Definition: Statistics, in plural sense, is defined as a set of numerical data and observations.Examples: Vital Statistics, Income, Household Expenses, IQ Scores, Blood Pressure, Anxiety Level, etc.Definition: Statistics, in singular sense, is defined as the branch of science that deals with the collection, presentation, analysis of data and interpretation of results.

Definition: The data are the collection of numbers, facts, and records which are the results of measurements or observations of variables.

Definition: A variable is a trait, attribute, or property of things, person or places that changes in quality, quantity or magnitude. It is also a trait, attribute or property that exhibits differences in quality, quantity or magnitude.

The following shows the relationship between variables and data:

Variables Data Length 2 meters

Weight 4 kilograms Age 6 years old Intelligence IQ of 112 Income $100 per day

• Two Main Divisions of Statistics• Descriptive Statistics – pertains to the

methods dealing with the collection, presentation, and analysis of a set of data without making conclusions, predictions, or inferences about a larger set.

• Goal: To provide a description of a particular data set for which the conclusions or the important characteristics apply only to the data set on hand.

• Inferential Statistics – pertains to the methods of dealing with making inferences, estimations or predictions about a larger set of data using the information gathered from a subset of the larger set.

• Goal: To provide not only a description of a particular data set but also to make prediction and inferences based on the available information gathered.

• Definition: Research may be defined as a purposive, systematic and scientific process of gathering, classifying, organizing, presenting and interpreting data for the solution of a problem, for prediction, for invention, for the discovery of truth, or for the expansion or verification of existing knowledge, all for the preservation and improvement of the quality of human life.

Definition: In research activities, the word population refers to the collection of all cases in which the researcher is interested. In its general sense, this pertains to the totality of objects, animals, persons, materials, happenings, or events under investigation.

Examples: 1. All graduate students of USJ-R.2. All companies manufacturing

motorcycles. 3. All registered voters of a major city.

Definition: A sample refers to a portion or a subset of the population from which the information is gathered.

Remark: A sample must be a representative of the population from which it is taken.

Examples:1. CAS graduate students of the

University of San Jose – Recoletos.

2. Companies manufacturing motocycles that have employees less than 1000.

3. All female registered voters of a major city.

Definition: A parameter is a value, usually a numerical value, that describes a population.

Remark: A parameter may be obtained from a single measurement or it may be derived from a set of measurements from the population

Definition: A statistic is a value, usually a numerical value, that describes a sample.

Remark: A statistic may be obtained from a single measurement, or it may be derived from a set of measurements from the sample.

Examples: Parameters Statistics Population Mean Sample Mean Population Variance Sample Variance Population Standard Sample Deviation Standard Deviation

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

Definition: A constant is a characteristic or condition that does not vary, but is the same for every individual.

The Design of Research Studies

I. The Correlational Method- the simplest way to look for

relationships between variables. - the two variables are observed to see

if there is a significant relationship.- provides no information about cause –

and – effect relationships.

Example 1: Suppose that a researcher wants to examine whether or not a relationship exists between length of time in an executive position and assertiveness. A large sample of executives takes a personality test designed to measure assertiveness. Also, the investigator determines how long each person has served in an executive – level job. Suppose that the investigator found that there is a relationship between the two variables – that the longer a person had an executive position, the more assertive that person tended to be.

Note: Naturally, one might jump to the conclusion that being an executive for a long time makes a person more assertive. But the plausible explanation for the relationship is that assertive people choose to stay or survive longer in executive positions than less – assertive individuals, that is, with the correlational method, it provides no information about cause – and – effect relationships.

Table 1: An example of data from a correlational study examining the relationship between height and weight.

_____________________________________ Subject Height (in cm) Weight (in g) _____________________________________ A 71 180 B 65 148

C 68 151 D 62 128

E 64 125 _____________________________________

II. The Experimental Method - establish a cause – and – effect

relationship between two variables.- the method of observing variables is

intended to show that changes in one variable are caused by changes in the other variable.

- one variable is manipulated while changes are observed in another variable.

Two Variables that are Studied by the Experimental Method

Independent Variable – variable that is manipulated by the researcher.- usually consists of two or more treatment

conditions to which subjects are exposed.- consists of antecedent conditions that were manipulated prior to observing the dependent variable.Dependent Variable – variable that is observed to assess a possible effect of the manipulation

Dependent Variable – variable that is observed to assess a possible effect of the manipulation.- the one that is observed for changes in order to assess the effect of the treatment.

Remark: Often an experiment will include a condition where the subjects do not receive any treatment known as the controlled condition and a condition where the subject do receive the experimental treatment called the experimental condition.

Table 2: An example of data from an experimental study examining the relationship between temperature and eating behavior. The researcher manipulated temperature to create three treatment conditions and then measured eating behavior for a sample of 5 rats in each of the three conditions.

_____________________________________________ Temperature

(Manipulated To Create Three Conditions) 70 Degrees 80 Degrees 90 Degrees _____________________________________________

24 20 17 20 19 19 Eating 18 16 18

Behavior 26 22 14 19 23 20

Definition: A confounding variable is an uncontrolled variable that is unintentionally allowed to vary systematically with the independent variable. It is a treatment condition other than the ones being manipulated or controlled in which the experiment is flawed and the researcher cannot interpret the results as demonstrating cause – and – effect relationship.

Figure 1: In the following experiment, the effect of instructional method (the independent variable) on test performance (the dependent variable) is examined. However, any difference between groups in performance cannot be attributed to the method of instruction. In this experiment, there is a cofounding variable. The instructor teaching the course varies with the independent variable, so that the treatment of the groups differs in more ways than one (instructional method and instructor vary)

Any difference?

ConfoundingVariable

ProfessorSmith

ProfessorJones

IndependentVariable Lecture

SectionLecture

With Lab

DependentVariable

Final Exam Scores

Final ExamScores

III. The Quasi – Experimental Method - concerns research studies that are

almost, but not quite, real experiments.- uses a non-manipulated variable to define

the conditions that are being compared.- the non-manipulated variable is usually a

subject variable (such as male versus female) or a time variable (such as before treatment versus after treatment).

- the non-manipulated variable that defines the conditions is called a quasi- independent variable.

Definition: A subject variable is a characteristic such as age or gender that varies from one subject to another.

Example: A researcher might want to compare communication skills scores for a group of males versus a group of females.

Definition: A time variable simply involves comparing individuals at different points in time.

Example: A researcher may measure depression before therapy and then again after therapy.

Table 3: An example of data from a quasi – experimental study examining the relationship between IQ and attitude toward school. The researcher used IQ to define three groups of students and then measured attitude toward school for the five students in each group.

________________________________________ Intelligence (Used To Create Three Groups) High IQ Medium IQ Low IQ _________________________________________ 78 63 43 74 52 51 81 79 60

76 72 49 91 63 52

Theories and Hypothesis

Definition: A theory - consists of a number of statements about the underlying mechanisms of a certain phenomena / principle.- help organize and unify many observations.

Definition: A hypothesis – a prediction about the relationship between variables.- in the context of an experiment, a hypothesis makes a prediction about how the manipulation of the independent variable will affect the dependent variable.

- in other kinds of research, a hypothesis predicts how a variable will behave under different circumstances or at different points in time.

- a hunch about the result that will be obtained from the study.

Constructs and Operational Definition

Definition: Constructs – are hypothetical concepts that are used in theories to organize observations in terms of underlying mechanisms.- help describe the mechanisms that underlie in

a certain phenomena.

Examples: Intelligence, personality types, motives,etc.

Definition: An operational definition – defines a construct in terms of specific operations or procedures and the measurements that result from them.

Components of an Operational Definition

I. It describes a set of operations or procedures for measuring construct.

II. It defines the construct in terms of the resulting measurements.