Discrete Variable There is a natural gap between the values Continuous Variable The values can be arbitrarily close together Ordinal Variable Categories that have a natural ordering Nominal Variable Categories that have no natural ordering Interval Data No meaningful zero point can t multiply or divide but the difference between two values is meaningful Ratio Data Meaningful zero point can multiply and divide Time Series Data Ordered data values over time Cross Sectional Data Data values observed at a single point in time Bias A sample that does not represent the population Selection Bias Problem in sampling scheme systematic tendency to exclude one kind of individual from the survey Difference between population of interest and effective population Non Response Bias Subjects don t answer skip questions Response Bias Subjects lie interviewer effect Sample The part of the population we actually examine and for which we do have data Statistic Is a number describing a characteristic of a sample Convenience Sampling Collected in the most convenient manner for the researcher ask whoever is around Bias Opinions limited to individuals present Voluntary Sampling Individuals choose to be involved Bias Sample design systematically favors a particular outcome Simple Random Sampling Every possible sample of a given size has an equal chance of being selected Stratified Random Sampling Divide population into subgroups called strata according to some common characteristic Select a simple random sample from each subgroup Combine samples from subgroups into one Cluster Sampling Divide population into several clusters each representative of the population e g county Select a simple random sample of clusters Systematic Random Sampling Decide on sample size n Divide ordered e g alphabetical frame of N individuals into groups of k individuals k N n Randomly select one individual from the 1st group Select every kth individual thereafter Sample Survey Designed to ask questions of a small group of people in order to learn something about the entire populations Explanatory Variable Predictor cause available variable Explains changes in the response variable independent variable Response Variable Predicted effect interesting variable Measures or records an outcome of a study dependent variable Simpson s Paradox An association or comparison that holds for all of several groups can reverse direction when the data are combined aggregated to form a single group Continuous Data May take on any value in some interval Range Largest data point Smallest data point Form Linear curved clusters no pattern Strength How closely the points fit the form Direction Positive negative no direction Right Skewed Left Skewed Symmetric Mean Add up the data and divide by the number of observations Median An equal number of observations more and less than the median Mode Peak in the distribution Quartiles Middle observation above the median and below the median Inter Quartile Range IQR Q3 Q1 Standard Deviation Average squared distance from the mean Square root of variation n i 1 X i X 2 n 1 S n i 1 X i X 2 n 1 2 S Variance Average of the squared deviations Shows variation about the mean z value mean st dev zx zy x x sx y y sy Correlation Coefficient Is a measure of the direction and strength of a linear relationship It is calculated using the mean and the standard deviation of both the x and y variables Correlation can only be used to describe quantitative variables Categorical variables don t have means and standard deviations The correlation coefficient r r does not distinguish between x and y r has no units of measurement r ranges from 1 to 1 Correlation of zero means no linear relationship Correlation is not affected by changes in the center or scale of either zxzy variable Correlation is sensitive to unusual observations Lurking Variable A variable not included in the study design that n 1 does have an effect on the variables studied Regression Line A straight line that describes how a response variable y changes as an explanatory variable x changes Correlation vs Regression The correlation is a measure of spread scatter in both the x and y directions in the linear relationship In regression we examine the variation in the response variable y given change in the explanatory variable x Coefficient of Determination r represents the percentage of the variance in y vertical scatter from the regression line that can be explained by changes in x Residual The distances from each point to the least squares regression line give us potentially useful information about the contribution of individual data points to the overall pattern of scatter 2 Is the square of the correlation coefficient r2 r
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