A Project by Yezi Zora Yang, Yihao Zhou, and Kaelyn Lemon Statistical Modeling 155, Fall 2013
We began our study with the question: Is the multiculturalism requirement (at Macalester College) effective? We decided that we would focus mainly on whether the classes currently available for fulfilling the multiculturalism requirement are enough to make the requirement effective. We considered the requirement to be effective if the classes available teach students about multiculturalism (effectiveness in the point of view of the school administration) as well as if the requirement is not unduly difficult for students to fulfill (effectiveness in the point of view of the students).
Therefore, the questions that motivated our study were: Are the classes offered effectively teaching multiculturalism? Are the classes offered in each department area sufficient to meet the requirements of students?
*Whenever we use solely “requirement” in this report, we specifically refer to Macalester College's multiculturalism graduation requirement. To fulfill this requirement, students must take one class that is considered by the school to teach about multiculturalism. Such classes can theoretically be in any department as they are “devoted to the study of social groups in the U.S.; including analysis of forces that create, contest, or maintain power, identity, or difference” (http://www.macalester.edu/academics/americanstudies/majorsminors/multiculturalism/).
We initially looked at the past offerings of classes that fulfilled the multiculturalism requirement, and found that the majority were in the Humanities and Arts, and the rest mostly in the Social Sciences, with very few in the Natural Sciences. We then created a survey, and found that overall the currently offered classes are effective in teaching multiculturalism, although professors may want to work on specifically teaching about what multiculturalism is as making Social Science classes more interesting. We found that students are affected by the distribution of classes among department areas, especially those in the Natural Sciences. Our data leads us to suggest that Macalester College work on offering more classes to fulfill the multiculturalism requirement in the Natural Sciences and Social Sciences.
Before designing our survey, we collected data published on the registrar website for Macalester College (http://www.macalester.edu/registrar/schedules/) about past class offerings that fulfilled the multiculturalism graduation requirement. The data available started from Fall 2007 and went to Spring 2014, thus encompassing 6 years of class offerings.
Our variables for this data are:
Year- 2007 through 2014
Semester- Fall or Spring
Level- 100, 200, 300, or 400, based on the class designation system of Macalester College. This is important because the higher the level of a class, the more likely the class is to have a prerequisite that must be taken first. A prerequisite limits the number of students that the class is realistically available to.
Department- The four letter designation used by Macalester College (ex. ENGL is English)
require(mosaic)
## Loading required package: mosaic Loading required
## package: grid Loading required package: lattice
##
## Attaching package: 'mosaic'
##
## The following objects are masked from
## 'package:stats':
##
## D, IQR, binom.test, cor, cov, fivenum, median,
## prop.test, sd, t.test, var
##
## The following object is masked from
## 'package:base':
##
## max, mean, min, print, prod, range, sample, sum
opts_chunk$set(fig.width = 5, fig.height = 4, out.width = "50%", dev = "svg",
tidy = FALSE)
options(width = 50)
dataSource = "https://docs.google.com/spreadsheet/pub?key=0AnEWI_gMkW2ndHhTYnVCekpFbUJnbGVwb0Zpd21uRFE&output=csv"
class = fetchGoogle(dataSource)
head(class)
## Case Year Semester Level Department
## 1 1 2007 Fall 100 AMST
## 2 2 2007 Fall 300 HISP
## 3 3 2007 Fall 100 HIST
## 4 4 2007 Fall 200 HIST
## 5 5 2007 Fall 200 HIST
## 6 6 2007 Fall 200 HIST
tally(~Department, data=class)
##
## AMST ANTH ART CLAS ECON EDUC ENGL ENVI
## 36 8 3 1 9 18 33 3
## GEOG GEOL HISP HIST HMCS INTL LING MCST
## 7 1 17 44 3 4 8 7
## MUSI PHIL POLI PSYC RELI SOCI THDA WGSS
## 6 9 23 23 18 17 8 6
## Total
## 312
tally(~Level, data=class)
##
## 100 200 300 400 Total
## 82 148 71 11 312
Over 1/3 of all classes fulfilling the multiculturalism requirement were in either History, American Studies, or English, all of which are Humanities departments. Also, nearly half of all classes were 200 level classes, which means there is some possibility that they could have had prerequisites that students must take beforehand. A total of merely 8 classes in the Natural Sciences fulfilled the requirement, which is 2.6% of all classes.
We thus predicted that students studying the Natural Sciences would have the most trouble meeting the requirement, and that few students would have fulfilled the requirement in the Natural Sciences.
When making our survey to collect data from students, we collapsed the departments into three department areas: Humanities and Arts, Social Sciences, and Natural Sciences. We chose these groupings because they are groupings used by Macalester College, especially in the area of graduation requirements. According to our definitions, the departments that have offered classes fulfilling the multiculturalism requirement are grouped into these three areas as follows:
Humanities and Arts: AMST, ART, CLAS, EDUC, ENGL, HISP, HIST, HMCS, MCST, MUSI, PHIL, RELI, THDA, WGSS (70% of offered classes)
Social Sciences: ANTH, ECON, ENVI, INTL, LING, POLI, SOCI (27.4% of offered classes)
Natural Sciences: GEOG, GEOL (2.6% of offered classes)
This grouping shows that the Humanities and Arts have the broadest offering of classes that fulfill the requirement, as over half of the departments that have offered multiculturalism classes fall in this area.
The survey that we sent out to Macalester students is as follows. We posted the survey on the Sophomore facebook page and sent the survey out to all Macalester students through the Daily Piper. Our sampling frame was thus all Macalester students (as the Daily Piper is sent to all students) with an emphasis on Sophomores.
We asked students to respond to how well they know what multiculturalism is and to rate the requirement as proxies for how effective the requirement is. We further collected information on students' involvement in different department areas, grouped into Humanities and Arts, Social Sciences, and Natural Sciences, to determine if the effectiveness of the requirement differs for different types of studies. We hypothesized that grade level and department in which students fulfilled the requirement might be important variables as well. Finally, we asked students to give suggestions on which classes could be added to the list of those that fulfill the requirement, both to compare this to our data from the registrar of classes offered currently and in the past, and to help us suggest meaningful changes to the requirement for benefit of future students.
dataSource2="https://docs.google.com/spreadsheet/pub?key=0AiZQVzSzqnWBdFVJN3A5cHpVMG16b3JJVnVNeTJSNXc&single=true&gid=0&output=csv"
survey=fetchGoogle(dataSource2)
names(survey)[2]= "GradeLevel"
names(survey)[3]= "Fulfillment"
names(survey)[4]= "Understanding"
names(survey)[5]= "FulfillmentPlan"
names(survey)[6]= "InterestLevel"
names(survey)[7]= "NewClass"
names(survey)[8]= "Rating"
names(survey)[9]= "HumAInvolve"
names(survey)[10]= "SSInvolve"
names(survey)[11]= "SciInvolve"
require(plyr)
## Loading required package: plyr
##
## Attaching package: 'plyr'
##
## The following object is masked from
## 'package:mosaic':
##
## count
options(na.rm=TRUE)
newLevels = c("I have no idea"="No", "I have a vague idea"="Little", "I think so"="Some", "Absolutely"="Yes")
survey$Understanding=revalue(survey$Understanding, newLevels)
## The following `from` values were not present in
## `x`: I have no idea
survey$Understanding=factor(survey$Understanding, levels=newLevels)
newLevels2= c("Humanities and Arts"="HumA", "Humanities and Arts, Social Sciences"="HumASS", "N/A (absolutely no idea what class I might take)"="none", "Social Sciences"="SS", "Social Sciences, Natural Sciences"="SSSci", "Natural Sciences"="Sci")
survey$FulfillmentPlan=revalue(survey$FulfillmentPlan, newLevels2)
## The following `from` values were not present in
## `x`: Natural Sciences
survey$FulfillmentPlan=factor(survey$FulfillmentPlan, levels=newLevels2)
newLevels3=c("No, probably not"="Low", "I might, but I would not be as motivated"="Moderate", "Yes, definitely"="High")
survey$InterestLevel=revalue(survey$InterestLevel, newLevels3)
survey$InterestLevel=factor(survey$InterestLevel, levels=newLevels3)
newLevels4= c("Humanities and Arts"="HumA", "Social Sciences"="SS", "Natural Sciences"="Sci")
survey$NewClass=revalue(survey$NewClass, newLevels4)
survey$NewClass=factor(survey$NewClass, levels=newLevels4)
newLevels5= c("1-2 classes"="Min", "3-4 classes"="Moderate", "5-7 classes"="Heavy", "8 or more classes"="Max")
survey$HumAInvolve=revalue(survey$HumAInvolve, newLevels5)
survey$HumAInvolve=factor(survey$HumAInvolve, levels=newLevels5)
survey$SSInvolve=revalue(survey$SSInvolve, newLevels5)
survey$SSInvolve=factor(survey$SSInvolve, levels=newLevels5)
survey$SciInvolve=revalue(survey$SciInvolve, newLevels5)
survey$SciInvolve=factor(survey$SciInvolve, levels=newLevels5)
head(survey)
## Timestamp GradeLevel Fulfillment
## 1 11/24/2013 13:07:31 Sophomore No
## 2 11/24/2013 20:48:31 Sophomore No
## 3 11/24/2013 20:48:38 Sophomore Yes
## 4 11/24/2013 20:49:38 Sophomore Yes
## 5 11/24/2013 20:51:08 Sophomore Yes
## 6 11/24/2013 20:51:23 Sophomore Yes
## Understanding FulfillmentPlan InterestLevel
## 1 Some HumA Moderate
## 2 Some SS Moderate
## 3 Yes SS High
## 4 Yes SS High
## 5 Some HumA High
## 6 Some HumASS High
## NewClass Rating HumAInvolve SSInvolve
## 1 Sci 8 Max Moderate
## 2 HumA 5 Max Max
## 3 SS 7 Heavy Max
## 4 SS 10 Moderate Max
## 5 SS 10 Max Heavy
## 6 Sci 10 Moderate Max
## SciInvolve
## 1 Max
## 2 Moderate
## 3 Min
## 4 Min
## 5 Min
## 6 Moderate
We edited the responses from the survey to be manageable for analysis. Above is an example of how the responses appear. Our variables are:
GradeLevel: The current standing of a student, with levels Freshman, Sophomore, Junior, and Senior
Fulfillment: Whether or not a student has fulfilled the multiculturalism requirement, with levels Yes and No
Understanding: How well a student understands what “multiculturalism” means, with levels No (does not understand), Little (small amount of understanding), Some (moderate amount of understanding), and Yes (completely understands)
FulfillmentPlan: The department area a student has filled or will fill the requirement in, with levels HumA (Humanitites and Arts), HumASS (Humanities and Arts and Social Science), SS (Social Science), Sci (Natural Science), SSSci (Social Science and Natural Science), and none (no fulfillment plan)
InterestLevel: The student's interest in the class he/she used to fulfill the requirement, with levels Low, Moderate, and High
NewClass: The department area to which the student would most like to see a new class added that fulfills the requirement, with levels HumA (Humanities and Arts), SS (Social Science), and Sci (Natural Science)
Rating: A rating from 1 to 10 of the effectiveness of the multiculturalism requirement
HumAInvolve: A student's involvement in the Humanities and Arts, with levels Min (1-2 classes, equal to the graduation requirement for the area), Moderate (3-4 classes), Heavy (5-7 classes, the range of classes of someone with a minor in the area), and Max (8+ classes, enough classes to major in the area or have two minors)
SSInvolve: A student's involvement in the Social Sciences, with levels Min (1-2 classes, equal to the graduation requirement for the area), Moderate (3-4 classes), Heavy (5-7 classes, the range of classes of someone with a minor in the area), and Max (8+ classes, enough classes to major in the area or have two minors)
SciInvolve: A student's involvement in the Natural Sciences, with levels Min (1-2 classes, equal to the graduation requirement for the area), Moderate (3-4 classes), Heavy (5-7 classes, the range of classes of someone with a minor in the area), and Max (8+ classes, enough classes to major in the area or have two minors)
We had a total of 90 responses to our survey. One case was omitted for missing information.
tally(~GradeLevel, data=survey)
##
## Freshman Junior Senior Sophomore Total
## 7 20 10 52 89
tally(~Fulfillment, data=survey)
##
## No Yes Total
## 38 51 89
Our participants were primarily Sophomores, most likely due to the fact that the survey was posted on the Macalester Sophomore facebook page. About 8% of respondents were Freshmen, 11% Seniors, and 22% Juniors. Although our sample is not representative of the distribution of grade level among Macalester students, our data is still useful, especially in application to current Juniors and Sophomores. This is not necessarily bad, as Sophomores and Juniors are the most likely to be currently trying to fulfill the requirement while having the experience at Macalester to have some basic knowledge of the requirement as well as what they plan to study. We also received a fairly even split of participants who have and have not fulfilled the requirement.
mean(Rating, data=survey)
## [1] 6.719
mean(Rating~GradeLevel, data=survey)
## Freshman Junior Senior Sophomore
## 5.857 6.500 8.300 6.615
m=mm(Rating~GradeLevel, data=survey)
confint(m)
## group 2.5 % 97.5 %
## 1 Freshman 3.725 7.989
## 2 Junior 5.239 7.761
## 3 Senior 6.516 10.084
## 4 Sophomore 5.833 7.398
We instructed participants to give a rating of the effectiveness of the multiculturalism requirement from 1 to 10. A mean of nearly 7 suggests that overall students believe the requirement to be effective. It appears that students in higher grades rate the requirement as more effective, however, there is not sufficient evidence to back this trend.
mean(Rating~Fulfillment, data=survey)
## No Yes
## 5.395 7.706
m1=mm(Rating~Fulfillment, data=survey)
confint(m1)
## group 2.5 % 97.5 %
## 1 No 4.548 6.241
## 2 Yes 6.975 8.437
Based on 95% confidence intervals, students who had fulfilled the requirement rated the effectiveness of the requirement significantly higher than students who had not fulfilled the requirement. We can be 95% confident that our interval includes the mean rating of students who fulfilled the requirement, which means that on average these students rated the requirement as effective.
tally(~GradeLevel+Fulfillment, data=survey)
## Fulfillment
## GradeLevel No Yes Total
## Freshman 6 1 7
## Junior 7 13 20
## Senior 1 9 10
## Sophomore 24 28 52
## Total 38 51 89
The trend of whether or not a student has fulfilled the requirement as compared by grade level follows our prediction based on previous knowledge of Macalester. Grade Level and Fulfillment appear to be positively correlated- a student with a higher grade level is much more likely to have fulfilled the requirement. However, we do not know if this trend as represented by our data is statistically significant.
survey$UnderstNew1=survey$Understanding
survey$Understn1 = factor(survey$UnderstNew1, labels=(1:length(levels(factor(survey$UnderstNew1)))))
UnderstNum=as.numeric(survey$Understn1)
tally(~Understanding, data=survey)
##
## No Little Some Yes Total
## 0 12 47 30 89
mean(UnderstNum, data=survey)
## [1] 2.202
m2=mm(UnderstNum~Fulfillment, data=survey)
m2
##
## Groupwise Model Call:
## UnderstNum ~ Fulfillment
##
## Coefficients:
## No Yes
## 2.03 2.33
confint(m2)
## group 2.5 % 97.5 %
## 1 No 1.818 2.235
## 2 Yes 2.154 2.513
The variable UnderstNum is the variable Understanding where the levels are numbers (Little=1, Some=2, and Yes=3). An average of approximately 2 means that the average participant believed he/she had a good idea of what multiculturalism is but was not completely sure. The confidence interval shows that there was no significant difference in understanding between participants who had fulfilled the requirement and participants who had not fulfilled the requirement. We would hope to see a significant difference of the lower bound of Yes at least 1 greater (as this would related to one understanding level of the original ordinal variable) than the upper bound of No for participants who have taken a multiculturalism class in order to say that the classes are effectively teaching students about multiculturalism. We therefore cannot conclude based on our data that the requirement is effective in this respect.
survey$Interest2 = factor(survey$InterestLevel, labels=(1:length(levels(factor(survey$InterestLevel)))))
InterestNum=as.numeric(survey$Interest2)
mean(InterestNum, data=survey)
## [1] 2.157
m3=lm(InterestNum~FulfillmentPlan, data=survey)
m3
##
## Call:
## lm(formula = InterestNum ~ FulfillmentPlan, data = survey)
##
## Coefficients:
## (Intercept) FulfillmentPlanHumASS
## 2.4516 -0.0516
## FulfillmentPlannone FulfillmentPlanSS
## -1.1183 -0.4794
## FulfillmentPlanSSSci
## -1.4516
confint(m3)
## 2.5 % 97.5 %
## (Intercept) 2.1611 2.74215
## FulfillmentPlanHumASS -0.5604 0.45717
## FulfillmentPlannone -1.8398 -0.39680
## FulfillmentPlanSS -0.8757 -0.08303
## FulfillmentPlanSSSci -3.0951 0.19191
The variable InterestNum is the variable Interest where the levels of interest in the class taken to fulfill the multiculturalism requirement have been changed to numbers (lower number=lower level of interest). A mean of approximately 2 corresponds to moderate interest (versus low or high). The 95% confidence interval shows that students fulfilling the requirement in the Social Sciences are significantly less interested in the class used to fulfill the requirement than those fulfilling the requirement in the Humanities and Arts. However, especially as our original variable was not quantitative, the possibly very small decrease in interest for classes in the Social Sciences is not very useful.
survey$HumArt = factor(survey$HumAInvolve, labels=(1:length(levels(factor(survey$HumAInvolve)))))
HumANum=as.numeric(survey$HumArt)
mean(HumANum, data=survey)
## [1] 2.764
survey$SoSci = factor(survey$SSInvolve, labels=(1:length(levels(factor(survey$SSInvolve)))))
SSNum=as.numeric(survey$SoSci)
mean(SSNum, data=survey)
## [1] 3.045
survey$NatSci = factor(survey$SciInvolve, labels=(1:length(levels(factor(survey$SciInvolve)))))
SciNum=as.numeric(survey$NatSci)
mean(SciNum, data=survey)
## [1] 2.483
The above “Num” variables are quantitative variables based on the levels of involvement in each respective department area, with 1 equating 1-2 classes and 4 equating 8+ classes. Our participants thus overall had heavy involvement in the Humanities and Arts and Social Sciences and moderate to heavy involvement in the Natural Sciences.
modx=lm(Rating~Understanding, data=survey)
summary(modx)
##
## Call:
## lm(formula = Rating ~ Understanding, data = survey)
##
## Residuals:
## Min 1Q Median 3Q Max
## -6.467 -1.894 0.533 2.106 3.833
##
## Coefficients:
## Estimate Std. Error t value
## (Intercept) 4.167 0.775 5.38
## UnderstandingSome 2.727 0.868 3.14
## UnderstandingYes 3.300 0.917 3.60
## Pr(>|t|)
## (Intercept) 6.4e-07 ***
## UnderstandingSome 0.00231 **
## UnderstandingYes 0.00053 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.68 on 86 degrees of freedom
## Multiple R-squared: 0.135, Adjusted R-squared: 0.114
## F-statistic: 6.69 on 2 and 86 DF, p-value: 0.002
Students' ratings of the effectiveness of the multiculturalism requirement significantly increased as understanding of multiculturalism increased. Understanding explained about 11% of the variation in Rating, and the model is better than a model with random variables.
mod1=lm(Rating~Fulfillment+Understanding, data=survey)
summary(mod1)
##
## Call:
## lm(formula = Rating ~ Fulfillment + Understanding, data = survey)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5.768 -1.768 0.232 1.946 4.486
##
## Coefficients:
## Estimate Std. Error t value
## (Intercept) 3.514 0.751 4.68
## FulfillmentYes 1.958 0.556 3.52
## UnderstandingSome 2.297 0.825 2.78
## UnderstandingYes 2.582 0.885 2.92
## Pr(>|t|)
## (Intercept) 1.1e-05 ***
## FulfillmentYes 0.00069 ***
## UnderstandingSome 0.00661 **
## UnderstandingYes 0.00452 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.52 on 85 degrees of freedom
## Multiple R-squared: 0.245, Adjusted R-squared: 0.218
## F-statistic: 9.18 on 3 and 85 DF, p-value: 2.49e-05
anova(mod1)
## Analysis of Variance Table
##
## Response: Rating
## Df Sum Sq Mean Sq F value Pr(>F)
## Fulfillment 1 116 116.3 18.28 5e-05
## Understanding 2 59 29.5 4.63 0.012
## Residuals 85 541 6.4
##
## Fulfillment ***
## Understanding *
## Residuals
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
We were interested to see how fulfillment of the multiculturalism requirement and understanding of what multiculturalism is affected students' ratings of the effectiveness of the multiculturalism requirement. We believed that students who have taken a class about multiculturalism have more knowledge about whether or not the classes offered are effective. We therefore hoped to see these students rate the requirement as more effective (or at least not less effective) than students who had not fulfilled the requirement in order to conclude that the classes are effective in teaching multiculturalism. Although we were not able to say based on our sample that students who had fulfilled the requirement had a higher understanding of multiculturalism, we still believe that this may be the case in the larger population of Macalester students and thus wanted to control for the possible causal pathway in which Fulfillment causes Understanding, which causes effectiveness.
The significant F-values for the explanatory variables support that they are better at explaining the variation in ratings than random variables. The significant F-value for the whole model supports that overall the model explains for variation in ratings than a model with random explanatory variables. Overall, the variables Understanding and Fulfillment explain nearly 22% of the variation in ratings.
The significant t-value on the FulfillmentYes coefficient supports the coefficient being nonzero. Therefore, students who have fulfilled the multiculturalism requirement rated its effectiveness significantly higher than did students who have not fulfilled the requirement, at the same level of understanding of multiculturalism.
There are multiple possible interpretations for this result. For example, it could be that students who are having difficulties finding a class to fulfill the requirement are frustrated and thus more likely to negatively rate the requirement. It could also be that students who have taken a class about multiculturalism have more knowledge about the effectiveness of the classes in teaching multiculturalism, and that the high rating means that classes are effective in doing so. These are not the only options, nor are they mutually exclusive.
The significant t-values for the Understanding coefficients support that these coefficients are greater than zero. Students with a greater understanding of multiculturalism gave statistically significantly higher ratings of effectiveness, regardless of whether or not they had taken a class about multiculturalism.
mod2=lm(Rating~FulfillmentPlan+HumAInvolve+SSInvolve+SciInvolve, data=survey)
summary(mod2)
##
## Call:
## lm(formula = Rating ~ FulfillmentPlan + HumAInvolve + SSInvolve +
## SciInvolve, data = survey)
##
## Residuals:
## Min 1Q Median 3Q Max
## -6.587 -1.216 0.374 1.701 4.884
##
## Coefficients:
## Estimate Std. Error t value
## (Intercept) 7.391 1.460 5.06
## FulfillmentPlanHumASS -0.859 0.892 -0.96
## FulfillmentPlannone -2.834 1.211 -2.34
## FulfillmentPlanSS -1.161 0.711 -1.63
## FulfillmentPlanSSSci -4.993 2.803 -1.78
## HumAInvolveModerate 0.537 1.069 0.50
## HumAInvolveHeavy -0.423 1.199 -0.35
## HumAInvolveMax 0.947 1.143 0.83
## SSInvolveModerate 0.878 1.070 0.82
## SSInvolveHeavy 1.268 1.101 1.15
## SSInvolveMax 0.820 0.883 0.93
## SciInvolveModerate -0.977 0.800 -1.22
## SciInvolveHeavy -0.608 1.548 -0.39
## SciInvolveMax -1.812 0.808 -2.24
## Pr(>|t|)
## (Intercept) 2.9e-06 ***
## FulfillmentPlanHumASS 0.339
## FulfillmentPlannone 0.022 *
## FulfillmentPlanSS 0.107
## FulfillmentPlanSSSci 0.079 .
## HumAInvolveModerate 0.617
## HumAInvolveHeavy 0.725
## HumAInvolveMax 0.410
## SSInvolveModerate 0.414
## SSInvolveHeavy 0.253
## SSInvolveMax 0.356
## SciInvolveModerate 0.226
## SciInvolveHeavy 0.696
## SciInvolveMax 0.028 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.64 on 75 degrees of freedom
## Multiple R-squared: 0.268, Adjusted R-squared: 0.141
## F-statistic: 2.11 on 13 and 75 DF, p-value: 0.0227
anova(mod2)
## Analysis of Variance Table
##
## Response: Rating
## Df Sum Sq Mean Sq F value Pr(>F)
## FulfillmentPlan 4 88 22.10 3.16 0.019
## HumAInvolve 3 37 12.35 1.77 0.161
## SSInvolve 3 30 10.05 1.44 0.238
## SciInvolve 3 36 12.11 1.73 0.168
## Residuals 75 524 6.99
##
## FulfillmentPlan *
## HumAInvolve
## SSInvolve
## SciInvolve
## Residuals
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
tally(~FulfillmentPlan, data=survey)
##
## HumA HumASS none SS SSSci Sci Total
## 31 15 6 36 1 0 89
We wanted to know if different department areas differed in the effectiveness of their classes in teaching multiculturalism. We therefore looked at Rating as explained by FulfillmentPlan.
No respondents fulfilled or planned to fulfill the requirement in the Natural Sciences. Roughly the same amount of participants fulfilled the requirement in Humanities and Arts and Social Sciences. Only 6 students had no plan for fulfilling the requirement, which means that the majority of students who had not fulfilled the requirement did have an idea of what class they might take.
The F-values of both the explanatory variable FulfillmentPlan and the model as a whole are significant, which means that they are better at explaining variation than random variables and models. The involvement variables were not any better than random variables. The model as a whole explained about 14% of variation in ratings (adjusted value).
The t-values of the coefficients show that our data was not enough to say that students who fulfilled (or plan to fulfill) the requirement in the Humanities and Arts (intercept term) had significantly different ratings than students who fulfilled the requirement in the Social Sciences or in both department areas, as the corresponding coefficients could be zero. We therefore cannot say that the effectiveness of the requirement is different when taken as a Humanities and Arts class as when taken as a Social Science class. Also, there was only one respondent who fulfilled the requirement in Natural Sciences and Social Sciences, so there was not enough data to draw conclusions about this option.
tally(~Fulfillment+SciInvolve, data=survey)
## SciInvolve
## Fulfillment Min Moderate Heavy Max Total
## No 7 10 1 20 38
## Yes 24 9 3 15 51
## Total 31 19 4 35 89
mod3=lm(Rating~SciInvolve+Fulfillment, data=survey)
summary(mod3)
##
## Call:
## lm(formula = Rating ~ SciInvolve + Fulfillment, data = survey)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5.745 -1.489 0.209 1.623 5.209
##
## Coefficients:
## Estimate Std. Error t value
## (Intercept) 6.422 0.643 9.98
## SciInvolveModerate -0.453 0.767 -0.59
## SciInvolveHeavy -1.888 1.361 -1.39
## SciInvolveMax -1.631 0.663 -2.46
## FulfillmentYes 1.954 0.581 3.37
## Pr(>|t|)
## (Intercept) 6.2e-16 ***
## SciInvolveModerate 0.5558
## SciInvolveHeavy 0.1691
## SciInvolveMax 0.0159 *
## FulfillmentYes 0.0012 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.56 on 84 degrees of freedom
## Multiple R-squared: 0.23, Adjusted R-squared: 0.193
## F-statistic: 6.27 on 4 and 84 DF, p-value: 0.000184
anova(mod3)
## Analysis of Variance Table
##
## Response: Rating
## Df Sum Sq Mean Sq F value Pr(>F)
## SciInvolve 3 90 30.0 4.58 0.0051 **
## Fulfillment 1 74 74.4 11.33 0.0012 **
## Residuals 84 551 6.6
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Slightly different from the requirement having different effectiveness for students who fulfilled it in different department areas, we wanted to know whether the requirement is more effective for students studying in different department areas. We therefore looked at Ratings as explained by SciInvolve (involvement in the Natural Sciences), controlling for whether or not students had fulfilled the requirement, as students in the Natural Sciences seem to be less likely to have fulfilled the requirement (Over 77% of students with the minimum involvement in the Natural Sciences have fulfilled the requirement, while only 43% of students with the maximum involvement have fulfilled the requirement). We also modeled Rating by involvement in the other two department areas, but we did not find a significant difference in Rating for different levels of involvement in either area.
The F-values of both explanatory variables as well as the model as a whole were significant, which means that the model was better at explaining variation than a random model and SciInvolve and Fulfillment were better than random variables. The model explained about 19% of variation in ratings.
The t-values of the coefficients of the different levels of involvement were all not significant, except for the maximum involvement in the Natural Sciences. This means that participants with the highest involvement in the Natural Sciences (most likely students majoring in the Natural Sciences) rated the effectiveness of the requirement significantly lower than did other students. This suggests that the multiculturalism classes are less effective for students of the Natural Sciences.
Our first question was: Are the classes offered effectively teaching multiculturalism? Our answer overall is mixed, though we would lean toward saying yes. On one hand, the overall effectiveness of the requirement was rated at 6.7, and students who had fulfilled the requirement rated it higher than students who hadn't. This supports the requirement being effective, as the classes ought to be more effective for students that have taken them than students who haven't. We found as well that students who had a better understanding of multiculturalism rated the requirement as more effective. Although this was true for both students who had and had not fulfilled the requirement, it lends support to our use of student ratings as a measurement of effectiveness, as an increase in effectiveness ratings is correlated with an increase in student understanding. Furthermore, we did not find a difference in effectiveness (as measured by student ratings) between classes in different department areas (excluding Natural Sciences, for which we had no data). However, this result could simply be due to a lack of sufficient data to find the actual difference. Still, based on our data it remains a possibility that classes in different department areas are equally effective.
On the other hand, we did not find that students who had fulfilled the requirement had a better understanding of what multiculturalism is than students who had not fulfilled the requirement. This could be due to lack of sufficient data to find a difference in understanding between the two groups. However, it remains that we do not have support from our data to say that the requirement is effective in this aspect. We also found that students who fulfilled the multiculturalism requirement in the Social Sciences were less interested in the classes they took to fulfill the requirement than students who took classes in the Humanities and Arts. While the decrease in interest was potentially very small, this is a worrisome trend. We know from previous experience that students who are less interested in a class tend to care less about the class, and are then likely to learn less from the class than students who are interested.
With regard to the effectiveness of the classes currently offered to fulfill the multiculturalism requirement, we suggest that departments in the Social Sciences work on making currently offered classes slightly more interesting to students. We cannot say what specifically is making the classes less interesting, so further research should be done to address this issue. We also suggest further research as to whether current classes in all departments are increasing students' understanding of multiculturalism. We tentatively suggest that more should be done to teach students about what multiculturalism is in the classes that fulfill the requirement.
Our second question was: Are the classes offered in each department area sufficient to meet the requirements of students? Our answer is resoundingly no. To begin with, we found that The vast majority (70%) of multiculturalism classes are offered in the Humanities and Arts, while much fewer (26.4%) are offered in the Social Sciences, and practically none (2.6%, out of 312) are offered in the Natural Sciences. This incredibly uneven distribution suggests that students in the sciences might struggle to fit the requirement into their graduation plan while working towards their major.
Our survey results furthered this conclusion. We found that students with maximum involvement in the Natural Sciences (8 or more classes) rated the requirement as less effective than all other students. We hypothesize that this is due to the lack of multiculturalism classes in the Natural Sciences, which means that students in the Natural Sciences do not have the same opportunities as other students to fit the requirement into their major plans.
tally(~NewClass, data=survey)
##
## HumA SS Sci Total
## 18 40 31 89
tally(~NewClass+HumAInvolve, data=survey)
## HumAInvolve
## NewClass Min Moderate Heavy Max Total
## HumA 0 5 3 10 18
## SS 3 14 11 12 40
## Sci 5 14 6 6 31
## Total 8 33 20 28 89
tally(~NewClass+SSInvolve, data=survey)
## SSInvolve
## NewClass Min Moderate Heavy Max Total
## HumA 6 3 2 7 18
## SS 1 2 4 33 40
## Sci 9 8 5 9 31
## Total 16 13 11 49 89
tally(~NewClass+SciInvolve, data=survey)
## SciInvolve
## NewClass Min Moderate Heavy Max Total
## HumA 6 4 1 7 18
## SS 22 10 2 6 40
## Sci 3 5 1 22 31
## Total 31 19 4 35 89
To help students meet the multiculturalism requirement, we suggest that more Social Science and Natural Science classes be offered to fulfill the requirement. Currently, comparatively few classes that fulfill the requirement are offered in these departments. Furthermore, students specifically responded that more classes in these areas would be the most helpful to help them fulfill the requirement. Even students greatly involved in the Humanities and Arts requested more classes in the sciences over classes in the humanities. The most common request was for a class in the Biology department, although the Economics department was also a popular request. We suggest that the Biology and Economics departments attempt to offer classes that meet the multiculturalism requirement. We understand that it might be more difficult to come up with classes in the natural and social sciences that address multiculturalism than in the humanities, but we believe that an effort to do so would be very positive for students and therefore worth the effort.