Statistics for Psychology

1. REVIEW OF
STATISTICS

2. WHAT IS STATISTICS?
• The science of data gathering and treatment.
• Collection of data
• Data Analysis
• Interpretation of Data
• Inferring the Sample Data to a Population

3. SCALES OF
MEASUREMENT
• Measurement
• Act of assigning numbers or symbols to characteristics
of things
• Can be categorized as discrete or continuous
• Error
• Always involved
• Collective influence of factors on a test score or
measurement beyond what is specifically measured

4. SCALES OF
MEASUREMENT
• Nominal
• Catregorization/distinction
• Ordinal
• Classification
• Rank-ordering
• Interval
• Equal intervals
• Exactly equal to any other unit
• Ratio
• Has an absolute zero point

5. FREQUENCY
DISTRIBUTION
• Distribution
• Set of test scores arrayed for recording/study
• Raw Score
• Straightforward, unmodified number
• Frequency Distribution
• List of scores along with the number of times a score has
occurred
• Can be listed on intervals (grouped)

6. PERCENTILES
• Replaces simple ranks when trying to adjust for the
score in a group
• “What percent of scores fall below a particular score?”
• Divides the total frequency for a set of observations
into hundredths

7. MEASURES OF CENTRAL
TENDENCY
• “The middlemost score/s in a distribution”
• Mean
• average
• Median
• Middle score in a distribution
• 50th Percentile
• Mode
• Frequently occurring score

8. MEASURES OF
VARIABILITY
• “the average distance between scores”
• Range
• Difference between highest and lowest score
• Interquartile Range
• Difference between the third and first quartile
• Semi-Quartile Range
• Interquartile range divided by 2
• Variance
• Square of deviation scores
• Standard Deviation
• Square root of variance

9. SKEWNESS
• “Absence of symmetry”
• Positive Skew: relatively few scores falls on the high end;
• Q3 – Q2 > Q2 – Q1
• Negative Skew: relatively few scores falls on the low end
• Q3 – Q2 < Q2 – Q1

10. KURTOSIS
• Steepness of a distribution to the center

11. NORMAL CURVE
• Began in the mid-18th
Century in the work
of Abraham
DeMoivre and
Marquis de LaPlace
• Karl Pearson termed
it as the normal curve
• Bell-shaped
• Smooth
• Asymptotic
• Ranges from
negative infinity to
positive infinity

12. STANDARD SCORES
• Raw scores converted from one scale to another, where the
other score has arbitrarily set mean and standard deviation
• Z-scores: difference between the raw score and a mean divided
by the standard deviation
• T-scores: mean is set at 50 and std. deviation is set at 10
• Sten: standard ten; mean is set at 5.5 and std. deviation is set at
2; used in SAT and GRE
• Stanine: used by US Airforce; mean is set at 5 and std. deviation
is set at 2; no decimals
• A Scores: mean is set at 500 and std. deviation is set at 100
• IQ Scores: mean is set a5 100 and std. deviation is set at 15;
used for IQ score interpretation

13. STANDARD SCORES

14. CORRELATION
• Expression of the degree
and direction of
correspondence between
variables
• Runs from -1 to +1
• Graph is demonstrated in a
scatterplot

15. Correlation Coefficients When to use?
Pearson’s r 2 set of scores from the same
respondents in interval-ratio level of
measurement
Spearman’s rho 2 sets of scores from the same
respondents with a sample size less
than 30 and in an ordinal level of
measurement
Kendall’s tau 2 sets of ordinal data from
participants either less than or more
than 30 in an ordinal level of
measurement
Kendall’s W More than two sets of ranking in
ordinal level and the rankings come
from several raters
Phi-Coefficient 2 or more sets of frequencies;
nominal in nature
Point Biserial Only 2 dichotomous variables
Multiple correlation 3 or more sets of Pearson

16. REGRESSION
• A method used to make
predictions about scores on
one variable from
knowledge of scores on
another variable
• Y = bX + a
• b = slope
• a = y-intercept

17. REGRESSION
• For any variable, the mean is the point of least squares
• Residual: the difference between Y and the predicted
value of Y; the best-fitting line keeps this to a minimum
• Standard Error of Estimate: measures the accuracy of
prediction; standard deviation of the residuals
• Coefficient of Determination: total variation in scores;
squared value of r
• Coefficient of Alienation: measure of non-association
between variables.

18. MULTIPLE REGRESSION
• Find linear combination of three variables
• Transform all variables into single units
• Two predictor variables that are highly correlated with the
criterion will not both have large regression coefficients if
they are highly correlated with each other as well.

19. DISCRIMINANT
ANALYSIS
• Used to determine the linear combination of
variables that provide maximum discrimination
between categories
• Determine whether a group of variables predict
success or failure

20. FACTOR ANALYSIS
• Study interrelationships among set of variables
without reference to criterion