Indexing and Inference
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Good-HW2-A-Poli-101.pdf
Poli 101 HW 2
1. Concept for Dependent Variable: Belief in/acknowledgement of racial discrimination towards African Americans in the US today, measured by the perceived notions of police treatment on the basis of race, the general level of perceived discrimination that African Americans receive, as well as the perceived frequency with which police officers stop African Americans as opposed to other races.
o American National Election Studies (ANES) 2016 Pre-‐test/Pilot Data o Dependent Variable 1/DV1 o disc_police: Police discrimination
o “In general, do the police treat whites better than blacks, treat blacks better than whites, or treat them both the same?”
o Missing Values/Recodes: I recoded the 8/9 (don’t know/missing) category responses as missing because they only accounted for three of the respondents. I then recoded the indicator name from disc_police into “policetreat” for ease of viewing/analysis. I recoded the initial 7 categories into three categories with respect to how police treat two groups of people: “treat blacks better,” “same,” and “treat whites better” so as to simplify the cross-‐tabulation process, as well as making the data ordinal by coding the responses to “treat blacks better” as 0, “same” as .5, and “treat whites better” as 1, in order to make the high score evidence of belief in discrimination on the basis of race.
o Descriptive Statistics: This data are ordinal, so the mode and the median are most meaningful measures of central tendency for these measures, along with analysis of the frequency distribution table. The median demonstrates that the middle of the data was in fact found on the 1 or the category that believed that police treat white people better than African Americans, supported by the fact that 60% of the responses fell in this category. This is also seen in the mode, or the most frequent response being that of those who believe whites are treated better by police.
Mean .7896 Median 1.000 Mode 1.000 Std. Deviation .26995 Skewness .-‐771 Kurtosis -‐.539 o DV2 o disc_b: Discrimination towards African Americans.
o “How much discrimination is there in the United States today against each of the following groups?”
§ For our purposes the responses for “blacks” were analyzed.
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o Missing values/recodes: I declared missing values for 8/9 categories, (don’t know/skipped). I renamed disc_b into “discrim” to clearly show it is asking about discrimination in general, and I recoded the 5 original categories into 3: I combined “a great deal” and “a lot” responses into the new category of “a lot” and coded it as 1, I made the “moderate” responses into .5 and kept that label, and I combined the “a little” and “none” responses, renamed this category “little to none” and coded it as 0, giving the low score to those that do not think African Americans experience discrimination in the US, and the high score to those that do believe this is true, in keeping with the scoring range of the recoding of the first indicator for the dependent variable.
o Descriptive Statistics: This question is also an ordinal measure, so the most meaningful measure of central tendency here are the median and mode. The median reflects that the middle of the data falls in the moderate category, where 33.6% of respondents agreed that there is a moderate level of discrimination towards African Americans in the US today. The mode was 1, indicating that the category with the highest number of responses was “a lot,” with 38.1% of responders agreeing that African Americans face a lot of discrimination in the US today.
Mean .5498 Median .5000 Mode 1.00 Std. Deviation .40469 Skewness -‐.183 Kurtosis -‐1.451
o DV3 o Stopblack: Racial Profiling
o “How often do you think police officers stop black people on the street without a good reason?”
o Missing Values/Recodes: I declared missing values for 8/9 categories, and I renamed the indicator racialprof to show that it is a question pertaining to police use of racial profiling/discrimination on the basis of race. I then adjusted the 5 given categories into 3 new categories, combining the never/rarely categories into the new “rarely, if ever” category and recoding it with the low score/0, leaving the sometimes category alone and recoding it with the middle score of .5, and combining the somewhat often/very often category into the “often” category and recoding it with the high score of 1 in order to keep this scoring consistent throughout the dependent variable indicator recodes.
o Descriptive Statistics: The data produced from this indicator is again ordinal and as such the same measures of descriptive statistics will be used to analyze the data. The median shows that the middle of the data falls into “sometimes” category, where respondents believe that police officers sometimes stop black people for no reason, and the mode, or the category
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with the highest response rate is 1, or the “often” category, where respondents agreed that police officers often stop black people for no reason.
Mean .6918 Median .5000 Mode 1.00 Std. Deviation .33463 Skewness -‐.629 Kurtosis -‐.668
o Reliability Analysis: This alpha score indicates that there is an acceptable level of reliability between the three indicators for the dependent variable tested, .637. If any of the three indicators were to be deleted, the Cronbach alpha score would decrease. Thus, with this alpha score, I can conclude that these indicators are related enough to combine into an index.
Cronbach’s Alpha Cronbach’s Alpha Based on Standardized Items
N of Items
.637 .651 3
Item Total Statistics: Scale Mean
If Item Deleted
Scale Variance if Item Deleted
Corrected Item-‐Total Correlation
Squared Multiple Correlation
Cronbach’s Alpha if Item Deleted
Policetreat 1.2425 .379 .471 .222 .537 discrim 1.4824 .250 .474 .230 .522 racialprof 1.3400 .328 .435 .191 .554 2. Summary Index of Dependent Variable: Raw Index Statistics:
Mean 2.0325 Median 2.0000 Std. Deviation .77920 Skewness -‐.304 Kurtosis -‐.933
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Raw Index Frequency Percent Valid Percent Cumulative Percent .00 6 .8 .8 .8 .50 27 3.9 3.9 4.7 1.00 94 13.7 13.8 18.6 1.50 134 19.6 19.7 38.3 2.00 123 18.1 18.2 56.4 2.50 124 25.2 18.2 74.7 3.00 172 99.4 25.3 100.0 Total 680 99.4 100.0 Missing System 4 .6 Total 684 100.0 3. Recoded Index: There are substantial differences between the mean for the raw and recoded index summary measures, as well as a slight increase in the standard deviation. The other noticeable change to the recoded index is that the labels have been recoded, and the categories have been recoded to 1,2,3 and then low, medium and high by attempting to cut the cumulative percent column into thirds. It is not exactly cut into 33.3%, but it was as close to that standard as I could achieve. Statistics: Mean 1.8705 Median 2.0000 Std. Deviation
.78762
Skewness .233 Kurtosis -‐1.353 Index: Frequency Percent Valid Percent Cumulative
Percent Low 260 38.1 38.3 38.3 Medium 247 36.2 36.4 74.7 High 172 25.2 25.3 100.0 Total 680 99.4 100.0 Missing System 4 .6 Total 684 100.0
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4. Independent Variables: o IV1: o follow: political awareness
o “Some people seem to follow what's going on in government and public affairs most of the time, whether there’s an election going on or not. Others aren’t that interested. Would you say you follow what’s going on in government and public affairs most of the time, some of the time, only now and then, or hardly at all?”
o Concept being measured by IV1: The concept being measured here is level of involvement and knowledge of current political affairs in the US.
o Recodes/Missing Variables: I declared the missing values for this indicator (8,9), as well as renamed the variable “poli.” This indicator has four categories measured at the ordinal level so I recoded them similarly to the dependent variables, where the categories that were close were combined; the ‘most of the time’ and ‘some of the time’ categories became ‘often’ as well as the high scoring category of 1, the ‘only now and then category became ‘sometimes’ and .5 as the middle category, and the ‘only now and then’ and ‘hardly at all’ were combined to form ‘rarely’ with the score of 0.
o The relevant summary measures are as follows, and show that the middle of the data falls in the often category, as well as the mode, showing that most respondents, or 77.9%, are aware of the current political climate and issues.
Mean .8506 Median 1.000 Mode 1.000
o IV2: race_ident: Importance of racial identity. o “How important is being (respondent’s perspective race) to
your identity?” o Concept: This indicator was chosen to measure the importance or
significance of ones own race or ethnicity to their life and experiences. o Recodes/Missing Variables: Missing variables were taken care of, and
I renamed the variable ‘race_import,’ as well as recoded the ordinal data into a three category indicator, combining the ‘extremely important’/’very important’ categories into a single ‘very important’ category with the score of 1, I kept the ‘moderately important’ category but recoded it with the appropriate .5, and combined the ‘not important at all’ and the ‘a little important’ categories into the ‘of little importance’ category, scored with a 0. This variable displays a good amount of variation, and the median is found within the ‘moderately important’ category that has 21.8% of the respondents, and the mode lies within the ‘very important’ category, where 46.6% of the respondents answered.
Mean .5749 Median .5000 Mode 1.00
o IV3:
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o Skintone: The respondents pick the hand that matches most closely with their skin tone.
o “As you know, human beings display a wide variety of physical characteristics. One of these is skin color. Displayed below is a skin color scale that ranges from 1 to 10. The 10 shades of skin color are represented by a hand of identical form, but differing in color. Which hand shown below comes closes to your skin color?
o Concept: The indicator is measuring the pigmentation/the darkness or lightness of the respondents skin, as a secondary measure to questions of race and ethnicity.
o Recodes/Missing Values: Missing values were declared, as well as the skipped and not asked categories present on the frequency table for this indicator. This measure approaches interval level data with the way they associated a skin tone with a number 1-‐10, so I thought it best not to make any further adjustments so as not to collapse skin tone categories.
o The median fell within the 2 category, associated with a light skin tone and the mode also fell within this category, signifying that most respondents are relatively fair skinned. The mean shows that the average skin tone was somewhere in between a 2 and a 3 with the “hand scale” the questionnaire provided.
Mean 2.60 Median 2.00 Mode 2
o Relationship between IV1 and the Indexed DV.
o The first cross tab will be of the Recoded index and the Independent Variable known as poli.
Political Awareness
Belief in/acknowledgment of racial discrimination in the US.
o Cramer’s V: .068 o Kendall’s Tau-‐b: .055 o Analysis: The relationship between ones general political awareness and
their acknowledgment or belief in racial discrimination occurring in the US
rarely sometimes often low %
within poli
35.2% 45.3% 37.4%
medium % within poli
46.3% 35.8% 35.3%
high % within poli
18.5% 18.9% 27.3%
Total 100.0% 100.0% 100.0%
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today is a very weak but positive relationship, demonstrated by the main diagonal growing in size as it reaches the bottom of the cross tab as well as the (+) tau-‐b. Tau-‐b was used because the data were ordinal and the table square. This combination of variables was hypothesized to represent a relationship because I thought that the more in-‐tune someone is to the news and the hot-‐button political topics of the day that they would have more exposure to stories pertaining to the systemic racial discrimination at work in the US today.
o Relationship between IV2 and the Indexed Dependent Variable:
How Important Race is to Your Identity Belief in/ acknowledgement of racial discrimination in the US.
o Cramer’s V: .081 o Kendall’s Tau-‐b: .062 o Analysis: The relationship between the importance of racial identity and the
belief or acknowledgement of racial discrimination in the US is a very weak positive relationship. The main diagonal increases slightly but then decreases as it reaches the end of the cross tab table. There does seem to be a relationship between those that believed their racial identity was very important to them and those that strongly believe in the existence of racial discrimination in the US, as well as a relationship to those who believe their racial identity to be of little importance to them as well as do not strongly agree in the prevalence of racial discrimination in the US.
o Relationship between IV3 and the Indexed Dependent variable.
Skin Tone Belief in/ acknowledgement of racial discrimination in the US.
Of little importance
Moderately important
Very important
low % within identity
40.8% 39.6% 36.0%
medium % within identity
35.7% 42.3% 34.1%
high % within identity
23.5% 18.1% 30.0%
total 100.0% 100.0% 100.0%
1 2 3 4 5 6 7 8 10 low % count
w/in skin tone
37.1% 44.0% 50.0% 36.0% 22.2% 8.3% 0% 0% 0%
med % count w/in skin tone
36.2% 39% 25.5 %
44% 37% 25 %
0% 0% 0%
high % count w/in skin tone
26.7% 17% 24.5 %
20.0 %
40.7 %
66.7 %
100 %
100 %
0%
tota l
100.0% 100 %
100 %
100 %
100 %
100 %
100 %
100 %
100 %
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o Cramer’s V: .221 o Tau-‐C: .076 o Analysis: This data was interval by ordinal and was rectangular so Tau-‐c was
appropriate. There is a positive but weak relationship between skin tone and the belief and/or acknowledgement of racial discrimination in the US. It is difficult to analyze this crosstab in terms of main and off diagonals, but there does seem to be a relationship between those who have deeper skin tones and those that belief strongly that racial discrimination exists in the US today. This relationship was hypothesized because it was assumed that there would be a strong association between those that are most likely to experience racism based on their complexion and those that are aware of racial discrimination in the US.
o Chi-‐square Analysis for the 3 Crosstabs: o For the Political Awareness x Belief in Racial Discrimination in the US
Crosstab: o Pearson’s Chi-‐square=6.364, df=4, p=.174 o The results of the chi-‐square analysis show that this is a non-‐
significant relationship, or that any relationship that could be found in the crosstab is due to chance.
o For the Importance of Racial Identity x Belief in Racial Discrimination in the US Crosstab:
o Pearson’s chi-‐square=8.838, df=4, p=.065 o The results of running the chi-‐square test on this crosstab show that
any relationship is only marginally significant, and in other words may well be due to chance.
o For the Skin Tone x Belief in Racial Discrimination in the US Crosstab: o Pearson’s chi-‐square=44.16, df=16, p=0.00. o The results of this chi-‐square analysis are very different to those of
the crosstabs analyzed before it, and show that the sample is very likely representative of the population, and demonstrates high significance.
o ANOVA Analysis: o Political AwarenessàBelief in or Awareness of Racial Discrimination in US
ANOVA Sum of
Squares Df Mean Square F Sig.
Between Groups
2.384 2 1.192 1.926 .147
Within Groups
418.931 677 .619
Total 421.314 679
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Mean Plot:
o Analysis: The ANOVA panel shows that the significance is .147, which further confirms the non-‐significant relationship produced by chi-‐sqaure. The means plot shows the mean differences in belief in racial discrimination across the awareness of current political events. In analyzing the multiple comparisons table produced by ANOVA, there are no mean differences of any significance, they are all .1 or higher. Thus, the hypothesis is unsupported by the data.
o Importance of Racial IdentityàBelief in Racial Discrimination in the US ANOVA Sum of
squares df Mean
Square F Sig.
Between groups
3.103 2 1.551 2.511 .082
Within groups
418.212 677 .618
total 321.314 679
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Mean Plot: o Analysis: The ANOVA panel shows that the significance is .082, which is a
marginally significant level, although may still be due to chance. There are no mean differences with any notable significance for this ANOVA. Thus the hypothesis is not supported by the data.
o Skin ToneàBelief in Racial Discrimination in US ANOVA Sum of
squares Df Mean
Square F Sig.
Between groups
17.746 8 2.218 3.714 .000
Within groups
266.377 446 .597
Total 284.123 454
Mean Plot:
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o Analysis: The f score for the ANOVA panel shows a 0.00 significance, which means that the relationship or any differences within the crosstab is not due to chance, and is highly significant. Thus the hypothesis for this data may be supported.
4. The last independent variable, or Skin tone, demonstrated the greatest relationship to the indexed dependent variable, which was belief in racial discrimination in the US today. This was demonstrated by Skin Tone having the highest measure of association at 0.076 for Kendall’s Tau-c, and also by being the only independent variable tested to have any notable measure of significance, at 0.00 for chi-square and ANOVA, which indicates that the relationship between these two variables, though relatively weak, is not due to chance. Overall the findings in this experiment were weak. There was no independent variable that demonstrated a high level of association with the dependent variable, although the indexed dependent variable did have an acceptable cronbach’s alpha of .637. There was one significant relationship between those that identified with the darkest skin tones on the scale and those that most strongly believed that there is racial discrimination in the US. The data was weighted according to the ANES data codebook specifications.
