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Statistics SectionUnivariateOne variableDescriptive3 typesShape of the distributionNormal curve (bell curve)Skewness: not symmetrical; it has a tail in one directionPositively skewed means the tail is on the right. The mean will be greater than the median.Negatively skewed means the tail is on the left. The mean will be lower than the median.KurtosisMesokurtic: bell curveLeptokurtic: really skinnyPlatykurtic: looks like a plateau; no common answersMeasures of central tendencyMode: frequently occurring categoryMedian: middle (50% percentile); (n+1)/2 finds itMean: averageMeasures of dispersionHow spread out the cases areRange: maximum score minus the minimum scoreStandard deviation: quantity calculated to indicate the extent of deviation for a group as a wholeZ-scores: number of standard deviations that you are away from the meanNominal: only calculate the modeOrdinal: calculate mode, median, rangeInterval/ratio: full slew of statisticsComputer statistic programsSPSSStataSASBivariate statistics2 variables; we want to asses their relationshipWe can ask 3 things:Is there a relationship?How much does one variable influence the other?How likely is it that the relationship exists by chance?2 discrete variablesExample: gender and marital status. Strength of prison security and political party of the stateWe use a cross-tabsActual statistic is “chi-square”Cross-Tabs3 criteria for causation (just a review)1. Association2. Temporal orderNon-spuriousnessThings to do (in order):1) Look at the title2) Look at the variablesThe independent variable will add up to 100 along that categoryIf the above trick doesn’t work, you think about temporal order. (in the example from class, sex obviously comes before delinquency, therefore the sex is the independent variableLast resort way to figure out the independent variable is that the independent variable is usually the variable on the top of the table3) Describe the relationshipYou read one category of the dependent variable for both categories of the independent variable“20% of males are delinquent”“10% of females are delinquent”“Therefore males are more likely to be delinquent”* If the difference is less than 5% there is NO difference*2 continuous variablesWe calculate a correlationStatistic for correlation is “r”1 discrete and 1 continuousWe use a t-testStatistic is “t”T-test:Split the discrete variable into 2 groups (male and female; whites and everyone else; high school graduates and everyone else)When looking at the graphs of the test, look at the significance. Then chose if you reject the null or not.Alpha level = .05If it is less than .05 we there is a relationship (we reject the null)Correlation (r)2 continuous variablesMeasures the linear association between two variablesPearson’s CorrelationTells us 3 things:1) The strength of the relationship0 = no relationship.01 - .29 = weak.30 - .59 = moderate.60 - .99 = strong1 = perfect2) The direction of the relationshipPositive or negative numberPositive: as one increases so does the other (two variables move in the same direction)Negative: as one increases the other decreases (the two variables change in opposite directions)Ranges from -1  1Positive number = positiveNegative number = negative3) The significance of the relationshipp-value = significance levelWe want to see if it’s a true relationship or if it occurs by chanceIn order to have a significance you must have a hypothesisNull hypothesis = H0= no relationshipResearch = H1 = whatever I think is going to happenWhen we reject the null hypothesis we think our research hypothesis is trueYou usually reject the null hypotheses if only 5 out of 100 samples would give us the observed relationship when the actual relationship in the population is 0Alpha level = .05If it is less than .05 we there is a relationship (we reject the null)When we fail to reject the null hypothesis we think there is no relationshipMultivariate statistics2 or more variablesWe examine the relationship between 2 variables while holding one or more variable constantExample: single parent households and delinquencyHowever we think that delinquency is caused by lack of parental supervisionWe use OLS regression“Ordinary Least Squares”Looks similar to a correlation when drawn in 2DBut much more complicated when in 3D and with more variablesMinimizes the sum of the square distances to the lineThe distance from each point to the line is error, so we cant to minimize the errorThe resulting line is the line that describes the relationshipY=A + BX***Constant: predicted value of (y/dv) when (all x’s and iv’s) are zeroY is the dependent variableX is the independent variableB is the slope of the lineSlope is also called the regression coefficientThe change in y for one unit change in xA is the interceptAlso known as the constantWhere the line crosses the y axisTells us the predicted value of y when x is 0We can add more variables because we can have more then one independent variableY=a+b1X1 + b2X2Example:Y=10000+2000X1 (education) + 1000X2 (age)***B1: change in (y/dv) for a one-unit change in (X1/IV) controlling for X2/IV)For B1 use the number2000 is the change in income for a one unit change in education controlling for ageResearch Methods Unit 3• Survey Researcho Most widely used method/technique for data gathering for social researcho We can ask people about their behavior “Have you done this?” Don’t want to be too ambiguouso We can ask about attitudes, beliefs, opinionso We can ask people about their characteristics Age, marital status, ect. o Self classification Asking people to put themselves into a category that may not be straight forward• Example: race? Liberal vs. conservativeo We can ask people about their expectations Do you plan to move to a new home in the next year? Do you plan on buying a new car in 6 months In criminology, we ask people about hypothetical crimeo We can ask people about knowledge Sometimes we want to gauge how much people know You can ask:• Who is our current mayoro 2 forms of questions: Open-ended• Have not answer choices provided; free response• Advantages:o Allow us to have more in depth analysis• Disadvantages:o A lot of worko Must use something called coding You read through each answer and place them into categories, then each category is given a number Relies on the interpretation of the researchero Some answers given can be completely irrelevant


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FSU CCJ 4700 - Research Methods Unit 3

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