Sample • Usually populations are so large that a researcher cannot examine the entire group. Therefore, a sample is selected to represent the population

population- all of the individuals of interest

Sample- individuals selected to participate in the research study

Variables can be classified as discrete or

continuous.

• Discrete variables(such as class size)

consist of indivisible categories, and

continuous variables(such as time or

weight) are infinitely divisible into whatever

units a researcher may choose. For

example, time can be measured to the

nearest minute, second, half-second, etc.

Real Limits

• To define the units for a continuous

variable, a researcher must use real limits

which are boundaries located exactly half-

way between adjacent categories.

Measuring Variables

• To establish relationships between

variables, researchers must observe the

variables and record their observations.

This requires that the variables be

measured.

• The process of measuring a variable

requires a set of categories called a scale

of measurement and a process that

classifies each individual into one

category.

4 Types of Measurement Scales

1. A nominal scaleis an unordered set of

categories identified only by name.

Nominal measurements only permit you

to determine whether two individuals are

the same or different.

2. An ordinal scaleis an ordered set of

categories. Ordinal measurements tell

you the direction of difference between

two individuals.

4 Types of Measurement Scales

3. An interval scaleis an ordered series of equal-

sized categories. Interval measurements

identify the direction and magnitude of a

difference. The zero point is located arbitrarily

on an interval scale.

4. A ratio scaleis an interval scale where a value

of zero indicates none of the variable. Ratio

measurements identify the direction and

magnitude of differences and allow ratio

comparisons of measurements.

Correlational Studies

• The goal of a correlational study is to

determine whether there is a relationship

between two variables and to describe the

relationship.

• A correlational study simply observes the

two variables as they exist naturally.

Experiments

• The goal of an experiment is to

demonstrate a cause-and-effect

relationship between two variables; that is,

to show that changing the value of one

variable causes changes to occur in a

second variable.

Experiments (cont.)

• In an experiment, one variable is manipulated

to create treatment conditions. A second

variable is observed and measured to obtain

scores for a group of individuals in each of the

treatment conditions. The measurements are

then compared to see if there are differences

between treatment conditions. All other

variables are controlled to prevent them from

influencing the results.

• In an experiment, the manipulated variable is

called the independent variable and the

observed variable is the dependent variable.

Other Types of Studies

• Other types of research studies, know as

non-experimental or quasi-

experimental, are similar to experiments

because they also compare groups of

scores.

• These studies do not use a manipulated

variable to differentiate the groups.

Instead, the variable that differentiates the

groups is usually a pre-existing participant

variable (such as male/female) or a time

variable (such as before/after).

Other Types of Studies (cont.)

• Because these studies do not use the

manipulation and control of true

experiments, they cannot demonstrate

cause and effect relationships. As a

result, they are similar to correlational

research because they simply

demonstrate and describe relationships

Data

• The measurements obtained in a research

study are called the data.

• The goal of statistics is to help researchers

organize and interpret the data.

Descriptive Statistics

• Descriptive statistics are methods for

organizing and summarizing data.

• For example, tables or graphs are used to

organize data, and descriptive values such

as the average score are used to

summarize data.

• A descriptive value for a population is

called a parameter and a descriptive

value for a sample is called a statistic.

Inferential Statistics

• Inferential statistics are methods for using

sample data to make general conclusions

(inferences) about populations.

• Because a sample is typically only a part of the

whole population, sample data provide only

limited information about the population. As a

result, sample statistics are generally imperfect

representatives of the corresponding population

parameters.

Sampling Error

• The discrepancy between a sample

statistic and its population parameter is

called sampling error.

• Defining and measuring sampling error is

a large part of inferential statistics.

Notation

• The individual measurements or scores obtained

for a research participant will be identified by the

letter X (or X and Y if there are multiple scores

for each individual).

• The number of scores in a data set will be

identified by N for a population or n for a sample.

• Summing a set of values is a common operation

in statistics and has its own notation. The Greek

letter sigma, Σ, will be used to stand for "the sum

of." For example, ΣX identifies the sum of the

scores.

Order of Operations

1. All calculations within parentheses are done

first.

2. Squaring or raising to other exponents is done

second.

3. Multiplying, and dividing are done third, and

should be completed in order from left to right.

4. Summation with the Σ notation is done next.

5. Any additional adding and subtracting is done

last and should be completed in order from left

to right.