Mathematics 243
One quantitative variable review
1. Box 3.
(a) Parameter
(b) Data collection scheme
(c) Inference tool
2. Box 6. Four different data collection paradigms.
(a)
(b)
(c)
(d)
3. The t model.
Normal populations and the central limit theorem.
Day 33 - April 5
It is often assumed that family physicians are able to provide a higher quality of medical care because of the greater
degree of continuity inherent in their practices. The authors attempted to measure the association between continuity
and quality of medical care using pregnancy as a tracer condition. Using a retrospective cohort study design, two
groups of pregnant women were identified-those cared for in the family practice (FP) centers and those cared for
in the obstetric (OB) clinics. Process and outcome of medical care were measured along with patient satisfaction.
Provider continuity, as measured by the SECON value, was much higher in the FP group, and was highly correlated
with the presence of an ”attitudinal contract” between patient and physician. Although not statistically significant,
four times as many newborns from the OB group were admitted to the neonatal intensive care unit. FP group
newborn weight averaged 220 grams more than the OB group (P < 0.05). This difference remained after control
for covariates. While not reaching statistical significance, patient satisfaction scores tended to be higher for the FP
group in two of three categories measured. The results suggest that continuity of care was associated with better
patient outcome and satisfaction. Directions for causal interpretation and future research are discussed. Key words:
continuity; quality of care; patient satisfaction. (Med Care 1983, 21:1204-1210)
The primary purpose of conducting this study was to determine if there is a significant relation between health
motivation and participation in health promotion programs in a sample of community-dwelling older adults (n = 106).
Health motivation was measured using Cox’s Health Self-Determinism Index, and participation in health promotion
programs was measured by tallying the self-reported number of programs attended within the past year by each
individual. The effects of selected demographic variables on these two variables were also examined. The conceptual
framework guiding the study was the Health-Promoting Self-care System Model (Simmons. 1990). Intrinsically
motivated older persons attended fewer programs (p < .01) than those who were more extrinsically motivated.
The Fagerstrom Scale was administered to assess the respondents’ dependence on nicotine. At the first testing the
range of scores was from 1 to 9 (M = 5.71 , SD = 1.96,N = 85).At the second testing 8 weeks later, the scores of
the sample who continued to smoke ranged from 1 to 10 (M = 4.7, SD = 2.09. N = 76).Significant differences were
found between the first and second testing for matched pairs, t(75) = 4.54. n = 76,p = .0001) with participants at
the second testing reporting lower mean dependency scores. No further significant differences were noted between
scores at subsequent time periods.
The cholinesterase inhibitor physostigmine (PHYS) was investigated in a double-blind, placebo-controlled, randomized, crossover trial of 10 male patients with moderate to severe obstructive sleep apnea. PHYS (0.12 ţg/minute/kg,
7-hour infusion) reduced mean apnea/hypopnea index (AHI) by 13.6 (95% confidence interval [CI], 2.2 − 25.1). Mean
total sleep time was reduced by 74 minutes (95% CI, 33.9 − 114.9).
Results of Survey: All Male
African American and Anglo Athletes (N = 327)
Motivation item
Anglos
(n = 287)
(mean and SD)
1.
2.
3.
4.
5.
6.
7.
2.067
1.941
3.182
1.767
1.881
2.753
2.518
Road trip options
Preregistration
Field trip choice
Graduation choice
Final exam study
Roommate choice
Late start options
African Americans
(n = 40)
(mean and SD)
(1.000)
(0.838)
(0.778)
(1.272)
(0.890)
(1.392)
(1.196)
2.179
1.949
3.077
2.564
1.564
3.359
2.256
*p < .05. **p < .01.
2
(0.997)
(0.724)
(0.739)
(1.392)
(0.680)
(1.181)
(1.141)
t value
0.661
0.058
0.794
3.626
2.139
2.593
1.286
Probability
.509
.954
.428
.000**
.033*
.010*
.200
Mathematics 243
One quantitative variable review
Day 33 - April 5
Dataframe: bball2007 – data on all 2007 baseball teams.
One quantitative variable
>
>
>
>
hist(bball2007$HR)
hist(bball2007$HR,freq=F)
boxplot(bball2007$HR)
t.test(bball2007$HR,mu=200,alt='less')
Two quantiative variables
>
>
>
>
>
>
boxplot(HR~LEAGUE,data=bball2007)
aggregate(HR~LEAGUE,data=bball2007,FUN=summary)
t.test(HR~LEAGUE,data=bball2007)
# independent samples formula notation)
A=bball2007$HR[bball2007$LEAGUE=='A']
N=bball2007$HR[bball2007$LEAGUE=='N']
t.test(A,N)
# alternate way to use t (two vectors)
Paired data
What is an estimate of the mean difference of SATM and SATV scores for individual test takers?
> t.test(sr$SATM,sr$SATV,paired=T)
> t.test(sr$SATM-sr$SATV)
# data from one pair in same row
# exactly the same test, one sample test on differences
Test II
1. Format: 15 multiple choice or fill-in the blank problems and two free-response problems.
2. Covers Day 17 through Day 30.
3. Investigations in Rossman-Chance –
ˆ Investigation 3.3. (Sleep deprivation) Randomized comparative experiment (randomization test).
ˆ Investigation 3.5. (Dead left-handers) Two independent samples (two independent sample t test).
ˆ Investigation 3.8. (Cloud Seeding) Randomized comparative experiment. (using two independent sample t
instead of randomization, also transforming data)
ˆ Investigation 3.9 (Chip melting) Paired data.
ˆ Investigation 3.12. (Smoke alarms) Paired binary data.
4. Important concepts from outside the investigations.
ˆ Measuring center and spread (notes from homework for March 1).
ˆ Densities as models of populations (Day 20)
ˆ The Central Limit Theorem (March 9 outline and Khan Academy videos)
ˆ How does student’s t distribution come into the discussion? (March 12 and Student’s article)
5. The outline of Day 28 is a useful review of inference.
6. What is the mean of a confidence interval?
4