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Types of Statistics
• 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
Descriptive 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?
p.396 Sekaran
(Economist article)
Descriptive Statistics
• 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
p.397 Sekaran
Descriptive Statistics
• 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
Types of Variables
• Categorical
• Nominal; Ordinal
• Can compute frequencies & mode for nominal
• For ordinal variables, carefully interpret
descriptive statistics
• Continuous
• Interval; Ratio
• Can compute descriptive statistics
Copyright © 2003 John Wiley & Sons, Inc. Sekaran/RESEARCH 4E
MOD. A
Types of Inferential Statistics
• 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)
p.394 Sekaran
Key Assumptions
• 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
Inferential Statistics
Statistical techniques used for different types of variables
Type of Independent Variable
Continuous Categorical
Type of
Dependent
Variable
Continuous Correlation
(2 var),
Regression
T-test (2 groups); ANOVA
Categorical
Chi-square, Phi, Kappa,
Spearman rank correlation
See also p. 405 Sekaran
Tests of Mean Differences
• 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 Association
• 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
250
r = .76; r2 = 58%
Vince Carter
Weight (pounds)
210
170
Tom Cruise
130
Julia Roberts
90
150
Calista Flockhart
160
170
180
Height (cm)
190
200
For Male Celebrities: r = .27; r2 = 7%
250
Weight (pounds)
210
170
130
90
150
160
170
180
Height (cm)
190
200
250
For Female Celebrities: r = .78; r2 =61 %
Weight (pounds)
210
170
130
90
150
160
170
180
Height (cm)
190
200
Tests of Association
• 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?
405-407 Sekaran
Difference between r & ß
r
predictor
criterion
ß
criterion
predictor
control
Difference between R & R2
unique
R2
explained
control
criterion
predictor
R2 not explained
control
R2 =R
R=multiple correlation
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