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Learn the basics of descriptive and inferential statistics, explore variables, data reduction, and measures of association. Discover the levels of measurement and how they impact statistical analysis.
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Statistics • A set of mathematical techniques used by social scientists to organize and manipulate data for the purpose of answering questions and testing theories
Variable • Any trait that can change values from case to case
Independent Variable Dependent Variable
Descriptive Statistics • When the researcher needs to summarize or describe the distribution of a single variable • When the researcher wishes to understand the relationship between two or more variables
Data Reduction • Process of allowing a few numbers to summarize many numbers • Is the basic goal of single-variable (or univariate) descriptive statistical procedures
Measures of Association • Understand the relationship between two or more variables • Allow to quantify the strength and direction of a relationship
Inferential Statistics • Wish to generalize findings from a sample to a population • Population – total collection of all cases that the researcher wishes to understand better • Involves using information from samples (carefully chosen subsets of the defined populations) to make inferences about populations
Discrete Variable • It has a basic unit of measurement that cannot be subdivided • Eg. # of people per household
Continuous Variable • If the measurement can be subdivided infinitely • Eg. time • Always approximating and rounding off the scores • Reported as discrete
Level of Measurement • Nominal • Ordinal • Interval-ratio (I/R)
Nominal • Classification into categories is the only measurement procedure permitted • Not numerical • Compared to each other only in terms of the number of cases classified in them
Nominal • Categories not higher or lower along some numerical scale • Eg. gender, religious affiliation • Mutually exclusive and exhaustive • Categories are relatively homogeneous
Ordinal • Classify into categories • Allow categories to be ranked • High to low, more or less than another • Eg. SES: upper class, middle class, working class, lower class
Ordinal • Represents only a position • The distance between the scores cannot be described in precise terms • Averages cannot be used
Interval-Ratio (I/R) • They are measured in units that have equal intevals • Eg. age, # of siblings • Have a true zero • Zero indicates the absence or complete lack of whatever is being measured • Eg. education, income
Levels of measurement is the first guideline to use in selecting a statistic