STA 261 Study Guide - Final Guide: Standard Deviation, Contingency Table, Design Patterns

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Published on 4 Jul 2016
School
Department
Course
Module 1:
Descriptive vs. Inferential Statistics
oDescriptive- summarizing the data, Mean, Median, Standard Deviation,
Graphical Displays
oInferential- drawing conclusions about a population based on a sample,
confidence intervals, hypothesis tests
Statistical Question: a question that can be answered by collecting data- can’t have
an answer that is just based on a single number.
Sample vs. Population
oSample- a subset, or part of the entire group of individuals of interest
oPopulation- entire group of individuals or items of interest
Parameter vs. statistic
oParameter- a value that is computed from the whole population (a fixed
value)
oStatistic- a value that is computed from the sample (a variable value- changes
from sample to sample)
Module 2:
Categorical vs. Quantitative Data
oCategorical:
Can be numerical
Doesn’t make sense to add, subtract, or average the values
oQuantitative:
Are numerical
Adding, subtracting, or averaging the values has meaning
Possible to change into qualitative data when looking at groups
Two different types: discrete and continuous
Discrete- finite or countable (# rooms), isolated points on a
number line, associated with counting
Continuous- an interval or a collection of intervals of real
numbers (height), any number in a continuous interval, the set of
all possible values is in an interval of numbers, associated with
measuring.
Data Displays for Catergorical Data:
oFrequency and relative frequency tables
oPie Charts
oBar charts and pareto charts
Displays for Quantitative Data:
oDotplots
oStemplots
oHistograms
oTime Series Plots
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oBoxplots
oRange= Maximum value – minimum value
Reported when reporting mean, median, or mode
oIQR= Q-Q1
Reported when reporting median
oStandard Deviation
Reported when reporting means
SOCS
oShape: mention modality and skewness
Lower Fence= Q1-1.5(IQR)
Upper Fence= Q3+1.5(IQR)
oCenter: report which measure of center that best describes the “typical” value
Mean, median, or mode
Mean=Standard Deviation
Median=IQR
Mode=Range
Z-Scores
oA measure associated with each observation that indicates the distance from
the population mean in standard deviations
oA measure of relative standing
oCan be used to compare observations from different populations
Z= (observation-mean)/(standard deviation)
The Empirical Rule
oOnly applies to approx. normal distributions
oApprox. 68% of all obs. w/in 1 std. dev. Of mean
oApprox 95% of all obs. w/in 2 std. dev of mean
oApprox. 99.7% of all obs. w/in 3 std. dev of mean (Almost all obvesvations
Module 3:
Obsevationa Studies can only reveal association or correlation
Retrospective Study- conducting an analysis on the past
oIdentify subject with a specific characteristic and then look into their history
to find thins that may be related
oProne to errors
oExample: Case- control study (used in medical research)
Prospective Study- identifying subjects in advance and then collecting data as
events unfold
oCohort Study
Sample Survey- takes cross section of a population at a given time
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oCross-Sectional Study
Designed Experiments- researches impose treatments and controls
oHelp to establish causation
oCalled randomized, comparative experiments
Factor- a variable of interest
Levels of a factor- the specific values the experimenter chooses for a factor
Treatment- the combination of specific levels from all the factors that an
Control Group- the group that participates in the experiment and whose treatment is
nothing
oUsed to compare results to other levels of the factors
Blinding- disguising the prupose of the experiment, disguising the different levels
of an experiment, etc. Two main classes of individuals who can affect the outcome
of an experiment. Those who could nfluence the results, those who evaluate the
results.
oSingle-blind experiment
When all the individuals in either one of the classes mentioned above
are blinded
oDouble-blind experiment
When everyone in both classes are blinded
Placebo- a “fake” treatment that looks just like the treatments being tested
The Placebo Effect- subjects treated with a placebo sometimes improve
Blocking and Matching
oUsed when groups of experimental units are similar
oIsolates the variability due to the differences between the block so that we
can see the differences caused by the treatments more clearly
oRandomized Block Design- randomization occurs only within blocks
oMatching is often used in observational studies
Subjects are paired because they are similar in ways that are not being
studied
Matching reduces variation, similar to blocking
4 Principles of Experimental Design
oControl
Control sources of variation by making conditions as similar as
possible for all treatment grouos
oRandomization
Allows us to equalize the effects of unknown or uncontrollable sources
of variation
oReplication
Apply each treatment ot a number of subjects
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Document Summary

Descriptive vs. inferential statistics: descriptive- summarizing the data, mean, median, standard deviation, Graphical displays: inferential- drawing conclusions about a population based on a sample, confidence intervals, hypothesis tests. Statistical question: a question that can be answered by collecting data- can"t have an answer that is just based on a single number. Sample vs. population: sample- a subset, or part of the entire group of individuals of interest, population- entire group of individuals or items of interest. Parameter vs. statistic: parameter- a value that is computed from the whole population (a fixed value, statistic- a value that is computed from the sample (a variable value- changes from sample to sample) Doesn"t make sense to add, subtract, or average the values: quantitative: Adding, subtracting, or averaging the values has meaning. Possible to change into qualitative data when looking at groups. Discrete- finite or countable (# rooms), isolated points on a number line, associated with counting.