quantitative approaches plan statistical basics i types of ... · quantitative approaches! lesson...

Quantitative approaches!

Lesson 7: !Statistical basics I!


Plan!1.  Types of analysis!2.  Types of variables : nominal, ordinal, interval, metric!3. !Measures of central tendency: mode, median, mean!4.  Measures of variability: variance and standard deviation!


Useful resources!

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

http://www.socialresearchmethods.net/


1. Types of analysis!


Types of analysis!!- descriptive or inferential!

!- univariate, bivariate, multivariate!


Descriptive vs. inferential analysis!!"Descriptive analysis is about the data you have in hand. Inferential analysis involves making statements - 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)!


Univariate, bivariate, multivariate!-  univariate : uses 1 variable!

-  bivariate: uses 2 variables!

-  multivariate: uses 3 and more variables!


Univariate, bivariate, multivariate!-  "Univariate analysis involves getting to know data

intimately by examining variables precisely and in detail. Bivariate analysis involves looking at axssociations between pairs of variables and trying to understand how those associations work. Multivariate analysis involves, among other things, understanding the effects of more than one independent variable at a time on a dependent variable."!!(Bernard, 2000: 502)!


Univariate, bivariate, multivariate: how to proceed!

1.  Look at the variables one by one: what is their range, mean, median, variance (is there variance!?), distribution (univariate)!

2.  Inspect associations between pairs of variables. How does the independent variable "influence" the dependent variable? (bivariate)!

3.  Look at the associations of several variables simultaneously. How do two or more independent variables influence a dependent variable at the same time? (multivariate)!


Bivariate analysis: questions to ask!1.  How big/important is the covariation? In other words,

how much better could we predict the score of a dependent variable in our sample if we knew the score of some independent variable? Covariation coefficients answer this question!

2.  Is the covariation statistically significant? Is it due to chance, or is it likely to exist in the overall population to which we want to generalize? Statistical tests answer this question.!

3.  What is it direction? (look at graphs)!4.  What is its shape? Is it linear or non linear? (look at

graphs)!


Multivariate analysis: questions to ask!1.  How is a relationship between two variables changed if a

third variable is controlled? (Multiple crosstabs, partial correlation, 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? (Factor analysis)!

4.  Which individuals tend to be similar concerning selected variables? (Cluster analysis)!


2. Types of variables : "nominal, ordinal, interval, metric!


Variables : nominal, ordinal, interval!Variables : !Nominal !have no inherent order!

! !example: party preference, male-female!

Ordinal !are ordered, but the distances are not !!quantifiable (we cannot add or subtract)!

! !example: agree a lot, agree a bit, disagree a !bit, disagree a lot!

Interval !can be measured numerically; it makes sense to to" !additions or subtraction "

!example : height, weight, income, !number !of cars!


Levels of measurement and covariation: Analysis!

!Depend. !Nominal !Ordinal !Interval!Independ.!

Nominal !Crosstabs ! !ANOVA!!! ! !!!! !!

Ordinal ! ! !!!! !!

Interval ! ! !Correlation !!!! ! ! !Regression!


3. Measures of central tendency: "mode, median, mean!


Definitions : 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!


Example : Size of 11 dwarfs!

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

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

9,7272 Mean

Mode


Example : Size of 11 dwarfs!Mode!

Median!

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

Mean 9.7272


Calculating mean, mode, median!

mean = y =y!

n

mean = y = 5 + 7 + 7 + 7 + 9 + 9 +11+12 +12 +13+1511

mean = y = 10711

= 9.727273

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

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


5. Measures of variability: "variance and standard deviation!


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

!Variance = the sum of the square of the individual departures from the mean divided by the degrees of freedom!

!Standard deviation = the square root of the variance. !


Variance!

mean = y =y!

n

variance = sum of squaresdegrees of freedom

= s2 =(y " y)2!

(n "1)

standard deviation = s =(y " y)2!

(n "1)


Example: Dwarfs in 3 gardens!


Size of dwarfs in 3 gardens!

Quantitative approaches! Quantitative approaches!

Size of dwarfs in 3 gardens!

A B C 3 5 3 4 5 3 4 6 2 3 7 1 2 4 10 3 4 4 1 3 3 3 5 11 !!5 !6!3!!!2 !5!10!

Garden

mean(A) = yA = 3

mean(B) = yB = 5

mean(C) = yC = 5

var(A) = sA2 = 1.3

var(B) = sB2 = 1.3

var(C) = sC2 = 14.2


Computing variance of dwarfs in garden C!

Var = s2 =(y ! y)"n !1

; y = 5

VarA =(3 ! 5)

2+ (3 ! 5)

2+ (2 ! 5)

2+ (1 ! 5)

2+ (10 ! 5)

2+ (4 ! 5)

2+ (3 ! 5)

2+ (11 ! 5)

2+ (3 ! 5)

2+ (10 ! 5)

2

(10 ! 1)

VarA =(!2)2

+ (!2)2+ (!3)2

+ (!4)2+ (5)2

+ (!1)2+ (!2)2

+ 62+ (!2)2

+ (5)2

9

VarA =4 + 4 + 9 +16 + 25 +1+ 4 + 36 + 4 + 25

9

VarA =128

9= 14.2


!!!

Boxplot = graphical summary of the variability of a variable!

75% quartile

Median (50% quartile)

Whiskers = lowest data point that are not outliers or extreme values. !

Boxplots!

25% quartile


Outliers != values that are between 1.5 and 3 times !the interquartile range!

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. !

Outliers and extreme values in boxplots!


Showing differences between means and variance graphically with „boxplots“!

quantitative approaches plan statistical basics i types of ... · quantitative approaches! lesson...

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