step 8: Conducting and interpreting multiple regression ----------------- # Now let's look at both predictors in the same model. Before we do this, it is sensible to center and standardise # the predictors. # # TASK: Look at the code below. Can you follow how the predictors are first centered (_c) and then standardised (_z)? # Here I do this by hand because I think it makes it clearer, even though there are functions that do this in # one step. If you want to know more, type ?scale() in the console window and read the help on that function. # Now run the code. joined_wide <- mutate(joined_wide, Dispersion_c = Dispersion - mean(Dispersion), Dispersion_z = Dispersion_c / sd(Dispersion_c), Pitch_c = Pitch - mean(Pitch), Pitch_z = Pitch_c / sd(Pitch_c)) # TASK: Now use the centered and standardised data for the multiple regression. Use the lm() function to run # a model for predicting trustworthiness mean ratings from Pitch and Dispersion, and store the model in # mod_pitchdisp_z. Use the summary() function to look at the output. # # HINT: lm(dv ~ iv1 + iv2, data = my_data) mod_pitchdisp_z <- lm(mean_rating ~ Pitch_z + Dispersion_z, joined_wide) mod_pitchdisp_z_sum <- summary(mod_pitchdisp_z) # QUESTION 5: What do you conclude from the output of this model? Is the overall model significant? Which predictors # are significant? How much variance does the model describe? Which model would you say is best for predicting # ratings of trustworthiness, the Pitch only, the Dispersion only or the Pitch+Dispersion model? # # ANSWER: Looking at the multiple linear regression model which contains both pitch and dispersion we can see # that it is a useful model ((F(2,29) = 7.81, p = .002) explaining 30.5% of the variance). However only pitch # is a significant predictor in this model (beta = 0.41, p = .001), whereas dispersion is not # (beta = 0.11, p = .361) and the multiple regression model actually describes less variance than # the pitch alone model. There is an argument to be made that the pitch only model is the best # model in the current analysis (describes more variance and is more parsimonious than the pitchdisp model). # Step 9: Checking assumptions -------------------------------------------- # Now that we've established which model best fits the data, let's check whether it meets the assumptions of # linearity, normality and homoscedasticity. # # HINT: crPlots() to check linearity # qqPlot() and shapiro.test() to check normality of the residuals # residualPlot() and nvcTest() to check homoscedasticity of the residuals # # QUESTION 6: What do you conclude from the graphs and output? Should we also check for collinearity? # # ANSWER: The component+residual plot suggest that the relationship is linear, while the qq-plot and the # result from the Shapiro Wilk test (not significant) suggest that the residuals are normally distributed. The # residuals are also homoscedastic, judging from the residual plot and the output of the non-constant variance # test (not significant). crPlots(mod_pitch) qqPlot(mod_pitch$residuals) shapiro.test(mod_pitch$residuals) residualPlot(mod_pitch) ncvTest(mod_pitch) # Step 10: Writing up the results ----------------------------------------- # TASK: Write up the results follow APA guidelines. # # 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. The APA Style 7th Edition Numbers and Statistics Guide (https://apastyle.apa.org/instructional-aids/numbers-statistics-guide.pdf) is also useful. # # ANSWER: Three regression models were fitted with mean rating for voice trustworthiness as outcome # variable. The predictor variables were pitch only, dispersion only, or both pitch and dispersion. # Using overall model significance and adjusted R-squared as a guide, it was concluded that the pitch only # model best fitted the data. The pitch only model significantly predicted trustworthiness (F(1, 30) = 14.83, # p < .001, Adjusted R2 = 0.31), accounting for 31% of the variance. Pitch was a significant # positive predictor (β = 0.02, p < 0.001); when pitch increased, trustworthiness also increased (see also Figure X). # The results for the dispersion only and the pitch and dispersion models can be seen in Table X.