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UMass Amherst PSYCH 240 - Variables & Descriptives and Distributions

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PSYC 240 1st Edition Lecture 2Sec. 1: VariablesStatistics-Statistics: mathematical tools for the organization, analysis, and interpretation of data-Descriptive statistics: summarize and describe a dataset-Inferential statistics: use data to make general conclusions (conclusions that go beyond the data at hand) Data Terminology-Variable: condition, characteristic, or measure that can take on different values-Value: one of the possible levels that a variable can take-Score: the value of a variable observed for a particular data-collection unit-Distribution: collection of scored across a number of data-collection unitsTypes of Variables-You have to know what kind of variable you are considering to know what kind of conclusions you can make based on that variable-Numeric/quantitative: values of the variable are numbersoEx. Response time; packs of cigarettes smoked per week-Nominal/categorical/qualitative: values of the variable are verbal labelsoEx. Lineup type; marital status-Sometimes researchers use numbers just to label different categoriesoEx. A researcher might code gender by using a 1 for males and a 2 for females. This is still a categorical variable, since the values don't actually code a numerical quantity -Continuous: variable for which there are NO gaps in the values that the variable can take. There are an infinite number of possible values btw any two scoresoEx. Speed; heart rate; height; response time-Discrete: variable for which there ARE gaps in the values that the variable can take. Some scores simply never occuroEx. Number of siblings; number of prior marriages-Ratio Variable: equal-interval variable for which a value of zero truly indicates the complete absence of what is being measuresoEx. Pounds of beef consumed in a year; bank account balanceo-The Fahrenheit and Celsius temp scales are equal-interval but NOT ratio, because zero degrees does not indicate the complete absence of hear (indeed,temperatures below zero are often observed)-The Kelvin scale is equal interval and is also ratio. Zero on this scale does not mean the complete absence of heat, and it is not possible for a temperature to be any colder than 0 degrees KelvinoZero doesn’t have to be a reasonable value of the variable for the variable to be on aratio scale-Ex. Height is on a ratio scale even though no one has a height of zerooWhy "Ratio"?-A variable must have a zero point to determine what ratio is formed by two of the values-Is one value half of another value? A third of the value? Twice the value? These questions can be answered for true ratio variables-The ratio btw two scores can be anything depending on where we put zero. This is why we can only make valid statements about ratios when we know where zero REALLY isTypes of Numeric Variables-Equal Interval: equal-sized changes in the variable represent equal-sized changes in what is being measuredoEx. Temp; weight-Ordinal: values of variable only indicate the rank of the scoreoEx. Finishing position in a race; rank in a class-Rating scales should probably be considered ordinal, but some researchers treat them asequal-interval. Watch out for thisoEx. People might assume that the difference in satisfaction btw people who give a 3 and a 4 is the same as the difference btw people who give a 6 and a 7, but this might not be true Objectives-Know the difference btw descriptive and inferential statistics and be able to recognize examples of both-Be able to define variable, value, and distribution, and be able to recognize examples of each-Know the different types of variable. Be able to decide if a given variables numeric versus nominal, equal-interval versus ordinal, continuous versus discrete, and on a ratio scale versus not on a ratio scale. Also be able to generate examples of variables that fit each category-Know that you can only make conclusions about the ratio btw two scored for variables on a ratio scale, and understand why this is the caseSec. 2: Descriptives and DistributionsSummarizing Variable-Once we have data to evaluate, we need to organize the data in ways our minds can understand-There are 3 pieces of information you need to know to have a complete picture of a variable: the central tendency, variability, and shape of the distribution of scores-We can convey this information with descriptive statistics and/or graphsCentral Tendency-The goal here is to give a number that described the "typical" score for the variable. This is called a measure of central tendency-The 2 most popular measures of central tendency are the mean and the medianoMean/Average: sum of the scored divided by the number of scores- -Properties of the mean:The sum of all deviation from the mean is zeroThe sum of the squared deviations from the mean is lower than the sumof the squared deviations from any other number-Mean is the "balance point". Deviations above it exactly cancel out deviations below is oMedian: value at the middle of a sorted set of scores-For an odd number of scored, sort the scores and take the value of the one in the middle-For an even number of scores, sort the scores and take the average of the two numbers in the middleoSometimes the median will have the same value as one or more of the actual scores,sometimes it won'toThere will usually be ab equal number of scores above and below the medianoThe only exception to this is variables that have more than one score with the same value as the


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