midterm chapters 1-3 Flashcards
CH 1-3 STATS
2 Types of Evidence
Observational
Evidential
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Anecdotal evidence
Evidence based on short stories or examples of interesting events
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Confounding variable
A variable that correlates with both the independent and dependent variables making it look like the two variables are directly related
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Placebo
An inert substance; a substance that looks like something else but is not composed of the same materials or ingredients
(ex. medicine vs. a sugar pill)
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Placebo effect
The tendency of people to respond favorably to any treatment, even if it is only inert
(Nocebo effect: the tendency of people to respond negatively to any treatment, even if it is only inert)
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Blinding
A technique used to keep the treatment assignment secret from the experimental subject
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Double-blinding
A technique used to keep the treatment assignments from both the experimental subjects and the persons making evaluations of the response
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Panel bias
Bias attributable to the study having influenced the behavior of the subjects
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Historical Controls
Controls are previous patients with the same illness who were treated with a different therapy than the one in question
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Problem with historical controls
Often there is a tendency for later patients to show a better response (even to the same therapy) than the previous patients with the same diagnosis
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Population
All subjects/animals/specimens/plants, and so on, of interest
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Sample (size n)
Subset of the population
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Effect of a biased sample
A biased sample systematically overestimates or systematically underestimates a characteristic of the population
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Qualifications of a simple random sample
a) Every member of the population has the same chance of being included in the sample
b) The members of the sample are chosen independently of each other
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Qualifications of a nonsimple random cluster sample
a) IDs are assigned to entire groups of individuals
b) Entire groups of individuals are selected for the sample
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Qualifications of a nonsimple stratified random sample
a) Population is divided into strata
b) Many random samples are taken-one within each stratum-and combined to comprise the sample
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Chance error due to sampling (sampling error)
A discrepancy between the sample and the population
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Sampling bias
Systematic tendency for some individuals of the population to be selected more readily than others
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Nonsampling error
Error that is not caused by the sampling method; An error that would have arisen even if the researcher had a census of the entire population
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Nonresponse bias
A bias caused by persons not responding to some of the questions in a survey or not returning a written survey
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Missing data
Observations that were planned but could not be made
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Variable
A characteristic of a person or a thing that can be assigned a number or a category
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Categorical variable
A variable that records which of several categories a person or thing is in
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Ordinal variable
A categorical variable in which the categories can be arrayed in a meaningful rank order
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Numeric variable
A variable that records the amount of something
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Continuous variable
A numeric variable that is measured on a continuous scale (includes decimals, fractions, etc.)
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Discrete variable
A numeric variable for which we can list the possible variables (integers)
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Observational unit
The persons or things on which we are measuring variables
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Frequency distribution
A display of the frequency (number of occurrences) of each value in the data set
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Bar chart
A simple graphic showing the categories that a categorical variable takes on and the number of observations in each category for the data in the sample
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Dotplot
A simple graph that can be used to show the distribution of a numeric variable when the sample size is small
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Histogram
Like a bar chart, except that a histogram displays a numeric variable, which means that there is a natural order and scale for the variable
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Relative frequency
= Frequency / n
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Mode
The central peak in a frequency distribution; the value with the most occurences
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Skewed to the right
The right tail is more stretched out than the left
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Skewed to the left
The left tail is more stretched out than the right
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Unimodal
The graph has only one mode
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Bimodal
The graph has two modes: can indicate the existence of two distinct subgroups of observational units
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Median ( ỹ)
The value that most nearly lies in the middle of the sample–the value that splits the ordered data into two equal halves
1/2 (n+1) denotes the rank position of the median within an ordered data set
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Mean ( ȳ)
Sum of the observations divided by the number of observations (average)
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Robust statistic
A statistic that is relatively unaffected by changes in a small portion of the data (even if the changes are dramatic ones)
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Boxplot
A visual representation of the five number summary
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Five number summary
Minimum, Quartile 1, Median, Quartile 3, Maximum
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First quartile (Q1)
Median of the data values in the lower half of the data set (between the minimum and median)
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Third quartile (Q3)
Median of the data values in the upper half of the data set (between the median and maximum)
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Interquartile Range (IQR)
The difference between the first and third quartiles
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Outlier
A data point that differs so much from the rest of the data that it doesn’t seem to belong with the other data
upper fence = Q1 - 1.5 * IQR
lower fence = Q3 - 1.5 * IQR
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Modified boxplot
A boxplot in which the outliers are graphed as separate points
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Univariate summary
A graphical or numeric summary of a single variable
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Bivariate summary
A graphical summary used to examine the relationship between pairs of variables
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Categorical-categorical relationship graphs
Bivariate frequency table
Stacked bar chart
Stacked relative frequency bar chart
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Numeric-categorical relationship graphs
side-by-side boxplots
side-by-side dotplots
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Numeric-numeric relationship graphs
Scatterplot
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Scatterplot
A graph that examines the relationships between two numeric variables, X and Y
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Lowless smooth line
A line on a scatterplot that is helpful in visualizing curved or nonlinear relationships in data
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Regression line
A line in scatterplots that is helpful in visualizing linear trends in data
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Range
The difference between the largest (maximum) and smallest (minimum) observations in a sample
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Standard deviation (s)
- find the deviations for all data points
- square all
- add all together
- divide the sum by n-1
- take the square root
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Coefficient of variation
The standard deviation expressed as a percentage of the mean
(standard deviation / mean) * 100%
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The empirical rule
68% within 1 standard deviation of the mean
95% within 2 standard deviations of the mean
> 99% within 3 standard deviations of the mean
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Population mean (μ)
= population average value of Y
Y=quantitative variable
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Population Standard Deviation (σ)
=square root (population average value of (Y - μ)^2)
Y=quantitative variable
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Sample Variance (s^2)
Square of the standard deviation (s)
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Effect of addition on the transformation of variables
- Linear transformation
- Add constant, c, to the variables
- Has no effect on standard deviation
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Effect of multiplication on the transformation of variables
- Linear transformation
- Multiply values by constant, c
- Multiply standard deviation by absolute value of c
