• Descriptive Statistics• e.g.,frequencies, percentiles, mean, median, mode,

ranges, inter-quartile ranges, sds, Zs• Describe data

• Inferential Statistics• e.g., t, ANOVA (F), correlations (r), regression

weights (ß); variance explained (R2)• Allow for inferences about population to be drawn

from sample data

Types of Statistics

• Frequencies, percentiles• Central Tendency

• Mean• Sum of all observations divided by total number of

observations

• Median• After arraying all observations in ascending/descending

order, the obs that divides the sample into two • For even number of observations take avg of 2 central obs

• Mode• Most frequently occurring observation

• When would one use means vs. medians? (Economist article)

Descriptive Statistics

p.396 Sekaran

• Variability• Range

• Difference between the two most extreme observations

• Inter-quartile range• Divide observations into quarters & use the middle half

• Standard Deviation• Take each observation’s difference from the mean,

square it, add all such squared differences, and divide the result by number of observations

• Variance• Square of standard deviation

Descriptive Statistics

p.397 Sekaran

• Variability (cont’d)• Confidence intervals

• The range of values in which the mean occurs 95% of the time

• Typically includes scores that are two standard errors above or below statistic

» Standard error: Type of standard deviation (for more see p. 287 Sekaran)

• Standard scores (Zs)• Deviation from the mean divided by standard deviation

• Mean of all Zs =0, sd=1

• Useful for computing interaction scores in regression analyses

Descriptive Statistics

• Categorical• Nominal; Ordinal• Can compute frequencies & mode for nominal• For ordinal variables, carefully interpret

descriptive statistics

• Continuous• Interval; Ratio• Can compute descriptive statistics

Types of Variables

MOD. ACopyright © 2003 John Wiley & Sons, Inc. Sekaran/RESEARCH 4E

• Parametric vs. non-parametric statistics• Non-parametric does not assume normal

distribution of data• T-test• ANOVA (F)• Correlations (r)

• Types of

• Multiple-regression (R)• Regression weights (ß); Variance explained (R2)

Types of Inferential Statistics

p.394 Sekaran

• Behavioral research explains individual differences in psychological variables• Good measures of psychological variables capture

individual differences

• Individual differences in psychological variables are normally distributed• Some psychological variables can be ‘transformed’

to be normally distributed

• Variables with normal distributions have interval properties & allow for computation of commonly used inferential statistics

Key Assumptions

Inferential Statistics

Statistical techniques used for different types of variables Type of Independent Variable Continuous Categorical

Continuous

Correlation (2 var), Regression

T-test (2 groups); ANOVA

Type of Dependent Variable

Categorical Chi-square, Phi, Kappa, Spearman rank correlation

See also p. 405 Sekaran

• T-test• Compares whether means of two groups are

different from each other 95% of the time• Compares differences on one independent variable• Paired t-test= Same group, two different times or

measurements• Can be used as a post-hoc or planned contrast

after conducting ANOVA analyses• Beware the number of t-tests done reduces confidence

level so use Scheffe’s, Duncan multiple range etc.

Tests of Mean Differences

• ANOVA (F-test)• Compares whether means of three or more groups

are different from each other 95% of the time• Compares two or more independent variables

• Tests interaction effects: Does the effect of one IV depend on the level of the other IV?

• Repeated measures ANOVA: Same sample, multiple times/measurements

• Sparingly conduct T-test to see if pairs of groups are significantly different from each other

Tests of Mean Differences

• Correlation coefficient (r) • Assesses whether 2 variables are ‘linearly’ related

to each other 95% of the time

• Reflects the direction and the strength of the relation

• Varies from –1 to +1.

• Better measure of the strength of a relation is the amount of explained variance (r2)

• Ranges from 0 to 100

• Difference between r=.3 & r=.4 is not the same as difference between r=.7 & r=.8

Tests of Association

• Types of Correlations• When both variables are continuous: Pearson

product-moment • When both variables are nominal (categorical)

• Two categories for each variable: Phi

• Multiple categories for each variable: Kappa

• When both variables are ordinal: Spearman rank

• Significance of r = t-test

Tests of Association

90

130

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Height (cm)

Wei

ght

(pou

nds)

Tom Cruise

Vince Carter

Calista Flockhart

Julia Roberts

r = .76; r2 = 58%

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130

170

210

250

150 160 170 180 190 200

Height (cm)

Wei

ght

(pou

nds)

For Male Celebrities: r = .27; r2 = 7%

90

130

170

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150 160 170 180 190 200

Height (cm)

Wei

ght

(pou

nds)

For Female Celebrities: r = .78; r2 =61 %

• Multiple correlation (R) • Describe relation between 3 or more variables

(e.g., 2 predictors and one criterion)• Two different formulae depending on whether or

not predictors are correlated with each other• Tests non-linear relationships

• Significance of R =F-test• Are variables related to each other 95% of the

time?

Tests of Association

405-407 Sekaran

Difference between r & ß

r

ßpredictor

criterion

predictor

criterion

control

Difference between R & R2

criterion

control

R2 not explained

control

predictor

R2 =RR=multiple correlation

unique R2 explained

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