Sunday, November 25, 2018

CHARACTERISTICS OF CORRELATIONAL DESIGN


CHARACTERISTICS OF CORRELATIONAL DESIGN
1.      Display of scores.(Scatterplot and Metrics)
2.      Association between scores.(Direction, Form and Strength)
3.      Multiple variable analysis.(Partial correlation and Multiple regression)

Display of scores
Plot the scores on a graph (Scatterplot) or present the scores in a table (correlation matrix.)

Scatterplot.
·         Researchers plot scores for two variables on a graph to provide a visual picture of the form of the scores.
·         This allows researchers to identify the type of association among variables and locate extreme scores.
·         Provide useful information about the form of association. Eg: scores are linear (straight line) curvilinear (U shaped).
·         Scatterplot are also called scatter diagram.
·          It is a pictorial image on a graph of two sets of scores for participants.

Correlation matrix.
·         A correlational matrix presents a visual display of scores of the correlation coefficients for all variables in a study. We list all variables on both a horizontal row and vertical column in the table.

Association between scores
After correlation researchers graph scores and produce a correlation matrix. They can then interpret the meaning of association between scores. This calls for understanding the direction of the association, the form of the distribution, the degree and strength of association.

            Direction of association.
·         It is very important to identify the intersection, or movement in a graph.
·         There is positive correlation and negative correlation.
·         Positive correlation – the points move the same direction. X increases Y also increases and X decreases Y also decreases.
·         Negative correlation ­­- the points moves opposite direction. When X increase Y decrease; X decrease, Y increase.

                        Form of the association.
                                    Correlational researchers identify the form of the plotted scores as linear or non linear.

(a)    Positive linear relationship
(b)   Negative linear relationship
(c)    No correlation
(d)   and (e) Curvilinear
Positive linear relationship
Low/high scores on one variable relate to low/high scores on the second variable.
Negative linear relationship
Low scores on one variable relate to high scores on the other variable.
No correlation
Scores on one variable does not tell us or predict any information about the possible scores on other variable.
Curvilinear
An increase, plateau, and decline in Y axis variable with the increasing values of the X axis variable.
Degree and strength of association.
The association between two variables or sets of scores is a correlation coefficient of -1 to +1, with 0.00 indicating no linear association at all. This association between two sets of scores reflects whether there is constant, predictable association between the scores.
If, correlation=  -1 or +1 = perfect linear correlation, values between -1 and +1 = predictable or constant, values are 0.00 = no linear or no relationship.
           
            Multiple variable analysis
In many correlational studies, researchers predict outcomes based on more than one predictor variable. Thus they need to account for the impact of each variable. Two multiple variable analysis approaches are partial correlation and multiple regression. Here predictor variable means independent variable.

            Partial correlation.
·         We study three, four or five variables as predictors of outcomes.
·         The type of variable called a ‘mediating’ or ‘intervening’ variable.
·         Stands between independent and dependent variable and influence them.
·         This variable is different from control variable that influence the outcomes in an experiment.
·         We use partial correlation to determine the amount of varience that an intervening variable explains in both in independent and dependent variable.
Multiple regression.
It is a statistical procedure for examining the combined relationship of multiple independent variable with a single dependent variable.




REFERENCE
John, W., Creswell. Educational research: planning, conducting and evaluating quantitative and qualitative research (4th ed.) 342-353

Wednesday, October 24, 2018

Concept of Correlation and It’s Uses in Educational Research


Concept of Correlation and It’s Uses in Educational Research
A correlation coefficient is a numerical measure of some type of correlation, meaning a statistical relationship between two variables. The variables may be two columns of a given data set of observations, often called a sample, or two components of a multivariate random variable with a known distribution.
Several types of correlation coefficient exist, each with their own definition and own range of usability and characteristics. They all assume values in the range from −1 to +1, where +1 indicates the strongest possible agreement and −1 the strongest possible disagreement. As tools of analysis, correlation coefficients present certain problems, including the propensity of some types to be distorted by outliers and the possibility of incorrectly being used to infer a causal relationship between the variables. Correlation is a statistical technique that can show whether and how strongly pairs of variables are related. For example, height and weight are related; taller people tend to be heavier than shorter people. The relationship isn't perfect. People of the same height vary in weight, and you can easily think of two people you know where the shorter one is heavier than the taller one. Nonetheless, the average weight of people 5'5'' is less than the average weight of people 5'6'', and their average weight is less than that of people 5'7'', etc. Correlation can tell you just how much of the variation in peoples' weights is related to their heights. Although this correlation is fairly obvious your data may contain unsuspected correlations. You may also suspect there are correlations, but don't know which are the strongest. An intelligent correlation analysis can lead to a greater understanding of your data.
Types of Correlation
·         Positive Correlation
·         Negative Correlation
·         Partial Correlation
·         Linear Correlation
·         Zero Order Correlation 
·         Scatter Plot Correlation
·         Spearman's Correlation
·          Non Linear Correlation
·         Weak Correlation
Positive correlation
A positive correlation is a correlation in the same direction.
Negative correlation
A negative correlation is a correlation in the opposite direction
Partial correlation
The correlation is partial if we study the relationship between two variables keeping    all other variables constant
Linear correlation
When the change in one variable results in the constant change in the other variable, we say the correlation is linear. When there is a linear correlation, the points plotted will be in a straight line
Zero order correlation 
zero correlation suggests that the correlation statistic did not indicate a relationship between the two variables.
Scatter plot correlation
A scatter plot is a type of mathematical diagram using cartesian coordinates to display values for two variables for a set of data. Scatter plots will often show at a glance whether a relationship exists between two sets of data.
Spearman's correlation
Spearman's rank correlation coefficient allows us to identify easily the strength of correlation within a data set of two variables, and whether the correlation is positive or negative.
Non linear correlation
When the amount of change in one variable is not in a constant ratio to the change in the other variable, we say that the correlation is non linear.
Weak correlation
The range of the correlation coefficient between -1 to +1. If the linear correlation coefficient takes values close to 0, the correlation is weak.
Uses in Educational Research
·         In correlational research we do not (or at least try not to) influence any variables but only measure them and look for relations (correlations) between some  set of variables.
·         In experimental research, we manipulate some variables and then measure the effects of this manipulation on other variables.
·         Experimental data may potentially provide qualitatively better information.
·         Only experimental data can conclusively demonstrate causal relations between variable.