Reproducing results from “The Sound of Intellect” Experiment 1 and Experiment 3a.
Do the following for paired samples t tests:
A paired samples t test is used to compare two means that were sampled from the same set of participants.
Seen in:
Statistically, a paired samples t test is just a one-sample t test on the difference scores.
Difference scores (AKA change scores):
\(\Delta{X} = X_2 - X_1\)
Was the average change greater than/less than/different from zero?
What cues do people use to infer intellect? Differences between reading, hearing, and watching (and hearing) a job candidate’s pitch.
Two research questions from experiment 1 that we’re looking at.
Do job candidates think their written pitch will be perceived more or less positively than their spoken pitch?
Do job candidates expect their chances of being hired to be different for their written and spoken pitches?
“Theoretically, such expectations matter because they indicate whether the cues that convey mental capacities in social interaction are obvious to those in the midst of the interaction. Practically, such expectations matter because they could guide how candidates approach potential employers. Candidates who believe their spoken pitch will be judged exactly the same as their written pitch may see no reason to seek voice time with a potential employer.”
The (implied) hypotheses are…
Candidates will predict written and spoken pitches will be perceived differently.
Candidates will predict that employers’ interest will vary based on whether they observed the written or spoken pitches.
Conduct a paired samples t test comparing participants’ predicted positivity ratings for their spoken and written pitches.
These are the packages we’ll be using in the lab today.
“…these predictions were underpowered given the sample size of only 18 candidates…” (p. 880)
How underpowered? How are we defining underpowered?
What is the smallest population effect 50% of samples of N = 18 would detect?
What is the smallest population effect 80% of samples of N = 18 would detect?
What is the smallest population effect 95% of samples of N = 18 would detect?
Use readxl::read_excel()
to import the Excel file.
## # A tibble: 18 x 10
## `P#` Company PosWrit HireWrit PosSpoke HireSpoke `Times given` Age Gender
## <dbl> <chr> <dbl> <dbl> <dbl> <dbl> <chr> <dbl> <chr>
## 1 1 Google 3 3 4 4 3 to 5 26 M
## 2 2 BCG 4 4 3 3 0 27 M
## 3 3 Sprint 4 4 4 4 2 31 F
## 4 4 Micros… 4 4 3 2 3 29 F
## 5 5 Kleine… 3 3 4 3 3 26 M
## 6 6 Raymon… 5 5 4 4 2-3 times, n… 29 M
## 7 7 McKins… 3 3 3 3 2 for job in… 28 F
## 8 8 Wilson… 4 3 4 4 0 28 M
## 9 9 Samsun… 4 4 3 3 0 32 M
## 10 10 Kraft … 1 1 5 4 1 28 M
## 11 11 Gates … 3 1 4 4 0 24 F
## 12 12 Spotify 2 2 4 3 0 28 M
## 13 13 Mattel 3 3 4 4 0 28 F
## 14 14 Coca C… 3 3 5 5 0 28 F
## 15 15 Accent… 3 3 2 2 1 30 M
## 16 16 MetLife 2 2 3 3 0 27 M
## 17 17 McKins… 3 2 3 2 2 32 F
## 18 18 Kaiser… 4 4 3 2 2 to 3 27 M
## # … with 1 more variable: Ethnicity <chr>
## tibble [18 × 10] (S3: tbl_df/tbl/data.frame)
## $ P# : num [1:18] 1 2 3 4 5 6 7 8 9 10 ...
## $ Company : chr [1:18] "Google" "BCG" "Sprint" "Microsoft" ...
## $ PosWrit : num [1:18] 3 4 4 4 3 5 3 4 4 1 ...
## $ HireWrit : num [1:18] 3 4 4 4 3 5 3 3 4 1 ...
## $ PosSpoke : num [1:18] 4 3 4 3 4 4 3 4 3 5 ...
## $ HireSpoke : num [1:18] 4 3 4 2 3 4 3 4 3 4 ...
## $ Times given: chr [1:18] "3 to 5" "0" "2" "3" ...
## $ Age : num [1:18] 26 27 31 29 26 29 28 28 32 28 ...
## $ Gender : chr [1:18] "M" "M" "F" "F" ...
## $ Ethnicity : chr [1:18] "Asian American" "White European" "Indian-American (Sub-continent)" "Indian" ...
## P# Company PosWrit HireWrit
## Min. : 1.00 Length:18 Min. :1.000 Min. :1.00
## 1st Qu.: 5.25 Class :character 1st Qu.:3.000 1st Qu.:2.25
## Median : 9.50 Mode :character Median :3.000 Median :3.00
## Mean : 9.50 Mean :3.222 Mean :3.00
## 3rd Qu.:13.75 3rd Qu.:4.000 3rd Qu.:4.00
## Max. :18.00 Max. :5.000 Max. :5.00
## PosSpoke HireSpoke Times given Age
## Min. :2.000 Min. :2.000 Length:18 Min. :24.00
## 1st Qu.:3.000 1st Qu.:3.000 Class :character 1st Qu.:27.00
## Median :4.000 Median :3.000 Mode :character Median :28.00
## Mean :3.611 Mean :3.278 Mean :28.22
## 3rd Qu.:4.000 3rd Qu.:4.000 3rd Qu.:29.00
## Max. :5.000 Max. :5.000 Max. :32.00
## Gender Ethnicity
## Length:18 Length:18
## Class :character Class :character
## Mode :character Mode :character
##
##
##
Compute means and standard deviations of how positively participants expected to be evaluated.
psych::describe()
This is a handy function that will describe columns in your data frame.
## vars n mean sd median trimmed mad min max range skew kurtosis
## PosSpoke 1 18 3.61 0.78 4 3.62 1.48 2 5 3 0.01 -0.67
## PosWrit 2 18 3.22 0.94 3 3.25 1.48 1 5 4 -0.42 -0.11
## se
## PosSpoke 0.18
## PosWrit 0.22
These participants did not predict that they would be evaluated differently when employers listened to their spoken pitches (M = 3.61, SD = 0.78) than when employers read their written pitches (M = 3.22, SD = 0.94), paired t(17) = 1.20, p = .25, d = 0.45.
“They also did not expect any difference in their likelihood of getting hired depending on whether employers listened to their spoken pitches (M = 3.28, SD = 0.89) or read their written pitches (M = 3.00, SD = 1.08), paired t(17) = 0.80, p = .44, d = 0.29.”
Add a column to your data frame that contains the difference between expected evaluation of spoken and written pitches.
There are two ways to do a paired-samples t test. The first is to do a one-sample t test of the difference scores.
Conduct a one sample t test against the null hypothesis that the mean of the difference scores is 0.
##
## One Sample t-test
##
## data: dta$PosDiff
## t = 1.1974, df = 17, p-value = 0.2476
## alternative hypothesis: true mean is not equal to 0
## 95 percent confidence interval:
## -0.2963399 1.0741177
## sample estimates:
## mean of x
## 0.3888889
Try the second way of getting the same result, which is using t.test()
with the argument paired = TRUE
.
##
## Paired t-test
##
## data: dta$PosSpoke and dta$PosWrit
## t = 1.1974, df = 17, p-value = 0.2476
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -0.2963399 1.0741177
## sample estimates:
## mean of the differences
## 0.3888889
##
## One Sample t-test
##
## data: dta$PosDiff
## t = 1.1974, df = 17, p-value = 0.2476
## alternative hypothesis: true mean is not equal to 0
## 95 percent confidence interval:
## -0.2963399 1.0741177
## sample estimates:
## mean of x
## 0.3888889
##
## Paired t-test
##
## data: dta$PosSpoke and dta$PosWrit
## t = 1.1974, df = 17, p-value = 0.2476
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -0.2963399 1.0741177
## sample estimates:
## mean of the differences
## 0.3888889
The assumptions are the same as for a one-sample t, but they are assumptions about the difference scores.
We can assess how tenable the normality assumption is in the same ways we did for the one-sample t test:
##
## Shapiro-Wilk normality test
##
## data: dta$PosDiff
## W = 0.86361, p-value = 0.01398