Who Listens To Music?

Genevieve Korst
December 5, 2015

Motivation: Topic

Why did you pick the topic you chose?

I enjoy observing people in social situations
I always listen to music when I walk to class,
I’ve noticed that not everyone always does,
I want to see if there was a specific group or demographic that did that more than others.

Motivation: Topic

What were you interested in investigating?

The differences in pre-class habits among different demographics.

What relationships did you hypothesize would exist among your variables?

I hypothesized that women would be more likely to listen to music while walking to class, but I didn’t think there would be a relationship between race/ethnicity and whether or not they listened to music.

Data Collection

Randomization - What did you do to get as “random” a sample as possible?
Records - How many sample records did you end up with
Outliers - Did you remove any outliers?

Data Collection

What did you do to get as “random” a sample as possible? I observed the students rather than surveyed them in order to prevent volunteer bias. I spread out my observations over multiple days and various locations in order to create a large enough and varied enough sample to control for selection bias.

How many sample records did you end up with? 1875,

Yes: 782 records
No: 1093 records

Did you remove any outliers? Yes, we remove a few of the outliers for the black students, because there were so few of them at a couple locations

Results tables

Report the results of your model in a table.
The table will look different depending on whether you ran an ANOVA or a GLM, but be sure you include the appropriate estimates/sums of squares and test statistics for each explanatory variable and interaction term, along with an appropriate measure of how well the model fits the data.

Results table: GLM


Call:
glm(formula = LinMod)

Deviance Residuals: 
     Min        1Q    Median        3Q       Max  
-0.76636  -0.08820   0.00397   0.13156   0.66312  

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept)   0.412165   0.013477  30.583   <2e-16 ***
RaceBlack    -0.010690   0.029535  -0.362    0.718    
RaceHispanic  0.010609   0.017039   0.623    0.535    
RaceWhite     0.009461   0.014501   0.652    0.516    
SexWomen     -0.005528   0.010937  -0.505    0.615    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for gaussian family taken to be 0.05520662)

    Null deviance: 4.3203  on 81  degrees of freedom
Residual deviance: 4.2509  on 77  degrees of freedom
AIC: -231.69

Number of Fisher Scoring iterations: 2


Call:
lm(formula = Yes.percent ~ Race * Sex, data = Obs_df, weights = Total.Obser)

Weighted Residuals:
     Min       1Q   Median       3Q      Max 
-0.73812 -0.07998 -0.00105  0.11486  0.68758 

Coefficients:
                       Estimate Std. Error t value Pr(>|t|)    
(Intercept)            0.421053   0.017129  24.581   <2e-16 ***
RaceBlack              0.007519   0.054296   0.138    0.890    
RaceHispanic          -0.011962   0.023978  -0.499    0.619    
RaceWhite              0.001483   0.020139   0.074    0.942    
SexWomen              -0.024711   0.025166  -0.982    0.329    
RaceBlack:SexWomen    -0.017895   0.065314  -0.274    0.785    
RaceHispanic:SexWomen  0.045527   0.034284   1.328    0.188    
RaceWhite:SexWomen     0.017414   0.029183   0.597    0.553    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.2361 on 74 degrees of freedom
Multiple R-squared:  0.04515,   Adjusted R-squared:  -0.04518 
F-statistic: 0.4998 on 7 and 74 DF,  p-value: 0.8318

Results table: GLM Residuals Normality

qqnorm(LinMod$residuals)
qqline(LinMod$residuals)

plot of chunk GLM Residuals Normality

Results table: GLM Residuals Variance

plot(LinMod$fitted.values, LinMod$residuals,
     xlab="Fitted Values", ylab="Residuals")
abline(h=0)

plot of chunk GLM Residuals Variance

Methods

Model - What software did you use? What function(s)?
Response variable - Description, Method of measurement, Units
Explanatory variable - Description, Method of measurement, Units

Method: GLM/ANOVA

What software did you use? What function(s)?

I used RStudio to in my analysis, utilizing the following functions:

qqnorm(), qqline(), plot(), lm()2

Response variable: The proportion of the population that listens to music on the way to class or not.

Explanatory variables:

Race/ethnicity
Gender

Method: Response Variable

Description: The response variable is the proportion of students listening to music on the way to class, as well as the proportion of students not listening to music. I made a table that had a column for each potential response of the ethnicities and genders and whether they listened to music.

Method of measurement: It was measured by observing the students at each of the locations and marking down a tally in each of the specific columns.

Units:: Count of people

Method: Explanatory Variables

Briefly describe your explanatory variables, how they were measured, and their units (if applicable).

Race/Ethnicity: The race and/or ethnicity of each student observed. For simplicity, I made the best approximation that I could of their combined race and ethnicity of the student. Students fell into four broad catagories:

Asian (hispanic and non-hispanic)
Black (hispanic and non-hispanic)
Hispanic (and white)
White (non-hispanic)

Method: Explanatory Variables

Briefly describe your explanatory variables, how they were measured, and their units (if applicable).

Sex: The biological sex of student observed (male or female).

Units: For each location that I observed, I recorded the count of people observed wearing headphones and not wearing headphones.

Descriptives: Response Variable

Report the appropriate descriptive statistics of your response variable. You can display these in a table like this

Percentage of Students Wearing Headphones

Race	Sex	avg	median	min	max	variance	range	sd
Asian	Men	0.423	0.412	0.316	0.562	0.004	0.246	0.061
Asian	Women	0.392	0.412	0.231	0.471	0.004	0.240	0.063
Black	Men	0.431	0.500	0.250	0.500	0.012	0.250	0.111
Black	Women	0.416	0.414	0.125	0.667	0.033	0.542	0.181
Hispanic	Men	0.410	0.400	0.350	0.474	0.002	0.124	0.039
Hispanic	Women	0.427	0.429	0.294	0.478	0.002	0.184	0.049
White	Men	0.423	0.417	0.395	0.477	0.000	0.082	0.022
White	Women	0.415	0.417	0.396	0.444	0.000	0.048	0.016

Descriptives: Explanatory Variables

Report the appropriate descriptive statistics for two of your main explanatory variables. You can report them in a table like the one above, or in a contingency table.

Contingency Table Percentage of Students Wearing Headphones

	Asian	Black	Hispanic	White
Men	80	9	81	210
Women	65	22	92	218

Discussion: Interpretation

Interpret the results of your model in context.

What does this analysis suggest about your variables?
Relate it back to the original goal outlined in your introduction!

Discussion: Limitations

Were there any limitations with your analysis?

Was there a known bias in your sample collection?
Did your data fail any assumptions?
Can you think of any confounding variables that you didn’t control for?

Assumptions

Which assumptions did you confirm? Include how you checked each assumption, and if space permits, include any graphs you created to check them.

Interaction of Explanatory Vars

Plot the interaction of your two explanatory variables (even if it is not significant). Briefly (1-2 sentences or bullet points) interpret the graph.

Implications

List at least one specific thing you would change if you were to replicate this research.

How would that change impact your data or results?
Did you find that the method you used was sufficient in answering your research question?

Citation

Source code available on Github

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