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By Posted on Posted in Methods No Comments

Here's the abstract of a PLoS One article, "Racial Bias in Perceptions of Others' Pain":

The present work provides evidence that people assume a priori that Blacks feel less pain than do Whites. It also demonstrates that this bias is rooted in perceptions of status and the privilege (or hardship) status confers, not race per se. Archival data from the National Football League injury reports reveal that, relative to injured White players, injured Black players are deemed more likely to play in a subsequent game, possibly because people assume they feel less pain. Experiments 1–4 show that White and Black Americans–including registered nurses and nursing students–assume that Black people feel less pain than do White people. Finally, Experiments 5 and 6 provide evidence that this bias is rooted in perceptions of status, not race per se. Taken together, these data have important implications for understanding race-related biases and healthcare disparities.

Here are descriptions of the samples for each experiment, after exclusions of respondents who did not meet criteria for inclusion:

  • Experiment 1: 240 whites from the University of Virginia psychology pool or MTurk
  • Experiment 2: 35 blacks from the University of Virginia psychology pool or MTurk
  • Experiment 3: 43 registered nurses or nursing students
  • Experiment 4: 60 persons from MTurk
  • Experiment 5: 104 persons from MTurk
  • Experiment 6: 245 persons from MTurk

Not the most representative samples, of course. If you're thinking that it would be interesting to see whether results hold in a nationally representative sample with a large sample size, well, that was tried, with a survey experiment as part of the Time Sharing Experiments in the Social Sciences. Here's the description of the results listed on the TESS site for the study:

Analyses yielded mixed evidence. Planned comparison were often marginal or non-significant. As predicted, White participants made (marginally) lower pain ratings for Black vs. White targets, but only when self-ratings came before target ratings. When target ratings came before self-ratings, White participants made (marginally) lower pain ratings for White vs. Black targets. Follow-up analyses suggest that White participants may have been reactant. White participants reported that they were most similar to the Black target and least similar to the White target, contrary to prediction and previous work both in our lab and others' lab. Moreover, White participants reported that Blacks were most privileged and White participants least privileged, again contrary to prediction and previous work both in our lab and others' lab.

The results of this TESS study do not invalidate the results of the six experiments and one archival study reported in the PLoS One article, but the non-reporting of the TESS study does raise questions about whether there were other unreported experiments and archival studies.

The TESS study had an unusually large and diverse sample: 586 non-Hispanic whites, 526 non-Hispanic blacks, 520 non-Hispanic Asians, and 528 Hispanics. It's too bad that these data were placed into a file drawer.

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By Posted on Posted in Race No Comments

Christopher D. DeSante published an article in the American Journal of Political Science titled, "Working Twice as Hard to Get Half as Far: Race, Work Ethic, and America’s Deserving Poor" (57: 342-356, April 2013). The title refers to survey evidence that DeSante reported indicating that, compared to hypothetical white applicants for state assistance, hypothetical black applicants for state assistance received less reward for hard work and more punishment for laziness.

The study had a clever research design: respondents were shown two applications for state assistance, and each applicant was said to need $900, but there was variation in the names of the applicants (Emily, Laurie, Keisha, Latoya, or no name provided) and in the Worker Quality Assessment of the applicant (poor, excellent, or no assessment section provided); respondents were then asked to divide $1500 between the applicants or to use some or all of the $1500 to offset the state budget deficit.

Table 1 below indicates the characteristics of the conditions and the mean allocations made to each alternative. In condition 5, for example, 64 respondents were asked to divide $1500 between hardworking Laurie, lazy Emily, and offsetting the state budget deficit: hardworking Laurie received a mean allocation of $682, lazy Emily received a mean allocation of $566, and the mean allocation to offset the state budget deficit was $250.

DeSanteReproductionTable1blog

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I'm going to quote DeSante (2013: 343) and intersperse comments about the claims. For the purpose of this analysis, let's presume that respondents interpreted Emily and Laurie as white applicants and Keisha and Latoya as black applicants. Reported p-values for my analysis below are two-tailed p-values. Here's the first part of our DeSante (2013: 343) quote.

Through a nationally representative survey experiment in which respondents were asked to make recommendations regarding who should receive government assistance, I find that American “principles” of individualism, hard work, and equal treatment serve to uniquely benefit whites in two distinct ways. First, the results show that compared to African Americans, whites are not automatically perceived as more deserving of government assistance.

Condition 7 paired Laurie with Keisha, neither of whom had a Worker Quality Assessment. Laurie received a mean allocation of $556, and Keisha received a mean allocation of $600. Keisha received $44 more than Laurie, a $44 difference that is statistically significant at p<0.01. So DeSante is technically correct that "whites are not automatically perceived as more deserving of government assistance," but this claim overlooks evidence from condition 7 that a white applicant was given LESS government assistance than an equivalent black applicant.

Instead of reporting these straightforward results from condition 7, how did DeSante compare allocations to black and white applicants? Below is an image from Table 2 of DeSante (2013), which reported results from eleven t-tests. Tests 3 and 4 provided the evidence for DeSante's claim that, "compared to African Americans, whites are not automatically perceived as more deserving of government assistance."

DeSante2013Table2

Here's what DeSante did in test 3: DeSante took the $556 allocated to Laurie in condition 7 when Laurie was paired with Keisha and compared that to the $546 allocated to Latoya in condition 10 when Latoya was paired with Keisha; that $9 advantage (bear with the rounding error) for Laurie over Latoya (when both applicants were paired with Keisha and neither had a Worker Quality Assessment) did not reach conventional levels of statistical significance.

Here's what DeSante did in test 4: DeSante took the $587 allocated to Emily in condition 4 when Emily was paired with Laurie and compared that to the $600 allocated to Keisha in condition 7 when Keisha was paired with Laurie; that $12 advantage for Keisha over Emily (when both applicants were paired with Laurie and neither had a Worker Quality Assessment) did not reach conventional levels of statistical significance.

So which of these three tests is the best test? My test had more observations, compared within instead of across conditions, and had a lower standard error. But DeSante's tests are not wrong or meaningless: the problem is that tests 3 and 4 provide incomplete information for the purposes of testing for racial bias against applicants with no reported Worker Quality Assessment.

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Here's the next part of that quote from DeSante (2013: 343):

Instead, the way hard work and "laziness" are treated is conditioned by race: whites gain more for the same level of effort, and blacks are punished more severely for the same level of "laziness."

Here's what DeSante did to produce this inference. Emily received a mean allocation of $587 in condition 4 when paired with Laurie and neither applicant had a Worker Quality Assessment; but hard-working Emily received $711 in condition 6 when paired with lazy Laurie. This $123 difference can be interpreted as a reward for Emily's hard work, at least in relation to Laurie's laziness.

Now we do the same thing for Keisha paired with Laurie: Keisha received a mean allocation of $600 in condition 7 when paired with Laurie and neither applicant had a Worker Quality Assessment; but hard-working Keisha received $607 in condition 9 when paired with lazy Laurie. This $7 difference can be interpreted as a reward for Keisha's hard work, at least in relation to Laurie's laziness.

Test 7 indicates that the $123 reward to Emily for her hard work was larger than the $7 reward to Keisha for her hard work (p=0.03).

But notice that DeSante could have conducted another set of comparisons:

Laurie received a mean allocation of $556 in condition 7 when paired with Keisha and neither applicant had a Worker Quality Assessment; but hard-working Laurie received $620 in condition 8 when paired with lazy Keisha. This $64 difference can be interpreted as a reward for Laurie's hard work, at least in relation to Keisha's laziness.

Now we do the same thing for Latoya paired with Keisha: Latoya received a mean allocation of $546 in condition 10 when paired with Keisha and neither applicant had a Worker Quality Assessment; but hard-working Latoya received $627 in condition 11 when paired with lazy Keisha. This $81 difference can be interpreted as a reward for Latoya's hard work, at least in relation to Keisha's laziness.

The $16 difference between Laurie's $64 reward for hard work and Latoya's $81 reward for hard work (rounding error, again) is not statistically significant at conventional levels (p=0.76). The combined effect of the DeSante test and my alternate test is not statistically significant at conventional levels (effect of $49, p=0.20), so -- in this dataset -- there is a lack of evidence at a statistically significant level for the claim that "whites gain more for the same level of effort."

I conducted a similar set of alternate tests for the inference that "blacks are punished more severely for the same level of "laziness"; the effect size was smaller in my test compared to DeSante's test, but evidence for the the combined effect was believable: a $74 effect, with p=0.06.

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Here's the next part of that quote from DeSante (2013: 343):

Second, and consistent with those who take the "principled ideology" approach to the new racism measures, the racial resentment scale is shown to predict a desire for smaller government and less government spending. However, in direct opposition to this ideology-based argument, this effect is conditional upon the race of the persons placing demands on the government: the effect of racial resentment on a desire for a smaller government greatly wanes when the beneficiaries of that government spending are white as opposed to black. This represents strong evidence that racial resentment is more racial animus than ideology.

DeSante based this inference on results reported in Table 3, reproduced below:

DeSante2013Table3

Notice the note at the bottom: "White respondents only." DeSante reported results in Table 3 based on responses only from respondents coded as white, but reported results in Table 2 based on responses from respondents coded as white, black, Asian, Native American, mixed race, or Other. Maybe there's a good theoretical reason for changing the sample. DeSante's data and code are posted here if you are interested in what happens to p-values when Table 2 results are restricted to whites and Table 3 results include all respondents.

But let's focus on the bold RRxWW line in Table 3. RR is racial resentment, and WW is a dichotomous variable for the conditions in which both applicants were white. Model 3 includes categories for WW (two white applicants paired together), BB (two black applicants paired together), and WB (one white applicant paired with one black applicant); this is very important, because these included terms must be interpreted in relation to the omitted category that I will call NN (two unnamed applicants paired together). Therefore, the -337.92 coefficient on the RRxWW variable in model 3 indicates that -- all other model variables held constant -- white respondents allocated $337.92 less to offset the state budget deficit when both applicants were white compared to when both applicants were unnamed.

The -196.43 coefficient for the RRxBB variable in model 3 indicates that -- all other model variables held constant -- white respondents allocated $196.43 less to offset the state budget deficit when both applicants were black compared to when both applicants were unnamed. This -$196.43 coefficient did not reach statistical significance, but the coefficient is important because the bias in favor of the two white applicants relative to the two black applicants is only -$337.92 minus -$196.43; so whites allocated $141.49 less to offset the state budget deficit when both applicants were white compared to when both applicants were black, but the p-value for this difference was 0.41.

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Here's a few takeaways from the above analysis:

1. The limited choice of statistical tests reported in DeSante (2013) produced inferences that overestimated the extent of bias against black applicants and missed evidence of bias against white applicants.

2. Takeaway 1 depends on the names reflecting only race of the applicant. But the names might have reflected something other than race; for instance, in condition 10, Keisha received a mean allocation $21 higher than the mean allocation to Latoya (p=0.03): such a difference is not expected if Keisha and Latoya were "all else equal."

3. Takeaway 1 would likely not have been uncovered had the AJPS not required the posting of data and replication files from its published articles.

4. Pre-registration would eliminate suspicion about research design decisions, such as decisions to restrict only some analyses to whites and to report some comparisons but not others.

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In case you are interested in reproducing the results that I discussed, the data are here, code is here, and the working paper is here. Comments are welcome.

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UPDATE (Nov 2, 2014)

I recently received a rejection for the manuscript describing the results reported above; the second reviewer suggested portraying the raw data table as a graph: I couldn't figure out an efficient way to do that, but the suggestion did get me to realize a good way to present the main point of the manuscript more clearly with visuals.

The figure below illustrates the pattern of comparison for DeSante 2013 tests 1 and 2: solid lines represent comparisons reported in DeSante 2013 and dashed lines represent unreported equivalent or relevant comparisons; numbers in square brackets respectively indicate the applicant and the condition, so that [1/2] indicates applicant 1 in condition 2.

 

Tests 1 and 2

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The figure below indicates the pattern of reported and unreported comparisons for black applicants and white applicants with no Worker Quality Assessment: the article reported two small non-statistically significant differences when comparing applicants across conditions, but the article did not report the larger statistically significant difference favoring the black applicant when a black applicant and a white applicant were compared within conditions.

Tests 3 and 4---

The figure below indicates the pattern of reported and unreported comparisons for the main takeaway of the article. The left side of the figure indicates that one of the black applicants received a lesser reward for an excellent Worker Quality Assessment and received a larger penalty for a poor Worker Quality Assessment, compared to the reward and penalty for the corresponding white applicant; however, neither the lesser reward for an excellent Worker Quality Assessment nor the larger penalty for a poor Worker Quality Assessment was present at a statistically significant level in the comparisons on the right, which were not reported in the article (p=0.76 and 0.31, respectively).

Tests Rest---

Data for the reproduction are here. Reproduction code is here.

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UPDATE (Mar 8, 2015)

The above analysis has been published here by Research & Politics.

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By Posted on Posted in Reproductions No Comments

Rattan et al. (2012) reported evidence, as indicated in the abstract, that:

...simply bringing to mind a Black (vs. White) juvenile offender led participants to view juveniles in general as significantly more similar to adults in their inherent culpability and to express more support for severe sentencing.

Data for the study were collected by the Time Sharing Experiments for the Social Sciences and are located here.*

In this post, I present results of an attempt to reproduce and extend this study.

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The first takeaway is substantive: the reproduction and extension suggest that Rattan et al. might have applied the incorrect theory to explain results because their reported analyses were limited to white respondents.

Here's part of a figure from Rattan et al. (2012):

RattanL

The figure indicates that white respondents in the study expressed more support for life in prison without parole when primed to think about a black juvenile offender than when primed to think about a white juvenile offender. The authors appear to attribute this racial bias to stereotypic associations:

The results also extend the established literature in social psychology examining the cognitive association between the social category "Black" and criminality, and raise the possibility that this race-crime association may be at odds with lay people’s typical notions about the innocence of juveniles. [citation removed]

But here are the results when observations from both white and black respondents are reported:

Blacks offered more support for life in prison without parole when primed to think of a white juvenile offender than when primed to think of a black juvenile offender. If there is a generalized effect here, it does not appear that the effect is caused by stereotypic associations of criminality with the social category "black." It seems more likely that the racial bias detected in the study reflected ingroup favoritism or outgroup antagonism among both whites and blacks.

Check out the working paper here for more detail on the results, a more nuanced breakdown of white responses, background on related research, and policy implications; feel free to comment on this blog post or to email comments regarding the working paper.

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The second takeaway is methodological: the reproduction and extension suggest that this study seems to suffer from researcher degrees of freedom.

One of the first things that I noticed when comparing the article to the data was that the article mentioned two dependent variables but there appeared to be four dependent variables in the survey; based on my analyses, the two dependent variables not mentioned in the study did not appear to provide evidence of racial bias. I suppose that I can understand the idea that these null findings reflect "failed" experiments in some way, but I'd have liked as a reader to have been informed that racial bias was detected for only half of the dependent variables.

I also noticed that the dataset had three manipulation check items, but only one of these manipulation checks was used in the analysis; of course, the manipulation check that was used was the most important manipulation check (remembering the race of the juvenile offender), but I'd have liked as a reader to have been informed that manipulation checks for the juvenile offender's age and crime were unused.

And I noticed -- and this is more a problem with SPSS and statistics training than with the Rattan et al. analysis -- that the weighting of observations in SPSS resulted in incorrectly deflated p-values. I discussed this problem here and here and here; data for the first link were the Rattan et al. (2012) data.

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* There are two datasets for the Rattan et al. (2012) study. I received the full dataset in an email from TESS, and this dataset was previously posted at the TESS archive; the dataset currently posted at the TESS archive contains a weight2 variable for only white respondents who met participation criteria, provided complete data, and finished the survey in one minute or longer.

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UPDATE (Mar 15, 2015)

Replaced the figure with results for white and black respondents, which should have ranged from 1 to 6. The original figure incorrectly ranged from 0 to 6.

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This R lesson is for confidence intervals on point estimates. See here for other lessons.

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Here's the first three lines of code:

pe <- c(2.48, 1.56, 2.96)
y.axis <- c(1:3)
plot(pe, y.axis, type="p", axes=T, pch=19, xlim=c(1,4), ylim=c(1,3))

The first line places 2.48, 1.56, and 2.96 into a vector called "pe" for point estimates; you can call the vector anything that you want, as long as R recognizes the vector name.

The second line sends the integers from 1 to 3 into the vector "y.axis"; instead of y.axis <- c(1:3), you could have written y.axis <- c(1,2,3) to do the same thing.

The third line plots a graph with pe on the x-axis and y.axis on the y-axis; type="p" tells R to plot points, axes=T tells R to draw axes, pch=19 indicates what type of points to draw, xlim=c(1,4) indicates that the x-axis extends from 1 to 4, and ylim=c(1,3) indicates that the y-axis extends from 1 to 3.

Here's the graph so far:

ci1---

Let's make the points a bit larger by adding cex=1.2 to the end of the plot command.

Let's also add a title, using a new line of code: title(main="Negative Stereotype Disagreement > 3").

ci2---

Let's add the 95% confidence interval lines.

lower <- c(2.26, 1.17, 2.64)
upper <- c(2.70, 1.94, 3.28)
segments(lower, y.axis, upper, y.axis, lwd= 1.3)

The first line indicates the lower ends of the confidence intervals; the second line indicates the upper ends of the confidence intervals; and the segments command draws line segments from the coordinate (lower, y.axis) to the coordinate (upper, y.axis), with lwd=1.3 indicating that the line should be slightly thicker than the default.

Here's what we have so far:

ci3---

Let's replace the x-axis and y-axis. First, change axes=T to axes=F in the plot command; then add the code axis(1, at=seq(1,4,by=1)) to tell R to draw an axis at the bottom from 1 to 4 with tick marks every 1 unit. Here's what we get:

ci4Let's get rid of the "pe" and "y.axis" labels. Add to the plot command: xlab="", ylab="". Here's the graph now:

ci5---

Let's work on the y-axis now:

names <- c("Baseline", "Black\nFamily", "Affirmative\nAction")
axis(2, at=y.axis, label=names)

The first line sends three phrases to the vector "names"; the \n in the phrases tells R to place "Family" and "Action" on a new line. Here's the result:

ci6Let's make the y-axis labels perpendicular to the y-axis by adding las=2 to the axis(2 line. [las=0 would keep the labels parallel.]

ci7Now we need to add a little more space to the left of the graph to see the y-axis labels. Add par(mar=c(4, 6, 2, 0)) above the plot command to tell R to make the margins 4, 6, 2, and 0 for the bottom, left, top, and right margins.

ci8---

Let's say that I decided that I prefer to have the baseline on top of the graph and Affirmative Action at the bottom of the graph. I could use the rev() function to reverse the order of the points in the plot, segments, and axis functions to get:

ci9---

Here is the whole code for the above graph. By the way, the graph above can be found in my article on social desirability in the list experiment, "You Wouldn't Like Me When I'm Angry."

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This R lesson is for the plot command. See here for other lessons.

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The start of this code is a bit complex. It's from R Commander, which is a way to use R through a graphical interface without having to write code.

library(foreign)

The library function with the foreign package is used to import data from SPSS, Stata, or some other software.

DWHouse <- read.dta("C:/house_polarization46_113v9.dta", convert.dates=TRUE, convert.factors=TRUE, missing.type=TRUE, convert.underscore=TRUE, warn.missing.labels=TRUE)

The above command reads data from Stata (.dta extension) and places the data into DWHouse. The house_polarization46_113v9.dta dataset is from Voteview polarization data, located here. [The v9 on the end of the dataset indicates that I saved the dataset as Stata version 9.]

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Here's the plot command:

plot(repmean1~year, type="p", xlim=c(1900,2012), ylim=c(-1,1), xlab="Year", ylab="Liberal - Conservative", pch=19, col="red", main="House", data=DWHouse)

Here are what the arguments mean: the tilde in repmean1~year plots repmean1 as a function of year, type="p" indicates to plot points, xlim=c(1900,2012) indicates the limits for the x-axis, ylim=c(-1,1) indicates the limits for the x-axis, xlab="Year" and ylab="Liberal - Conservative" respectively indicate labels for the x-axis and y-axis, pch=19 indicates to use the 19 plotting character [see here for a list of pchs], col="red" indicates the color for the pchs [see here for a list of colors], main="House" indicates the main title, and data=DWHouse indicates the data to plot.

Here's what the graph looks like so far:

plotgop---

The repmean1 plotted above is the Republican Party mean for the first-dimension DW-Nominate scores among members of the House of Representatives. Let's add the Democrats. Instead of adding a new plot command, we just add points:

points(demmean1~year, type="p", pch=19, col="blue", data=DWHouse)

Now let's add some labels:

text(1960,0.4,labels="GOP mean", col="red")
text(1960,-0.4,labels="Dem mean", col="blue")

The first command adds text at the coordinate x=1960 and y =0.4; the text itself is "GOP mean," and the color of the text is red. I picked x=1960 and y =0.4 through trial and error to see where the text would look the nicest.

Here's the graph now:

plotgopdem---

Notice that the x-axis is labeled in increments of 20 years (1900, 1920, 1940, ...). This can be changed as follows. First, add axes=F to the plot command to shut off axes; you could also write axes=FALSE); then add these axis lines below the plot command:

axis(1, at=seq(1900, 2020, 10))
axis(2, at=seq(-1, 1, 0.5))

The above lines tell R to plot axes at the indicated intervals. The first line arguments are: 1 tells R to plot an axis below [1=below, 2=left, 3=above, and 4=right], and the (1900, 2020, 10) sequence tells R to plot from 1900 to 2020 and place tick marks every 10 years. Here's the resulting graph:

plotgopdem20---

Notice that the x-axis and y-axis do not touch in the graph above. There's a few extra points plotted that I did not intend to plot: I meant to start the graph at 1900 so that the first point was 1901 (DW-Nominate scores are provided in the dataset every two years starting with 1879). To get the x-axis and y-axis to touch, add xaxs="i", yaxs="i" to the plot command. Let's also add box() to get a box around the graph, like we had in the first two graphs above.

plotgopdem20i

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Here is the whole code for the plot above.

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The first graph in this series is a barplot. This post will show how to add error bars to a barplot.

Here's the data that we want to plot, from a t-test conducted in Stata:

ttest---

Here's the first part of the code:

library(Hmisc)

The code above opens the Hmisc library, which has the error bar function that we will use.

means <- c(2.96, 3.59)

The code above places 2.96 and 3.59 into the vector "means".

bp = barplot(means, ylim=c(0,6), names.arg=c("Black", "White"), ylab="Support for life in prison without parole", xlab="Race of the convicted teen", width=c(0.2,0.2), xlim=c(0,1), space=c(1,1), las=1, main="Black Non-Hispanic Respondents")

The code above is similar to the barplot code that we used before, but notice that in this case the barplot is = bp. The remainder of the arguments are: means indicates what data to plot, ylim=c(0,6) indicates that the limits of the y-axis are 0 and 6, names.arg=c("Black", "White") indicates the names for the bars, ylab="Support for life in prison without parole" indicates the label for the y-axis, xlab="Race of the convicted teen" indicates the label for the x-axis, width=c(0.2,0.2) indicates the width of the bars, xlim=c(0,1) indicates that the limits of the x-axis are 0 and 1, space=c(1,1) indicates the spacing between bars, and main="Black Non-Hispanic Respondents" indicates the main title for the graph.

Here's the graph so far:

95a

---

Here's how to add the error bars:

se <- c(0.2346, 0.2022)
lower = c(means-1.96*se, means-1.96*se)
upper = c(means+1.96*se, means+1.96*se)
errbar(bp, means, upper, lower, add=T)

The first line sends the values for the standard errors into the vector "se". The second and third lines are used to calculate the ends of the error bars. The fourth line tells R to plot error bars; the add=T option tells R to keep the existing graph; without add=T, the graph will show only the error bars.

Finally, add the code box(bty="L") so that there is a line on the bottom of the graph. The bty="L" tells R to make the axis look like the letter L. Other options include C, O, 7, and U.

Here is the graph now:

95b---

It's not necessary to use the 1.96 multiplier for the error bars. The following code plugged in the lower and upper limits directly from the Stata output.

library(Hmisc)

means <- c(2.96, 3.59)

bp = barplot(means, ylim=c(0,6), names.arg = c("Black", "White"), ylab="Support for life in prison without parole", xlab="Race of the convicted teen", xpd=T, width=c(0.2,0.2), xlim=c(0,1), space=c(1,1), main="Black Non-Hispanic Respondents")

se <- c(0.2346, 0.2022)
lower = c(2.48, 3.19)
upper = c(3.42, 4.00)
errbar(bp, means, upper, lower, add=T)

box(bty="O")

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Here's what the graph looks like for the above, shortened code, with the bty="O":

95c

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Data from this post were drawn from here, with the article here. Click here for the graph code.

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If I remember correctly, my first introduction to R came when fellow Pitt graduate student Hirokazu Kikuchi requested that R be installed on the polisci lab computers. I looked into R and found this webpage based on a 2007 Perspectives on Politics article by Jonathan Kastellec and Eduardo Leoni. That link is a good place to start, but in this post I'll introduce a few lines of code to illustrate how nice and easy R can be. (Not that R is always easy.)

I'll indicate lines of R code in bold.

---

less5 <- c(40.91, 7.67, 7.11, 6.19, 15.65, 6.4, 4.57, 4.43, 2.42, 4.66)

The above command assigns the ten numbers (from 40.91 to 4.66) to a vector called "less5." c() is a concatenation function. The following command does the same thing:

 c(40.91, 7.67, 7.11, 6.19, 15.65, 6.4, 4.57, 4.43, 2.42, 4.66) -> less5

---

barplot (less5, main="Countries with a mean < 5", ylab="Percent", ylim=c(0, 40), names=c("1", "2", "3", "4", "5", "6", "7", "8", "9", "10"))

The barplot function tells R to plot a bar chart. These are the arguments: less 5 indicates the vector to plot, main="Countries with a mean < 5" indicates the main plot title, ylab="Percent" indicates the label for the y-axis, ylim=c(0, 40) indicates that the y-axis should run from 0 to 40, and names=c("1", "2", "3", "4", "5", "6", "7", "8", "9", "10")) indicates the set of names that should be placed below the set of bars.

Here's what this graph looks like, based on the two lines of code:

barplot1---

Let's plot three graphs together. Here's the code for graphs 2 and 3:

from56 <- c(18.35, 4.41, 5.68, 4.61, 22.63, 9.31, 7.63, 8.65, 4.99, 13.75)

barplot (from56, main="Countries with a mean > 5 and < 6", ylab="Percent", ylim=c(0, 40), names=c("1", "2", "3", "4", "5", "6", "7", "8", "9", "10"))

more6 <- c(7.99, 2.26, 3.37, 3.62, 17.29, 9.46, 8.95, 12.83 ,8.93, 25.3)

barplot (more6, main="Countries with a mean > 6", ylab="Percent", ylim=c(0, 40), names=c("1", "2", "3", "4", "5", "6", "7", "8", "9", "10"))

Let's put the par function at the top of the code to tell R how to plot these three graphs:

par(mfrow=c(1, 3))

The above line of code tells R to plot 1 row and 3 columns of plots. Here's the output:

barplot3This is the output for par(mfrow=c(3, 1)):

barplot3v---

That's it for this post: here is a text file of the code. By the way, the graph above can be found in my article on midpoint misperceptions.

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