Correlation Research

&Inferential Statisticsby

Atheer L. Khamoo & Wissam A. Askar

Table of Content• Definition• Purpose • Independent and dependent variables • Scatter plot• Correlation coefficient• Range of correlational coefficient• Types of correlational study

Correlational research

A correlational is the measurement of the relationship between two variables.

Correlation is a statistical technique that can show whether and how strongly pairs of variables are related.

The Goal of Correlational Research

The goal of correlational research is to find out whether one or more variables can predict other variables. Correlational research allows us to find out what variables may be related. However, the fact that two things are related or correlated does not mean there is a causal relationship. It is important to make a distinction between correlation and causation. Two things can be correlated without there being a causal relationship

Independent and Dependent Variables

• Independent variable: is a variable that can be controlled or manipulated.

• Dependent variable: is a variable that cannot be controlled or manipulated. Its values are predicted from the independent variable

Example

• Independent variable in this example is the number of hours studied.

• The grade the student receives is a dependent variable.

• The grade student receives depend upon the number of hours he or she will study.

Student Hours studied

% Grade

A 6 82

B 2 63

C 1 57

D 5 88

E 3 68

F 2 75

Definition of 'Pearson Coefficient'

• A type of correlation coefficient that represents the relationship between two variables that are measured on the same interval or ratio scale.

Pearson Correlation Coefficient

• A number between –1.0 and +1.0 describes the relationship between 2 variables:

• direction (+ positive or – negative)

• strength (from 0 to ±1)• r = +1.0 a very strong positive relationship• r = –1.0 a very strong negative relationship• r = 0 there is no relationship

Types of correlations

• A positive relationship exists when both variables increase or decrease at the same time. (Weight and height).

• A negative relationship exist when one variable increases and the other variable decreases or vice versa. (Strength and age).

• No Correlation indicates no relationship between the two variables. A correlation coefficient of 0 indicates no correlation

Scatter Plot• The independent and dependent can be

plotted on a graph called a scatter plot.• By convention, the independent variable is

plotted on the horizontal x-axis. • The dependent variable is plotted on the

vertical y-axis.

Plotting correlations

• each data point on the scatter plot indicates the score on both variables

• GPA and Study hours per week• 3.0 18• 2.4 14• 1.8 10• 2.7 11• 4 data points, one for each

student

Y-axis

18161410 1.0 2.0 3.0 4.0 x-axis

Range of correlation coefficient• In case of exact positive

linear relationship the value of r is +1.

• In case of a strong positive linear relationship, the value of r will be close to + 1.

Range of correlation coefficient• In case of exact negative

linear relationship the value of r is –1.

• In case of a strong negative linear relationship, the value of r will be close to – 1.

Range of correlation coefficient

In case of nonlinear relationship the value of r will be close to 0.

Types of Correlational Studies: 1. The Survey Method

• Survey and questionnaires are one of the most common methods used in educational research. In this method, a random sample of participants completes a survey, test, or questionnaire that relates to the variables of interest.

• Random sampling is a vital part of ensuring the generalizability of the survey results.

Advantages of the survey method

• It’s fast, cheap, and easy. Researchers can collect large amount of data in a relatively short amount of time.

• More flexible than some other methods

Disadvantages of the Survey Method:

• Can be affected by an unrepresentative sample or poor survey questions.

• Participants can affect the outcome. Some participants try to please the researcher, lie to make themselves look better, or have mistaken memories.

2. Archival Research• Archival research is the study of existing data.

The existing data is collected to answer research questions. Existing data sources may include statistical records, survey archives, and written records.

Advantages of Archival Research:

• The experimenter cannot introduce changes in participant behavior.

• Enormous amounts of data provide a better view of trends, relationships, and outcomes.

• Often less expensive than other study methods. Researchers can often access data through free archives or records databases.

Disadvantages of Archival Research:

• The researchers have not control over how data was collected.

• Important date may be missing from the records.

Inferential Statistics

Inferential Statistics

• One use of statistics is to be able to make inferences or judgments about a larger population based on the data collected from a small sample drawn from the population

• Statistical inference is a procedure by means of which you estimate parameters (characteristics of population) from statistics (characteristics of samples).

Population

Sample

Rationale of sampling• The inductive method involves making

observations and then drawing conclusions from these observation.

• Samples must be representative if you are to be able to generalize with reasonable confidence from the sample to the population.

• An unrepresentative sample is termed a biased sample

Steps in sampling1. Probability sampling It involves sample selection in which the

elements are drown by chance procedures.2. Nonprobability sampling It includes methods of selection in which

elements are not chosen by chance procedure.

The types of probability sampling

1. Simple random sampling2. Stratified sampling 3. Cluster sampling4. Systematic sampling

1. Simple random sampling

It comprise the following steps:

1. Define the population2. List all members of the population3. Select the sample by employing a procedure

where sheer chance determines which members on the list are drawn for the sample.

2. Stratified sampling

Population consists of a number of subgroups, or strata, that may differ in the characteristics being studied.

3. Cluster sampling

• With cluster sampling, the researcher divides the population into separate groups, called clusters. Then, a simple random sample of clusters is selected from the population.

4. Systematic sampling

A common way of selecting members for a sample population using systematic sampling is simply to divide the total number of units in the general population by the desired number of units for the sample population.

For example, if you wanted to select a random group of 1,000 people from a population of 50,000 using systematic sampling, you would simply select every 50th person, since 50,000/1,000 = 50.

Non probability sampling

1- Convenience sampling, It is a sampling method in which units are selected based on easy access/availability. which is regarded as the weakest of all sampling procedures, involves using available cases for study.2- Purposive sampling a type of nonprobability sampling in which the researcher consciously selects specific elements or subjects for inclusion in a study in order to ensure that the elements will have certain characteristics relevant to the study. 3- Quota Sampling involves selecting typical cases from diverse strata of a population. The quotas are based on known characteristics ( age, gender, social class, etc.,) of the population to which you wish to generalize.

Random Assignment

• When the primary goal of a study is to compares the outcomes of two treatments with the same dependent variable, random assignments is used. Here a chance procedure such as a table of random numbers is used to divide the available subjects into groups.

• Then a chance procedure such as tossing a coin is use to decide which group gets which treatments.

The size of the sample

How large should a sample be? • A larger sample is more likely to be a good representative

of the population than a smaller sample. However, the most important characteristic of a sample is its representativeness, not its size.

• A random sample of 200 is better than a random sample of 100, but a random sample of 100 is better than biased sample of 2500000.

The concept of sampling error

• The researcher has observed only a sample and not the entire population.

• Sampling error is “the difference between a population parameter and a sample statistic”.

Hypothesis Testing

A statistical hypothesis is an assumption about a population parameter. This assumption may or may not be true. Hypothesis testing refers to the formal procedures used by statisticians to accept or reject statistical hypotheses.

There are two types of statistical hypotheses.

• Null hypothesis. The null hypothesis, denoted by H0, is

usually the hypothesis that sample observations result purely from chance.

The null always says there is no relationship or difference.

H0 (null) is that mean1=mean2, meaning the mean scores are equal OR the difference between the mean scores is zero .

• Alternative hypothesis ( Hi )

• It means, there is a difference between two groups or there is a statistically significant difference of population.

• Types of alternative hypothesis.

- Non-directional - Directional

Example:Ho :- There is no statistically significant differs between teachers based on their gender in their attitude towards first language used of EFL classroom.

Hi :- There is a statistically significant differs between teachers based on their gender in their attitude towards first language used of EFL classroom. _ Non-directional; because they didn’t mention which one use more/less according to ( male/female)._ Directional; female teachers have more positive attitude than male towards use of first language in EFL in classroom.

Two types of errors can result from a hypothesis test.

• Type I error. A Type I error occurs when the researcher rejects a null hypothesis when it is true. This probability is also called alpha, and is often denoted by α.

• Type II error. A Type II error occurs when the researcher fails to reject a null hypothesis that is false. The probability of committing a Type II error is called Beta, and is often denoted by β.

• Type I _ reject true null ; Type II _ accept a false

State level of significance

• Level of significance = risk of rejecting a TRUE Hypothesis

• Determine the probability of getting the sample results by chance if the null is true.

• Small probability (p<.05) means reject null; there is a significant difference.

• Large probability ( p>.05) means do not reject; there is no significant difference.

Degrees of Freedom

• The number of degrees of freedom ( df ) is the number of observations free to vary around a constant parameter. To illustrate the general concept of degrees of freedom.

ReferencesAnderson, A. (1990). Fundamentals of educational research. USA: The falmer.

Ary, D. & et al., (2006). Introduction to research in education .(7th ed.). USA: Thomson.

Best, J. W. & Kahn, J. V. (2006). Research in education.(10th ed.) : USA: Pearson.

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