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Home , Bivariate analysis

Quantitative approaches! Quantitative approaches!

Lesson 7: ! Plan! Statistical basics I! 1. Types of analysis! 2. Types of variables : nominal, ordinal, interval, metric! 3. !Measures of : , , ! 4. Measures of variability: and !

Quantitative approaches! Quantitative approaches! Useful resources! 1. Types of analysis!

Rice Virtual Lab in ! http://onlinestatbook.com/rvls/index.html

http://www.socialresearchmethods.net/ Quantitative approaches! Quantitative approaches! Types of analysis! Descriptive vs. inferential analysis!

!- descriptive or inferential! !"Descriptive analysis is about the data you have in hand. Inferential analysis involves making statements - !- , bivariate, multivariate! inferences - about the world beyond the data you have in hand."! !"When you say that the average age of a group of telephone survey respondents is 44.6 years, that's a descriptive analytic statement. When you say that there is a 95% statistical probability that the true mean of the population from which you drew your sample of respondents is between 42.5 and 47.5 years, that's an inferential statement. You infer something about the rest of the world from data in your sample."! !(Bernard, 2000: 502)!

Quantitative approaches! Quantitative approaches! Univariate, bivariate, multivariate! Univariate, bivariate, multivariate!

- univariate : uses 1 variable! - " involves getting to know data intimately by examining variables precisely and in detail. - bivariate: uses 2 variables! Bivariate analysis involves looking at axssociations between pairs of variables and trying to understand how those associations work. Multivariate analysis involves, - multivariate: uses 3 and more variables! among other things, understanding the effects of more than one independent variable at a time on a dependent variable."! !(Bernard, 2000: 502)! Quantitative approaches! Quantitative approaches! Univariate, bivariate, multivariate: how to Bivariate analysis: questions to ask! proceed! 1. How big/important is the covariation? In other words, 1. Look at the variables one by one: what is their , how much better could we predict the score of a dependent mean, median, variance (is there variance!?), distribution variable in our sample if we knew the score of some (univariate)! independent variable? Covariation coefficients answer this question! 2. Inspect associations between pairs of variables. How does 2. Is the covariation statistically significant? Is it due to the independent variable "influence" the dependent chance, or is it likely to exist in the overall population to variable? (bivariate)! which we want to generalize? Statistical tests answer this question.! 3. What is it direction? (look at graphs)! 3. Look at the associations of several variables simultaneously. How do two or more independent 4. What is its shape? Is it linear or non linear? (look at variables influence a dependent variable at the same time? graphs)! (multivariate)!

Quantitative approaches! Quantitative approaches! 2. Types of variables : " Multivariate analysis: questions to ask! nominal, ordinal, interval, metric! 1. How is a relationship between two variables changed if a third variable is controlled? (Multiple crosstabs, , multiple regression, MANOVA)! 2. What is the overall variance of a dependent variable that can be explained by several independent variables. What are the relative strenghs of different predictors (independent variables)? (Multiple regression)! 3. What groups of variables tend to correlate with each other, given a multitude of variables? ()! 4. Which individuals tend to be similar concerning selected variables? ()! Quantitative approaches! Quantitative approaches! Levels of measurement and covariation: Variables : nominal, ordinal, interval! Analysis! Variables : ! !Depend. !Nominal !Ordinal !Interval! Nominal !have no inherent order! Independ.! ! !example: party preference, male-female!

Ordinal !are ordered, but the distances are not ! Nominal !Crosstabs ! !ANOVA! !quantifiable (we cannot add or subtract)! !! ! !! ! !example: agree a lot, agree a bit, disagree a !bit, disagree a !! !! lot! Ordinal ! ! !! Interval !can be measured numerically; it makes sense to to" !! !! !additions or subtraction " !example : height, weight, income, !number !of cars! Interval ! ! !Correlation!! !! ! ! !Regression!

Quantitative approaches! Quantitative approaches! 3. Measures of central tendency: " Definitions : Mode, Median, Mean! mode, median, mean! !Mode = !Value in the distribution of the variable !that comes up most frequently!

!Median = !Value in the distribution that has 50% !of !the values «#to its right#» and 50% of the !values «#to its left#». !

!Mean = !Sum of the values divided by n! Quantitative approaches! Quantitative approaches! Example : Size of 11 dwarfs! Example : Size of 11 dwarfs!

Mode! 5, 7, 7, 7, 9, 9, 11, 12, 12, 13, 15! 1. Size of 11 dwarfs: ! 13, 7, 5, 12, 9, 15, 7, 11, 9, 7, 12 (cm)! Median! = 5, 7, 7, 7, 9, 9, 11, 12, 12, 13, 15 ! Mean 9,7272

Mean 9.7272

5 7 7 7 9 9 11 12 12 13 15 Mode Median

Quantitative approaches! Quantitative approaches! 5. Measures of variability: " Calculating mean, mode, median! variance and standard deviation!

y mean = y = ! n 5 + 7 + 7 + 7 + 9 + 9 +11+12 +12 +13+15 mean = y = 11 107 mean = y = = 9.727273 11

median = 5, 7, 7, 7, 9, 9, 11, 12, 12, 13, 15 !

mode= 5, 7, 7, 7, 9, 9, 11, 12, 12, 13, 15 ! Quantitative approaches! Quantitative approaches! Variance and standard deviation : definitions! Variance!

!Variance and standard deviation are measures of the «#variability#» of a variable. In other words: how much ! y they «#vary#» around the mean. ! mean = y = n

!Variance = the sum of the square of the individual departures from the mean divided by the degrees of (y y)2 sum of squares 2 ! " freedom! variance = = s = degrees of freedom (n "1)

!Standard deviation = the square root of the variance. ! (y " y)2 standard deviation = s = ! (n "1)

Quantitative approaches! Quantitative approaches! Example: Dwarfs in 3 gardens! Size of dwarfs in 3 gardens! Quantitative approaches! Quantitative approaches! Size of dwarfs in 3 gardens! Garden

A B C mean(A) = yA = 3 3 5 3 mean(B) = y = 5 4 5 3 B 4 6 2 mean(C) = yC = 5 3 7 1 2 4 10 3 4 4 2 var(A) = sA = 1.3 1 3 3 2 3 5 11 var(B) = sB = 1.3 !!5 !6!3! 2 var(C) = sC = 14.2 !!2 !5!10!

Quantitative approaches! Quantitative approaches!

Computing variance of dwarfs in garden C! Boxplots! Boxplot = graphical summary of the (y ! y) Var = s2 = " ; y = 5 variability of a variable! n !1 2 2 2 2 2 2 2 2 2 2 (3 ! 5) + (3 ! 5) + (2 ! 5) + (1 ! 5) + (10 ! 5) + (4 ! 5) + (3 ! 5) + (11 ! 5) + (3 ! 5) + (10 ! 5) !!! VarA = (10 ! 1) 75% quartile 2 2 2 2 2 2 2 2 2 2 (!2) + (!2) + (!3) + (!4) + (5) + (!1) + (!2) + 6 + (!2) + (5) VarA = 9 4 + 4 + 9 +16 + 25 +1+ 4 + 36 + 4 + 25 Median (50% quartile) Var = A 9 128 25% quartile Var = = 14.2 A 9 Whiskers = lowest data point that are not outliers or extreme values. ! Quantitative approaches! Quantitative approaches! Showing differences between and Outliers and extreme values in boxplots! variance graphically with „boxplots“! Outliers != values that are between 1.5 and 3 times !the !

Extreme values != values that are more than 3 times the !interquartile range! Interquartile range != distance between the quartiles!

!In boxplots, outliers and extreme values are represented by circles beyond the whiskers. !