Random Variables
A variable that takes different values with certain probabilities
Example: Number of ear infections a child has up to age 2
Discrete random variable X=0,1,2,3,4
x
P(X=x)
.129
.264
.271
.185
.095
.039
.017
1.00
0
1
2
3
4
5
6
Defn. The expe
Biostatistics 200A
Prof. Ron Brookmeyer
Part 4 Page
1
SHAPES OF DISTRIBUTIONS
1. RIGHT SKEWED
Mean > median
2. LEFT SKEWED
Mean < median
3. SYMMETRIC
4. BIMODAL
Biostatistics 200A
Prof. Ron Brookmeyer
Part 4 Page
2
Biostatistics 200A
Prof. Ron Brookmeyer
NONPARAMETRIC METHODS
Statistical methods that
dont make parametric assumptions about distributions
insensitive to wild observations
can handle coarse quantitative variables
generally, based on ranks
Disadvantages
often less powerful than parametric meth
ALTERNATIVE APPROACH FOR COMPARING 2
PROPORTIONS (in LARGE SAMPLES)
The Chi-Square Statistic 2
Success
failure
X
a
b
n1
Y
c
d
n2
S
F
N
2
= c=
TS
(O E )
4cells
2
E
O=observed count in each of the 4 cells
E=expected count in each cell if Ho is true
Biostati
KEY COMPETENCIES TO BE A
SUCCESSFUL PRACTICING
BIOSTATISTICAN
1. Biostatistical methods and theory
2. Computation & Data Science
3. Collaboration with other researchers
4. Communication
Biostat 200A Prof. Brookmeyer
Class Notes Part 1 page 1
Probability
m
EXACT CONFIDENCE INTERVAL FOR
BINOMIAL PROBABILITY
X ~ binomial (N, p)
Observe the value x
Find exact (1-) x 100% confidence interval for p
KEY IDEA
EXPLOIT CONNECTION BETWEEN
CONFIDENCE INTERVALS AND HYPOTHESIS
TESTS
The set of all values of parameter wh
Biostatistics 200B:
Methods in Biostatistics B
Lecture 22:
One-Way Analysis of
Variance
(ANOVA), continued
One-way ANOVA model
We have 2 groups, = 1, , , with
observations in each group.
Assume the observations are all independent,
each population has
How do we estimate the population variance 2 ?
N
(x x )
The sample variance is:
S 2 = i =1
2
i
N 1
S2 is an unbiased estimator of 2
That means, E(S2)= 2
N
2
x
x
(
)
i
1
N
2
2
i =1
E
S
E
E
=
=
( xi x )
(
)
PROOF
N 1 N 1 i =1
1 N
2
2
E ( xi ) N ( X )
Biostatistics 200B:
Methods in Biostatistics B
Lecture 23:
One-way ANOVA,
continued
Analysis of variance for one-way
ANOVA
Recall that in the linear regression model we partitioned
the total sum of squares into a regression SS and error SS.
= +
( )2
COMPARISON OF TWO GROUPS
1. Paired Design
Before vs after
Twin studies
Matching
2. Independent Samples
Persons exposed vs persons unexposed
Persons treated vs. Persons untreated
Biostatisticss 200 A
Prof. Brookmeyer
Class Notes Part 7 page number
1
Exampl
STATISTICAL INFERENCE OF POPULATION MEAN, : CONTINUOUS DATA
One-sample
Hypothesis test for , 2 known (Z-test)
If Xn is a random sample from a normal population or a large random sample from any population with unknown mean and
known variance 2, then do
Ho
PhuongUyen Bui
Biostat100A_1D
ID#: 804443735
Lab 2: Descriptive Techniques in Summarization of
Public Health Data
I.
Analysis:
1. Summary of measures by subgroup for hemoglobin levels.
Acyanotic group
Measures
Median
Mean
Range (Max - Min)
IQR (75th -25th
1. 95% confidence interval for the mean was computed as [25,50] means it only
be said that 95% each of theses confidence intervals (more samples taken with
SAME n) would contain the TRUE mean of that particular distribution of the
sample. C.I. always esti
PhuongUyen Bui
Biostat100A_1D
ID#: 804443735
Lab 3
I.
Analysis:
1.
a) Ladders of powers transforms for the variable DAGE and CITH that
have large P values and small Chi2 values.
DAGE
Skewnes
Variable
Mean
Median
Range
SD
IQR
s
Raw
1
(Identity)
Square Roo
PhuongUyen Bui
ID#: 804443735
Lab4_Section 1D
Lab 4: Normal Distribution and The Form of the Sampling
Distribution of the Mean and Variance of a Random Variable
I.
ANALYSIS:
1. The sample mean and variance for the sample size of 5, 10, and 50.
Sample Size
PhuongUyen Bui
Biostat100A_1D
ID#: 804443735
Lab 1: Introduction to STATA
I.
1.
Analysis:
The distribution of decom data is skewed because the median is much
closer to the 25th percentile of the data (shown in the boxplot below).
Particularly, the distrib
Principles of Macroeconomics
Dr. Nora A. Underwood
BA2 302N
ECO 2013
Spring 2016
My Office Hours
Please feel free to stop by and see me during my office hours, or to make
an appointment if my office hours are not convenient for you. You may e-mail me at a
1/26/16
Week 4
Study Strategy
Exam 1 Tuesday and Wednesday
Review on Tuesday
Regular class on Thursday
Dont forget about the TA hours
Extra credit available Thursday and Friday
Read chapters 1 3
Review Connect problems
Can do again for practice
ECO 3411: QUANTITATIVE BUSINESS TOOLS II, Summer 2016
Summer Classes Monday-Thursday 7:30-9:20 am in BA I Room 107
Professor: Dr. Bradley M. Braun
Office Hours: M-R 9:30-10:30 am
Location: BA II Rm. 302Y
Note: I also talk with students before class with a
ECO 3411: Practice Exam 3
Rental Home Analysis for Seminole Co.
This timed capstone project uses methods you have already mastered. Data samples and results differ from
one student to the next and also between questions, so use the Excel output within eac
ECO 3411: Practice Exam 3
Rental Home Analysis for Seminole Co.
1.
This timed capstone project uses methods you have already mastered. Data samples and results differ from
one student to the next and also between questions, so use the Excel output within
ECO 3411 A Previous Exam [answers at the end, starred questions missed by majority of students]
Actual final has 76 questions, most questions and cases different, a few are the same but with different questions, and
theres also cases on matched-pairs, mul
Tips to Master Unit II and Doing Well on the Exam (In Class Review Session)
1. Is it statistical inference? If its based on random sample from the population, and is not entire population
2. Is it a testing vs. estimation problem? Answer is yes-or-no vs.
Mastering Unit I and Doing Well on the Exam
Data
1. univariate, bivariate, multivariate
2. time series or cross section? time series data is many time periods, cross section
from single time period
Models
3. descriptive stats (uni-), scatterplot (bi-), re
AAPMs TG-51 protocol for clinical reference dosimetry of high-energy photon and
electron beams
Peter R. Almond, Peter J. Biggs, B. M. Coursey, W. F. Hanson, M. Saiful Huq, Ravinder Nath, and D. W. O.
Rogers
Citation: Medical Physics 26, 1847 (1999); doi:
Chapter 2
Magnetic domain theory in static
Magnetic domains in ferromagnetic materials are generated in order to minimize the sum of energy
terms, e.g., the magnetostatic, the exchange, the anisotropy, and the Zeeman energies. In the case
the magnetic fil
eCommons@AKU
Department of Radiation Oncology
Medical College, Pakistan
May 2012
Validating dose rate calibration of radiotherapy
photon beams through IAEA/WHO postal audit
dosimetry service
Abdul Qadir Jangda
Aga Khan University
Sherali Hussein
Aga Khan