1.3 Statistics 1
*Passer chapters at the end
*Formulas may be awkwardly displayed due to formatting difficulties
MMC - Chapter 1
Describing Distributions
Mean
-> is sensitive to the influence of a few extreme observations (outliers)
-> not a resistant measure of center
-> only for reasonably symmetric distributions without outliers
Median
-> M
-> midpoint of distribution
-> half of the observation are smaller, the other half are larger
Five-number summary
-> Minimum, Q1, Median, Q3, Maximum
-> describes a skewed distribution/outliers better than the mean or the sd
-> Boxplot
Interquartile Range IQR
-> distance between the first and the third quartile
-> IQR = Q3-Q1
Outliers
-> 1,5 x IQR
Standard deviation
-> measures spread by looking how far the observations are from their mean
-> if the data points are further from the mean, there is higher deviation within the data set
-> sd measures spread about the mean and should be used only when the mean is chosen as the measure of the
center
-> s=0 only when there is no spread (all observations have the same value)
-> not resistant – a few outliers can make sd very large
-> only for reasonably symmetric distributions
Density curves
-> smooth approximation to the irregular bars of a histogram
-> always on or above the x-axis; the area is exactly underneath it
-> describes the overall pattern of a distribution
mode: peak point of the curve (location where the curve is the highest) median: the
point that divides the area under the curve in half
mean: balance point
, IQR: distance between first and third quartile
with the mean 0 and
the sd 1
MMC - Chapter 3
Sources of Data
Anecdotal Data
-> represents individual cases, which often come to our attention
because they are striking in some way
-> not necessarily representative of any larger group of cases
Available Data
-> data that were produced for some other purposes but that may help answer a question of interest
Observation vs. Experiment
-> we observe individuals and -> we deliberately impose
measure variables of interest but some treatment on individuals
don’t attempt to influence the and we observe their
responses responses.
Sample Survey
-> collects data from a sample of cases that represent some larger population of cases
Census
-> collects data from all cases in the population of interest
Confounding
-> occurs when the effects of two or more variables are related in such way that we need to take care in
assigning the effect to one or the other
Design of Experiments
Experimental units
=> the individuals on which the experiment is done; subjects, if they’re human beings
Treatments
=> experimental conditions applied to the units
Outcome
=> the measured variables that are used to compare the treatments
Factors
=> explanatory variables
Laboratory Experiments
-> simple design with only a single treatment
, -> Treatment -- Observe response Observe response
-> relies on the controlled environment of the laboratory to be protected from lurking variables
Comparative experiments/Comparison
-> randomly assigns treatment and control groups to avoid confounding
-> experiments should compare two or more treatments in order to prevent confounding
Randomization of Comparative Experiments
-> creates treatment groups that are similar before the treatments are applied
-> giving numerical labels to the experimental units and using a table of random digits to choose treatment groups
=> prevents bias or systematic favouritism
Bias
-> the design of a study is biased if it systematically favours certain outcomes
Principles of Experimental Design
1) compare two or more treatments -> this will control the effects of lurking variables on the response
2) randomize -> use impersonal chance to assign experimental units to treatments
3) repeat each treatment on many units to reduce chance variation in the results
Repetition
-> reduces the role of chance variation and makes the experiment more sensitive to differences among treatments
Double-blind
-> neither the subject nor the experimenter know which treatment any subject has received
-> avoids unconscious bias
Lack of realism
-> limits our ability to apply the conclusions of an experiment to the setting of greatest interest
Block Design
-> the random assignment of units to treatments is carried out separately within each block Block = a group of
experimental units/subjects that are known before the experiment to be similar in some way that is expected to
affect the responses to the treatments
-> second form of control is to restrict randomization by forming blocks
Matched Pairs Design
-> compares just two treatments
-> each subject receives both treatments or similar subjects are matched in pairs and each of them gets a different
treatment
e.g.: to compare two advertisements for the same product -> subjects with the same age, sex and income are
confronted with both advertisements
-> matched subjects are more similar than unmatched subjects
-> more efficient
*Passer chapters at the end
*Formulas may be awkwardly displayed due to formatting difficulties
MMC - Chapter 1
Describing Distributions
Mean
-> is sensitive to the influence of a few extreme observations (outliers)
-> not a resistant measure of center
-> only for reasonably symmetric distributions without outliers
Median
-> M
-> midpoint of distribution
-> half of the observation are smaller, the other half are larger
Five-number summary
-> Minimum, Q1, Median, Q3, Maximum
-> describes a skewed distribution/outliers better than the mean or the sd
-> Boxplot
Interquartile Range IQR
-> distance between the first and the third quartile
-> IQR = Q3-Q1
Outliers
-> 1,5 x IQR
Standard deviation
-> measures spread by looking how far the observations are from their mean
-> if the data points are further from the mean, there is higher deviation within the data set
-> sd measures spread about the mean and should be used only when the mean is chosen as the measure of the
center
-> s=0 only when there is no spread (all observations have the same value)
-> not resistant – a few outliers can make sd very large
-> only for reasonably symmetric distributions
Density curves
-> smooth approximation to the irregular bars of a histogram
-> always on or above the x-axis; the area is exactly underneath it
-> describes the overall pattern of a distribution
mode: peak point of the curve (location where the curve is the highest) median: the
point that divides the area under the curve in half
mean: balance point
, IQR: distance between first and third quartile
with the mean 0 and
the sd 1
MMC - Chapter 3
Sources of Data
Anecdotal Data
-> represents individual cases, which often come to our attention
because they are striking in some way
-> not necessarily representative of any larger group of cases
Available Data
-> data that were produced for some other purposes but that may help answer a question of interest
Observation vs. Experiment
-> we observe individuals and -> we deliberately impose
measure variables of interest but some treatment on individuals
don’t attempt to influence the and we observe their
responses responses.
Sample Survey
-> collects data from a sample of cases that represent some larger population of cases
Census
-> collects data from all cases in the population of interest
Confounding
-> occurs when the effects of two or more variables are related in such way that we need to take care in
assigning the effect to one or the other
Design of Experiments
Experimental units
=> the individuals on which the experiment is done; subjects, if they’re human beings
Treatments
=> experimental conditions applied to the units
Outcome
=> the measured variables that are used to compare the treatments
Factors
=> explanatory variables
Laboratory Experiments
-> simple design with only a single treatment
, -> Treatment -- Observe response Observe response
-> relies on the controlled environment of the laboratory to be protected from lurking variables
Comparative experiments/Comparison
-> randomly assigns treatment and control groups to avoid confounding
-> experiments should compare two or more treatments in order to prevent confounding
Randomization of Comparative Experiments
-> creates treatment groups that are similar before the treatments are applied
-> giving numerical labels to the experimental units and using a table of random digits to choose treatment groups
=> prevents bias or systematic favouritism
Bias
-> the design of a study is biased if it systematically favours certain outcomes
Principles of Experimental Design
1) compare two or more treatments -> this will control the effects of lurking variables on the response
2) randomize -> use impersonal chance to assign experimental units to treatments
3) repeat each treatment on many units to reduce chance variation in the results
Repetition
-> reduces the role of chance variation and makes the experiment more sensitive to differences among treatments
Double-blind
-> neither the subject nor the experimenter know which treatment any subject has received
-> avoids unconscious bias
Lack of realism
-> limits our ability to apply the conclusions of an experiment to the setting of greatest interest
Block Design
-> the random assignment of units to treatments is carried out separately within each block Block = a group of
experimental units/subjects that are known before the experiment to be similar in some way that is expected to
affect the responses to the treatments
-> second form of control is to restrict randomization by forming blocks
Matched Pairs Design
-> compares just two treatments
-> each subject receives both treatments or similar subjects are matched in pairs and each of them gets a different
treatment
e.g.: to compare two advertisements for the same product -> subjects with the same age, sex and income are
confronted with both advertisements
-> matched subjects are more similar than unmatched subjects
-> more efficient
