This document provides an overview of key concepts in psychological statistics. It defines statistics as procedures for organizing, summarizing, and interpreting information using facts and figures. It discusses populations and samples, variables and data, parameters and statistics, descriptive and inferential statistics, sampling error, and experimental and nonexperimental methods. It also covers scales of measurement, frequency distributions, measures of central tendency and variability, and the importance of measurement in research.

1. PSYCHOLOGICAL
STATISTICS
Presented by:
Mary Anne Portuguez, MP, RPm

2. Statistics
• Refers to a set of mathematical procedures for
organizing, summarizing, and interpreting
information.
• Consists of facts and figures such as average
income, crime rate, birth rate, average
snowfall, and so on.

3. Population and Samples
• Population, is the set
of all the individuals of
interest in a particular
study.
• Sample, is a set of
individual selected
from a population,
usually intended to
represent the
population in a
research study.

4. Variables and Data
• A variable is a characteristic or condition that
changes or has different values for different
individuals.
• Data, measurements or observations.

5. Parameter and Statistic
• Parameter is usually a numerical value that
describes a population.
• Statistic is usually a numerical value that
describes a sample.

6. Descriptive Statistics and Inferential
Statistics
• Descriptive statistics are statistical procedures
used to summarize, organize, and simplify
data.
• Inferential Statistics consist of techniques that
allows us to study samples and then make
generalizations about the populations from
which they were selected.

7. Sampling Error
• It is the discrepancy, or amount of error, that
exists between a sample statistic and the
corresponding population parameter.

8. Sample Figure
POPULATION OF 1000 COLLEGE STUDENTS
POPULATION PARAMETERS:
AVERAGE AGE= 21.3 YEARS
AVERAGE IQ= 112.5
65% FEMALE, 35% MALE
Sample #1
Eric, Jessica, Juan, Neri,
Karen
Sample Statistics:
Average Age= 19.8
Average IQ= 104.6
60% Female, 40% Male
Sample #2
Tom, Edward, Peter,
Mary, Ellla
Sampling Statistics:
Average Age= 20.4
Average IQ= 114.2
40% Female, 60% Male

9. Example: Study on Teaching Method
POPULATION OF FIRST-
GRADE STUDENTS
73,76,72,80,73,77,75,77,
75,74,77,77,72,75,76,76,
74,79,77,78,78,81
A
68,67,75,72,76,69,70,72,
68,74,73,73,70,70,69,70,
71,71,71,72,70
B
Data: Test scores for students
in each sample
STEP 1

10. Step 2:
Descriptive Statistics: Organize and Simplify.
Step 3:
Inferential Statistics: Interpret the results.

11. Sample Inference:
1. There actually is no difference between the two
teaching methods, and the sample difference is
due to chance.
2. There is a difference between the two methods,
and the sample data accurately reflect this
difference.
Note: The goal of inferential statistics is to help
researchers decide between the two
interpretations.

12. Relationship Between Variables
• Correlational Method, two different variables
ae observed to determine whether there is a
relationship between them.
• Sometimes correlational method are not
numerical values. Ex. A researcher could
measure home location (city or suburb) and
attitude toward a new budget proposal (for or
against) for a group of registered voters.

13. Comparing Two (or more) Groups of Scores:
Experimental and Nonexperimental
The Experimental method
Manipulation. The researcher manipulates one
variable by changing its value from one level to
another. A second variable is observed (measured) to
determine whether the manipulation causes changes
to occur.
Control. The researcher must exercise control over
the research situation to ensure that other,
extraneous variables do not influence the
relationship being examined.

14. Controlling Variables:
• Random assignment, each participant has an
equal chance of being assigned to each of the
treatment conditions.
• Matching design, to ensure equivalent groups
or equivalent environment.

15. Nonexperimental and Prepost Studies
• Nonequivalent groups, study comparing boys
and girls.The researcher has no ability to
control which participants go into which
group.
• Pre-post design, the two scores are obtained
by measuring the the same variable twice
under two different conditions at two
different times.

16. Example
BOYS GIRLS
17 15
19 15
12 14
Before
Therapy
After Therapy
17 12
19 10
16 14
Nonequivalent Design Pre-post Design
Looking for difference?

17. DISCRETE AND CONTINUOUS
VARIABLES
• A discrete variable consists of separate,
indivisible categories. No values can exist
between two neighboring categories. Ex.
Gender, Nationality, Occupation
• Continuous variable, there are an infinite
number of possible values that fall between
any two observed values. A continuous
variable is divisible into an infinite number of
fractional parts. Ex. Weight, Height

18. • Data collection requires that we make
measurements of our observations.
Measurement involves assigning individuals or
events to categories.
• The categories can simply be names such as
male/female or employed/unemployed, or they
can be numerical values such as 68 inches or 175
pounds. The categories used to measure a
variable make up a scale of measurement, and
the relationships between the categories
determine different types of scales.

19. Properties of Scales
• Magnitude is the property of “moreness.” A scale
has the property of magnitude if we can say that
a particular instance of the attribute represents
more, less, or equal amounts of the given
quantity than does another instance.
• Equal intervals. the difference between two
points at any place on the scale has the same
meaning as the difference between two other
points that differ by the same number of scale
units.
• Absolute 0 is obtained when nothing of the
property being measured exists.

20. Scales of Measurement
• A nominal scale consists of a set of categories that have
different names. Measurements on a nominal scale label and
categorize observations, but do not make any quantitative
distinctions between observations.
• An ordinal scale consists of a set of categories that are
organized in an ordered sequence. Measurements on an
ordinal scale rank observations in terms of size or
magnitude.
• Both an interval scale and a ratio scale consist of a series
of ordered categories (like an ordinal scale) with the
additional requirement that the categories form a series of
intervals that are all exactly the same size. Thus, the scale
of measurement consists of a series of equal intervals,
such as inches on a ruler.

21. Interval vs. Ratio
• Interval scale has an arbitrary zero point. the value 0
is assigned to a particular location on the scale
simply as a matter of convenience or reference. In
particular, a value of zero does not indicate a total
absence of the variable being measured.
• Ratio scale is anchored by a zero point that is not
arbitrary but rather is a meaningful value
representing none (a complete absence) of the
variable being measured.

22. Summary

23. Frequency Distribution
• It displays scores on a variable or a measure to
reflect how frequently each value was obtained.
• replace simple ranks when we want to adjust for
the number of scores in a group. It answers the
question, “What percent of the scores fall below
a particular score (Xi)?”
• specific scores or points within a distribution.
Percentile Ranks
Percentile

24. Difference in Percentile Rank and
Percentile

25. Central Tendency
• is a statistical measure to determine a single
score that defines the center of a distribution.
The goal of central tendency is to find the
single score that is most typical or most
representative of the entire group.

26. • The mean, also known as the arithmetic
average, is computed by adding all the scores
in the distribution and dividing by the number
of scores. The mean for a population is
identified by the Greek letter mu,
(pronounced “mew”), and the mean for a
sample is identified by M or X (read “x-bar”).

27. If the scores in a distribution are listed in order
from smallest to largest, the median is the
midpoint of the list. More specifically, the
median is the point on the measurement scale
below which 50% of the scores in the distribution
are located.
• The median, on the other hand, defines the
middle of the distribution in terms of
• scores. In particular, the median is located so that
half of the scores are on one side and
• half are on the other side.

28. Mode is the score or category that has the
greatest frequency.
“the customary fashion” or “a popular style.”

29. Variability
• It provides a quantitative measure of the
degree to which scores in a distribution are
spread out or clustered.
• Defined in terms of distance.
• It measures how well an individual represents
the entire distribution.

30. Measures of Variability
• Range, is knowing the highest and lowest.
Getting the largest score to the smallest score
in a distribution.
• Standard Deviation, it is the most commonly
used and the most important measure of
variability. It uses the mean of the distribution
as a reference point and measures variability by
considering the distance between each score
and the mean.

31. Measures of Variability
• Variance, the average squared distance from
the mean.

32. Measurement
The act or process of assigning numbers to
phenomena according to a rule.
Benefits
1. Objectivity. Allows theories to be tested.
2. Quantification. Allows more detail than
personal judgment.
3. Better communication.