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Month: August 2014

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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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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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Andrew Gelman linked to a story (see also here) about a Science article by Annie Franco, Neil Malhotra, and Gabor Simonovits on the file drawer problem in the Time Sharing Experiments for the Social Sciences. TESS fields social science survey experiments, and sometimes the results of these experiments are not published.

I have been writing up some of these unpublished results but haven't submitted anything yet. Neil Malhotra was kind enough to indicate that I'm not stepping on their toes, so I'll post what I have so far for comment. From what I have been able to determine, none of these studies discussed below were published, but let me know if I am incorrect about that. I'll try to post a more detailed write-up of these results soon, but in the meantime feel free to contact me for details on the analyses.

I've been concentrating on bias studies, because I figure that it's important to know if there is little-to-no evidence of bias in a large-scale nationally-representative sample; not that such a study proves that there's no bias, but reporting these studies helps to provide a better estimate for the magnitude of bias. It's also important to report evidence of bias in unexpected directions.

 

TESS 241

TESS study 241, based on a proposal from Stephen W. Benard, tested for race and sex bias in worker productivity ratings. Respondents received a vignette about the work behavior of a lawyer whose name was manipulated in the experimental conditions to signal the lawyer's sex and race: Kareem (black male), Brad (white male), Tamika (black female), and Kristen (white female). Respondents were asked how productive the lawyer was, how valuable the lawyer was, how hardworking the lawyer was, how competent the lawyer was, whether the lawyer deserved a raise, how respected the lawyer was, how honorable the lawyer was, how prestigious the lawyer was, how capable the lawyer was, how intelligent the lawyer was, and how knowledgeable the lawyer was.

Substantive responses to these eleven items were used to create a rating scale, with items standardized before summing and cases retained if there were substantive responses for at least three items; this scale had a Cronbach's alpha of 0.92. The scale was standardized so that its mean and standard deviation were respectively 0 and 1; higher values on the scale indicate more favorable evaluations.

Here is a chart of the main results, with experimental targets on the left side:

benardThe figure indicates point estimates and 95% confidence intervals for the mean level of evaluations in experimental conditions for all respondents and disaggregated groups; data were not weighted because the dataset did not contain a post-stratification weight variable.

The bias in this study is against Brad relative to Kareem, Kristen, and Tamika.

 

TESS 392

TESS study 392, based on a proposal from Lisa Rashotte and Murray Webster, tested for bias based on sex and age. Respondents were randomly assigned to receive a picture and text description of one of four target persons: Diane Williams, a 21-year-old woman; David Williams, a 21-year-old man; Diane Williams, a 45-year-old woman; and David Williams, a 45-year-old man. Respondents were asked to rate the target person on nine traits, drawn from Webster and Driskell (1983): intelligence, ability in situations in general, ability in things that the respondent thinks counts, capability at most tasks, reading ability, abstract abilities, high school grade point average, how well the person probably did on the Federal Aviation Administration exam for a private pilot license, and physical attractiveness. For the tenth item, respondents were shown their ratings for the previous nine items and given an opportunity to change their ratings.

The physical attractiveness item was used as a control variable in the analysis. Substantive responses to the other eight items were used to create a rating scale, with items standardized before summing and cases retained if the case had substantive responses for at least five items; this scale had a Cronbach's alpha of 0.91. The scale was standardized so that its mean and standard deviation were respectively 0 and 1; higher values on the scale indicate more favorable evaluations.

Here is a chart of the main results, with experimental targets on the left side:

rashotte The figure indicates point estimates and 95% confidence intervals for the mean level of evaluations in experimental conditions for all respondents and disaggregated groups; data were weighted. The bias in this study, among women, is in favor of older persons and, among men, is in favor of the older woman. Here's a table of 95% confidence intervals for mean rating differences for each comparison:

rashottetable

 

TESS 012

TESS study 012, based on a proposal from Emily Shafer, tested for bias for or against married women based on the women's choice of last name after marriage. The study's six conditions manipulated a married woman's last name and the commitment that caused the woman to increase the burden on others. Conditions 1 and 4, 2 and 5, and 3 and 6 respectively reflected the woman keeping her last name, hyphenating her last name, or adopting her husband's last name; the vignette for conditions 1, 2, and 3 indicated that the woman's co-workers were burdened because of the woman's marital commitment, and the vignette for conditions 4, 5, and 6 indicated that the woman's husband was burdened because of the woman's work commitment.

Substantive responses to items 1, 2, 5A, and 6A were used to create an "employee evaluation" scale, with items standardized before summing and cases retained if there were substantive responses for at least three items; this scale had a Cronbach's alpha of 0.73. Substantive responses to items 3, 4, 5B, and 6B were used to create a "wife evaluation" scale, with items standardized before summing and cases retained if there were substantive responses for at least three items; this scale had a Cronbach's alpha of 0.74. Both scales were standardized so that their mean and standard deviation were respectively 0 and 1 and then reversed so that higher scores indicated a more positive evaluation.

Results are presented for the entire sample, for men, for women, for persons who indicated that they were currently married or once married and used traditional last name patterns (traditional respondents), and for persons who indicated that they were currently married or once married but did not use traditional last name patterns (non-traditional respondents); name patterns were considered traditional for female respondents who changed their last name to their spouse's last name (with no last name change by the spouse), and male respondents whose spouse changed their last name (with no respondent last name change).

Here is a chart of the main results, with experimental conditions on the left side:

shafer

The figure displays point estimates and 95% confidence intervals for weighted mean ratings for each condition, adjusted for physical attractiveness. Not much bias detected here, except for men's wife evaluations when the target woman kept her last name.

 

TESS 714

TESS study 714, based on a proposal from Kimberly Rios Morrison, tested whether asking whites to report their race as white had a different effect on multiculturalism attitudes and prejudice than asking whites to report their ethnicity as European American. See here for published research on this topic.

Respondents were randomly assigned to one of three groups: respondents in the European American prime group were asked to identify their race/ethnicity as European American, American Indian or Alaska Native, Asian American or Pacific Islander, Black or African American, Hispanic/Latino, or Other; respondents in the White prime group were asked to identify their race/ethnicity from the same list but with European American replaced with White; and respondents in the control group were not asked to identify their race/ethnicity.

Respondents were shown 15 items regarding ethnic minorities, divided into four sections that we'll call support for multiculturalism, support for pro-ethnic policies, resentment of ethnic minorities, and closeness to whites. Scales were made for items from the first three sections; to create a "closeness to whites" scale, responses to the item on closeness to ethnic minorities were subtracted from responses to the item on closeness to nonminorities, to indicate degree of closeness to whites; this item was then standardized.

Here is a chart of the main results, with experimental conditions on the left side:

rios morrisonThe figure displays weighted point estimates and 95% confidence intervals. The prime did not have much influence, except for the bottom right graph.

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There's a LOT of interesting things in the TESS archives. Comparing reported results to my own analyses of the data (not for the above studies, but for other studies) has illustrated the inferential variation that researcher degrees of freedom can foster.

One of the ways to assess claims of liberal bias in social science is to comb through data such as the TESS archives, which let us see what a sample of researchers are interested in and what a sample of researchers place into their file drawer. Researchers placing null results into a file drawer is ambiguous because we cannot be sure whether placement in the file drawer is due to the null results or to the political valence of the null results; however, researchers placing statistically significant results into a file drawer has much less ambiguity.

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UPDATE (Sept 6, 2014)

Gábor Simonovits, one of the co-authors of the Science article, quickly and kindly sent me a Stata file of their dataset; that data and personal communication with Stephen W. Benard indicated that results from none of the four studies reported in this post have been published.

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I have posted a working manuscript on symbolic racism here, with its appendix here. Comments are welcome and appreciated. I'll outline the manuscript below and give some background to the research.

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On 27 October 2012, a Facebook friend posted a link to an Associated Press report "AP poll: Majority harbor prejudice against blacks." I posted this comment about the report:

sr1

During the Facebook discussion, I noted that it not obvious that the implicit measurements indicate racism, given the data on implicit preferences among blacks:

sr2

Bob Somersby at the Daily Howler noticed that the AP report provided data disaggregated by political party but failed to provide data disaggregated by race:

Although Ross and Agiesta were eager to tell you how many Democrats, Republicans and independents were shown to hold "anti-black feelings," they never tell you how many black respondents “hold anti-black feelings” as well!

Why didn't our intrepid reporters give us that information? We can't answer that question. But even a mildly skeptical observer could imagine one possible answer:

If substantial percentages of black respondents were allegedly shown to "hold anti-black feelings," that would make almost anyone wonder how valid the AP's measures may be. It would undermine confidence in the professors—in those men of vast erudition, the orange-shoed fellows who still seem to think that Obama trailed in the national polling all through the summer of 2008.

David Moore at iMediaEthics posted data disaggregated by race that he retrieved from the lead author of the study: based on the same method used in the original report, 30 percent of white Americans implicitly held anti-white sentiments, and 43 percent of black Americans implicitly held anti-black sentiments. Moore discussed how this previously-unreported information alters interpretation of the study's findings:

It appears that racism, as measured by this process, is much more complicated than the news story would suggest. We cannot talk about the 56% of Americans with "anti-black" attitudes as being "racist," if we do not also admit that close to half of all blacks are also "racist" – against their own race.

If we accept the measures of anti-black attitudes as a valid indicator of racism, then we also have to accept the anti-white measures as racism.

Moore did not tell us the results for black respondents on the explicit measures of racism, so that's the impetus behind Study 2 of the working manuscript.

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The explicit racism measure discussed in the AP report is symbolic racism, also known as racial resentment. Instead of explaining what symbolic racism is, I'll show how symbolic racism is typically measured; items below are from the American National Election Studies, but there were more items in the study discussed in the AP report.

Symbolic racism is measured in the ANES based on whether a survey respondent agrees strongly, agrees somewhat, neither agrees nor disagrees, disagrees somewhat, or disagrees strongly with these four items:

1. Irish, Italians, Jewish and many other minorities overcame prejudice and worked their way up. Blacks should do the same without any special favors.

2. Generations of slavery and discrimination have created conditions that make it difficult for blacks to work their way out of the lower class.

3. Over the past few years, blacks have gotten less than they deserve.

4. It's really a matter of some people not trying hard enough; if blacks would only try harder they could be just as well off as whites.

I hope that you can see why these are not really measures of explicit racism. Let's say that non-racist person A opposes special favors for all groups: that person would select the symbolic racist option for item 1, indicating a belief that blacks should work their way up without special favors. Person A is coded the same as a person B who opposes special favors for blacks because of person B's racism. So that's problem #1 with symbolic racism measures: the measures conflate racial attitudes and non-racial beliefs.

But notice that there is another problem. Let's say that person C underestimates the influence of slavery and discrimination on outcomes for contemporary blacks; person C will select a symbolic racism option for item 2, but is that racism? is that racial animosity? is that a reflection that a non-black person -- and even some black persons -- might not appreciate the legacy of slavery and discrimination? or is that something else? That's problem #2 with symbolic racism measures: it's not obvious how to interpret these measures.

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Researchers typically address problem 1 with control variables; the hope is that placing partisanship, self-reported ideology, and a few conservative values items into a regression sufficiently dilutes the non-racial component of symbolic racism so that the effect of symbolic racism can be interpreted as its racial component only.

In the first part of the working manuscript, I test this hope by predicting non-racial dependent variables, such as opposition to gay marriage. The idea of this test is that -- if statistical control really does sufficiently dilute the non-racial component of symbolic racism -- then symbolic racism should not correlate with opposition to gay marriage, because racism should not be expected to correlate with opposition to gay marriage; but -- if there is a correlation between symbolic racism and gay marriage -- then statistical control did not sufficiently dilute the non-racial component of symbolic racism.

The results indicate that a small set of controls often does not sufficiently dilute the non-racial component of symbolic racism, so results from symbolic racism research with a small set of controls should be treated skeptically. But a more extensive set of controls often does sufficiently dilute the non-racial component of symbolic racism, so we can place more -- but not complete -- confidence in results from symbolic racism research with an extensive set of controls.

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The way that I addressed problem #2 -- about how to interpret symbolic racism measures -- is to assess the effect of symbolic racism among black respondents. Results indicate that among blacks -- and even among a set of black respondents with quite positive views of their own racial group -- symbolic racism sometimes positively correlates with opposition to policies to help blacks.

Study 2 suggests that it is not legitimate for researchers to interpret symbolic racism among whites differently than symbolic racism among blacks, without some other information that can permit us to state that symbolic racism means something different for blacks and whites. Study 3 assesses whether there is evidence that symbolic racism means something different for blacks and whites.

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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

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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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