day 9 hypothesis and correlation for students

Thursday, December 4, 20141

Select a

General

Problem

Conduct

Literature

Review

Exhaustive

Review

Preliminary Search later

Expanded

Select Specific

Research Problem Question or hypothesis

Decide Design

And Methodology

Collect Data

Analyzes and

Present Data

Interpret

Findings

Statistical

Tables

Integrative

Diagrams

State Conclusion/

Generalization about Problem


Hypothesis is a prediction about the outcome of the study.

After the hypothesis is proposed, a study is designed to test that hypothesis.

The data collected in the study enable the researchers to decide whether the hypothesis is supported.

Hypothesis should be clearly and concisely stated and be testable.

For example,In a study of middle school students, their attitudes toward school are assessed using questionnaire and their school performance is measured using their GPA (Grade Point Average). One hypothesis in this study may predict that “the girls’ mean score on the questionnaire would be significantly higher than the boys’ mean score”, while another hypothesis may predict “ there is a positive correlation between students’ scores on the questionnaire and their GPA”.

1. The alternative hypothesis (HA or H1)2. The null hypothesis (Ho) HA or H1 predicts that there will be some

relationship between variables or difference between means or groups.

Example:“ There will be a positive correlation between students;

reading fluency and their reading comprehension scores.” or “ Students in classes where the teachers use differentiated instruction will score significantly higher on the end-of-year spelling test compared with students in similar classes where teachers do not use differentiated instruction.”

Ho. Predicts that “ There will be no positive correlation between

students’ reading fluency and their reading comprehension scores.” or “ Students in classes where the teachers use differentiated instruction will not score significantly higher on the end-of-year spelling test compared with students in similar classes where teachers do not use differentiated instruction.”

For example:We will conduct an experimental study to test the null hypothesis. This study would be conducted to test the effect of starting the school day half an hour later on students’ achievement test scores. In one junior high school in the district, the students would continue with the same schedule as in the past years. The null hypothesis in this study states that “there would be no difference in the mean scores on an achievement test between the students in the two junior high schools who start school at different times.”

Another example:The null hypothesis states that “ there would be no significant correlation between IQ and depression score in college students.”

This hypothesis would be tested using a random sample of two hundred students from one university. IQ and depression scores of those students would be obtained and correlated to test the null hypothesis.

Depression: a psychiatric disorder showing symptoms such as persistent feelings of hopelessness, dejection, poor concentration, lack of energy, inability to sleep, and, sometimes, suicidal tendencies

1. What is Correlation?2. Graphing correlation3. Pearson Product Momenta. Interpreting the correlation coefficientb. Hypothesis for correlationc. Computing Pearson Correlation4. Factors Affecting the Correlation5. The coefficient of Determination and

Effect Size

Correlation is the relationship or association between two or more numerical variables.

These variables have to be related to each other or paired.

Correlation is a statistical technique used to determine the degree to which two variables are related.

In the field of education, the correlation is used to administer two measures to the same group of people and then correlated their scores on one measure with their score on the other measure.

The strength , or degree of correlation, as well as the direction of the correlation (positive or negative), is indicated by a correlation coefficient.

The coefficient can range from -1.00, indicating a perfect negative correlation to 0.00, indicating no correlation, to +1.00 indicating a perfect positive correlation.

Correlation does not imply causation. Just because two variables correlate with

each other does not mean that one caused the other.

Correlation between two measures obtained from the same group of people can be shown graphically through the use of a scatter gram (or a scatter plot)

A scatter gram (or a scatter plot) is a graphic presentation of a correlation between two variables.

The figure of this scatter gram showing a positive correlation between two variables, X (number of hours spent studying) and Y (Final grade in course).The points on the scatter gram in this figure create a pattern that goes from the bottom left upward to the top right.

This is typical of a positive correlation in which an increase on one variable is associated with an increase in the other variable.The points on this scatter gram cluster together to form a tight, diagonal pattern.

That as X increases, Y increases

The figure of this scatter gram showing a negative correlation between age of car and reliability.

In a negative correlation, an increase in one variable is associated with a decrease in the other variable.

That as X increases, Y decrease

In statistics books, this part of relationship is called the direction of the relationship (i.e., it is either positive or negative)

The scatter gram contains points that do not form any clear pattern and are scattered widely

That there is no relationship between X and Y. This means that neither X nor Y can be used as a predictor of the other.

Correlation CoefficientCorrelation Coefficient

Statistic showing the degree of relation between two variables

Simple Correlation coefficient Simple Correlation coefficient (r)(r)

It is also called Pearson's correlation It is also called Pearson's correlation or product moment correlation or product moment correlationcoefficient. coefficient.

It measures the It measures the naturenature and and strengthstrength between two variables ofbetween two variables ofthe the quantitativequantitative type. type.

Simple Correlation coefficient Simple Correlation coefficient (r)(r)

In order to use Pearson’s correlation, In order to use Pearson’s correlation, the following requirement should be the following requirement should be satisfied:satisfied:

The scores are measured on an The scores are measured on an interval or ratio scale.interval or ratio scale.

The two variables to be correlated The two variables to be correlated should have a linear relationship (as should have a linear relationship (as opposed to curvilinear relationship)opposed to curvilinear relationship)

Interpreting the correlation coefficientInterpreting the correlation coefficient

After obtaining the correlation After obtaining the correlation coefficient, the next step is to coefficient, the next step is to evaluate and interpret it.evaluate and interpret it.

The sign of the correlation (negative The sign of the correlation (negative or positive) is not indicative of the or positive) is not indicative of the strength of the correlation.strength of the correlation.

A negative correlation is not A negative correlation is not something negative. What matters is something negative. What matters is the absolute value of the correlation.the absolute value of the correlation.

Cont...Cont...

Thus, a negative correlation of -0.93 Thus, a negative correlation of -0.93 indicates a stronger relationship than indicates a stronger relationship than a positive correlation of +0.80a positive correlation of +0.80

The The signsign of of rr denotes the nature of denotes the nature of association association

while the while the valuevalue of of rr denotes the denotes the strength of association.strength of association.

If the sign is If the sign is positivepositive this means the this means the relation is relation is direct direct (an increase in one (an increase in one variable is associated with an increase in variable is associated with an increase in the other variable and a decrease in one the other variable and a decrease in one variable is associated with avariable is associated with adecrease in the other variable).decrease in the other variable).

While if the sign is While if the sign is negative negative this means this means an an inverse or indirectinverse or indirect relationship (which relationship (which means an increase in one variable is means an increase in one variable is associated with a decrease in the other).associated with a decrease in the other).

The value of r ranges between ( -1) and ( +1)The value of r ranges between ( -1) and ( +1) The value of r denotes the strength of the The value of r denotes the strength of the

association as illustratedassociation as illustratedby the following diagram.by the following diagram.

-1 10-0.25-0.75 0.750.25

strong strongintermediate intermediateweak weak

no relation

perfect correlation

perfect correlation

Directindirect

If If rr = Zero = Zero this means no association or this means no association or correlation between the two variables.correlation between the two variables.

If If 0 < 0 < rr < 0.2 < 0.2 = Negligible to low ( no correlation). = Negligible to low ( no correlation).If If 0.2 ≤ 0.2 ≤ rr < 0.4 < 0.4 = Low correlation. = Low correlation.If 0.4 If 0.4 ≤ ≤ rr < 0.6 < 0.6 = Moderate correlation. = Moderate correlation.If If 0.60 ≤ 0.60 ≤ rr <0.80 <0.80 = High correlation. = High correlation.If 0.80If 0.80 ≤ ≤ r < r < l l = perfect correlation. = perfect correlation.

Source: Ruth Ravid 2011:120

InterpretationInterpretation

Depends on what the purpose of the study Depends on what the purpose of the study is… but here is a “is… but here is a “general guidelinegeneral guideline”...”...

• Value = magnitude of the relationship• Sign = direction of the relationship

How to compute the simple correlation coefficient (r(

Formula 1

Formula 2

SySx

YYXXnrXY∑ −−

=))((

1

ExampleExample::

A sample of 6 children was selected, data about their A sample of 6 children was selected, data about their age in years and weight in kilograms was recorded as age in years and weight in kilograms was recorded as shown in the following table . It is required to find the shown in the following table . It is required to find the correlation between age and weight.correlation between age and weight.

serial No

Age (years(

Weight (Kg(

1 7 122 6 83 8 124 5 105 6 116 9 13

Tasks

1. State the research question!2. State the hypothesis for correlation!3. Collect data in a table!4. Calculate the data by using Pearson Product

Moment!5. Determine the degree of relationship!6. Decide whether accept(retain) or reject the

null hypothesis!7. State the interpretation!

These 2 variables are of the quantitative type, one These 2 variables are of the quantitative type, one variable (Age) is called the independent and variable (Age) is called the independent and denoted as (X) variable and the other (weight)denoted as (X) variable and the other (weight)is called the dependent and denoted as (Y) is called the dependent and denoted as (Y) variables to find the relation between age and variables to find the relation between age and weight compute the simple correlation coefficient weight compute the simple correlation coefficient using the following formula:using the following formula:

Tasks

1. State the research question!2. State the hypothesis for correlation!3. Collect data in a table!4. Calculate the data by using Pearson Product

Moment!5. Determine the degree of relationship!6. Decide whether accept(retain) or reject the

null hypothesis!7. State the interpretation!

ExampleExample::

A researcher is to research the correlation betweenA researcher is to research the correlation between Anxiety and Test Scores. He collected the scores as Anxiety and Test Scores. He collected the scores as follows:follows:

Anxiety (X) Anxiety (X) :10, 8, 2, 1, 5, 6:10, 8, 2, 1, 5, 6

Test score(Y)Test score(Y) : 2, 3, 9, 7, 6, 5: 2, 3, 9, 7, 6, 5

1. State the research question!2. State the hypothesis for correlation!3. Collect data in a table!4. Calculate the data by using Pearson Product Moment!5. Determine the degree of relationship!6. Decide whether accept(retain) or reject the null

hypothesis!7. State the interpretation!

ReferencesReferences Main Sources

Coolidge, F. L.2000. Statistics: A gentle introduction. London: Sage.Kranzler, G & Moursund, J .1999. Statistics for the terrified. (2nd ed.). Upper Saddle River, NJ: Prentice Hall.Butler Christopher.1985. Statistics in Linguistics. Oxford: Basil Blackwell.Hatch Evelyn & Hossein Farhady.1982. Research design and Statistics for Applied Linguistics. Massachusetts: Newbury House Publishers, Inc.Ravid Ruth.2011. Practical Statistics for Educators, fourth Ed. New York: Rowman & Littlefield Publisher, Inc.Quirk Thomas. 2012. Excel 2010 for Educational and Psychological Statistics: A Guide to Solving Practical Problem. New York: Springer.

Other relevant sources

Agresi A, & B. Finlay.1986. Statistical methods for the social sciences. San Francisco, CA: Dellen Publishing Company.Bachman, L.F. 2004. Statistical Analysis for Language Assessment. New York: Cambridge University Press.Field, A. (2005). Discovering statistics using SPSS (2nd ed.). London: Sage. Moore, D. S. (2000). The basic practice of statistics (2nd ed.). New York: W. H. Freeman and Company.
