1 introduction to psychological statistics

PSYCHOLOGICAL STATISTICS

Presented by:Mary Anne Portuguez, MP, RPm

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.

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.

Variables and Data

• A variable is a characteristic or condition that changes or has different values for different individuals.

• Data, measurements or observations.

Parameter and Statistic

• Parameter is usually a numerical value that describes a population.

• Statistic is usually a numerical value that describes a sample.

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.

Sampling Error

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

Sample FigurePOPULATION OF 1000 COLLEGE STUDENTS

POPULATION PARAMETERS:AVERAGE AGE= 21.3 YEARSAVERAGE IQ= 112.565% FEMALE, 35% MALE

Sample #1Eric, Jessica, Juan, Neri,

Karen

Sample Statistics:Average Age= 19.8Average IQ= 104.6

60% Female, 40% Male

Sample #2Tom, Edward, Peter,

Mary, Ellla

Sampling Statistics:Average Age= 20.4Average IQ= 114.2

40% Female, 60% Male

Example: Study on Teaching MethodPOPULATION 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

Step 2:

Descriptive Statistics: Organize and Simplify.

Step 3:

Inferential Statistics: Interpret the results.

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.

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.

Comparing Two (or more) Groups of Scores: Experimental and Nonexperimental

The Experimental methodManipulation. 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.

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.

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.

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?

DISCRETE AND CONTINUOUSVARIABLES

• 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

• 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.

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.

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.

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.

Summary

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

Difference in Percentile Rank and Percentile

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.

• 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”).

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.

Mode is the score or category that has the greatest frequency.

“the customary fashion” or “a popular style.”

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.

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.

Measures of Variability

• Variance, the average squared distance from the mean.

MeasurementThe act or process of assigning numbers to phenomena according to a rule.

Benefits1. Objectivity. Allows theories to be tested.2. Quantification. Allows more detail than

personal judgment.3. Better communication.