Term
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Definition
a measure that can resist the influence of extreme observations
e.g Median |
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Term
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Definition
| midpoint of a distribution (i.e. the number such that half the observations are smaller and the other half are larger (n+1)/2 |
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Term
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Definition
1st Quartile is > 25% of observations
2nd Quartile = median
3rd Quartile is > 75% of observations |
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Term
| Quartiles (Freund/Perles) |
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Definition
the lower quartile (Q1) is the ¼(n+3)th observation
the second quartile (median) is the ½(n+1)th observation
the upper quartile (Q3) is the ¼(3n+1)th observation |
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Term
| Choosing a Summary (center/spread) |
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Definition
| Five number summary is usually better than mean and standard deviation for a distribution or one with strong outliers |
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Term
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Definition
| A curve that has area exactly 1 underneath it. The area under the curve and above any range of values is the proportion of values that fall in that range |
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| Mean of skewed distribution |
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Definition
| The mean of a skewed distribution is pulled toward the long tail |
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Term
| Normal Curve/Distribution |
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Definition
| Symmetric, single-peaked, and bell-shaped |
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Term
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Definition
68% of values fall within the 1 std dev from the mean
95% fall within 2 std dev from the mean
99.7% fall within 3 std dev from the mean |
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Term
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Definition
| subtract mean of distribution from value and divide by standard deviation (z-score) |
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Definition
| tells is how many standard deviations original value falls away from the mean and in what direction |
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Term
| Standard Normal Distribution |
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Definition
| The normal distribution with mean 0 and standard deviation 1 |
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Term
| Behavior of Mean of Skewed Distribution |
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Definition
| Mean moves farther toward long tail for a skewed curve |
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Term
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Definition
| minimum, Q1, Q2(Median), Q3 Maximum |
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Term
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Definition
| s is zero when there is no spread and gets larger as spread increases |
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Term
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Definition
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Term
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Definition
| sum of individual deviations squared divided by the degrees of freedom (i.e. n-1) |
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Term
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Definition
| Q3-Q1 (Outlier is 1.5 X IQR above Q3 or below Q1 |
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Term
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Definition
| Measures outcome of a study |
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Term
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Definition
| explains or influences changes in a response variable |
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Term
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Definition
| Plot explanatory variable on x-axis and response variable on the y-axis |
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Term
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Definition
| when above average of one variable tend to accompany above average of the other or below average values tend to occur together |
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Term
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Definition
| when above average value of one variable accompany below average values of the other and vice versa |
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Term
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Definition
| when points in a scatter plot lie in a straight line pattern |
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Term
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Definition
| the sum of the x deviations over std dev of x times the y deviations times 1/n-1 |
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Term
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Definition
| Correlation makes no distinction between x and y |
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Term
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Definition
| Because r uses standardized variables r doesn't change when change units of measurement for x and y or both |
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Term
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Definition
| Positive r indicates positive association and negative r indicates negative correlation |
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Term
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Definition
| r is always between -1 and 1 and strength increases as move away from 0 in either direction (r = +-1 points lie on straight line) |
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Term
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Definition
| correlation measure strength of linear relationship only not curved |
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Term
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Definition
| correlation is not resistant i.e. affected by outliers |
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Term
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Definition
| a straight line that describes how a response variable changes as an explanatory variable changes |
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Term
| Least-squares regression line |
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Definition
the line that makes the sum of the squares of the vertical distances of the data points from the line as small as possible
slope = r*(sy/sx)
intercepts = y-b*x |
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Term
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Definition
| along the regression line a change of one std dev in x corresponds to a change of r std dev in y in other words as correlation grows less strong the prediction moves kess in response to changes in x |
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Term
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Definition
| is the fraction of the variation in the values of y that is explained by the least-squares regression of y on x |
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Term
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Definition
The difference between an observed value of the response variable and the value predicted by the regression line
residual = obs y - predicted y |
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Term
| Mean of least-squares residuals |
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Definition
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Term
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Definition
| a scatterplot of the regression residuals against the explanatory variable |
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Term
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Definition
| point in extreme of x direction which has a strong influence on the position of the regression line |
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Term
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Definition
| observation that lies outside the overall pattern of the other observations |
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Term
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Definition
| the use of a regression line for prediction far outside the range of values of the explanatory variable |
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Term
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Definition
| correlations based on averages are usually too high when applied to individuals |
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Term
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Definition
| a variable that has an important effect on the relationship among the variables in a study but is not included amont the variables studied |
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Term
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Definition
| changing one of the variables causes changes in the other - usually caused by lurking variable |
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Term
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Definition
| an association between an explanatory variable and a response variable is not by itself good evidence that changes in x cause changes in y even if that association is strong |
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Term
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Definition
Association is strong
Association is consistent
Higher doses are associated with stronger responses
Cause precedes effect in time
Cause is plausible |
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Term
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Definition
| table defining two categorical variables |
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Term
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Definition
| row and column totals that appear at right and bottom margins of a two way table |
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Term
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Definition
| an association or comparison that holds for all of several groups can reverse direction when the data are combined to form a single group |
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Term
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Definition
| observes individuals and measures variables of interest but does not attempt to influence responses e.g. sampling |
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Term
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Definition
| study that deliberately imposes some treatment on individuals in order to observe their responses |
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Term
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Definition
| when two variables (explanatory or lurking) effects on a response variable cannot be distinguished from each other |
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Term
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Definition
| entire group of individuals we want info about |
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Term
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Definition
| subset of population that we actually examine in order to gather information |
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Term
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Definition
| method used to choose sample from population |
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Term
| Voluntary Response Sample |
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Definition
| sample where people choose themselves to respond to a general appeal. biased b/c people with strong opinions-especially negatve ones-are most likely to respond |
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Term
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Definition
| sample design that chooses the individuals easiest to reach |
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Term
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Definition
| systematic error; i.e. sample design that favors certain outcomes |
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Term
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Definition
| consists of n indviduals from a population chosen such that every set of n individuals has an equal chance to be selected |
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Term
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Definition
| sample technique that gives each member of the population a known chance of being selected |
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Term
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Definition
| divides population into groups of similar individuals called strata and then choosing a SRS from each stratum and combining the SRSs to form sample |
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Term
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Definition
| groups of similar individuals within a population used in stratified random sampling |
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Term
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Definition
Stage 1: Divide population into groups and select a sample of the groups
Stage 2: divided groups from one into smaller areas called blocks and take a stratified sample from the blocks
Stage 3: Sort individuals from blocks into clusters and take random sample of clusters |
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Term
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Definition
| when some groups in the population are left out of SRS. e.g. phone survey and 6% w/o phones |
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Term
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Definition
| when an individual chosen for the sample can't be contacted or refuses to cooperate |
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Term
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Definition
| bias caused by behavior of respondent or interviewer e.g. respondent lying, race or sex of interviewer |
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Term
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Definition
| bringing events in the past forward in memory to more recent time periods e.g. saw dentist 8 months ago and say yes to seeing dentist in the last 6 mos. |
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Term
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Definition
| wording of quesions in sample surveys can introduce bias |
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Term
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Definition
| list of individuals from which a sample is selected |
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Term
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Definition
| The individuals on which an experiment is done |
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Term
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Definition
| the experimental units when dealing with human beings |
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Term
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Definition
| experimental condition applied to the units |
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Term
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Definition
| the explanatory variable(s) in an experiment |
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Term
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Definition
| values of the factors in an experimental treatment |
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Term
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Definition
| use of chance to divide experimental units into groups in an experiment |
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Term
| Randomized Comparative Experiment |
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Definition
| An experiment that uses both comparison and randomization |
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Term
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Definition
| experimental design where all experimental units are allocated at random among all treatments |
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Term
| Statistically Significant |
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Definition
| An observed effect so large that it would rarely occur by chance |
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