Monitoring and Evaluation Studies - Statistics
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enPearson Correlation Coefficient Between Groups
http://mnestudies.com/research/pearson-correlation-coefficient-between-groups
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<h2>
Pearson Correlation</h2>
<p class="rtejustify">To illustrate how to compare correlation between two groups. The article would use dataset of <a href="http://www.hrnutshell.com/DownFiles/Islamic.sav"><strong>Islamic.sav</strong></a>. The Questionnaire was designed to evaluate the factors that affect people’s attitude towards Islamic banking. There may be situation when you need to compare the correlation coefficient between two groups. For instance in this dataset, we may need to compare the responses between male and female respondents. How to do it is described below If you wish to follow along with this example, you should start SPSS and open the <a href="http://www.hrnutshell.com/DownFiles/Islamic.sav"><strong>Islamic.sav</strong></a> file.</p>
<h2>
Correlation Coefficient between Two Groups</h2>
<h3>
Steps to compare Correlation Coefficient between Two Groups</h3>
<p>First we need to split the sample into two groups, to do this follow the following procedure</p>
<ol start="1" type="1">
<li>
From the menu at the top of the screen, click on <strong>Data</strong>, and then select <strong>Split File</strong>.</li>
<li>
Click on <strong>Compare Groups</strong>.</li>
<li>
Move the grouping variable (e.g. Gender) into the box labeled <strong>Groups based on</strong>. Click on <strong>OK</strong>.</li>
<li>
This will split the sample by gender.</li>
</ol>
<p class="rtejustify">Follow the steps in the article (<a href="http://hrnutshell.com/topics/topics-covered-group1-key-to-survival/research/data-analysis/item/278-running-pearson-correlation">Running Pearson Correlation</a>) to request the correlation between your variables of interest. The results will be reported separately for the two groups.</p>
<p class="rtejustify">It is Important to remember, when you are finished looking at males and females separately you will need to turn the <strong>Split File </strong>option off. It stays in place until you manually turn it off. To do this, make sure that you have the <strong>Data Editor</strong> Window open on the screen in front of you. Click on <strong>Data</strong>, <strong>Split File </strong>and click on the first button: <strong>Analyze all cases, do not create groups</strong>.</p>
<p class="rtejustify">The output generated from the correlation procedure is shown below.</p>
<h3>
Interpretation of output from correlation for two groups</h3>
<p class="rtejustify">From the output given above, the correlation between ATIB and SI for males was r=.262, while for females it was slightly higher, r=.293. Although these two values seem different, is this difference big enough to be considered significant? Detailed in the next section is one way that you can test the statistical significance of the difference between these two correlation coefficients. It is important to note that this process is different from testing the statistical significance of the correlation coefficients reported in the output table above. The significance levels reported above (for males: Sig. = .000; for females: Sig. = .116) provide a test of the null hypothesis.</p>
<p class="rtejustify">What might be confusing for you at this stage is that although the Correlation Coefficient for <strong>Male’s</strong> is low but it is still significant, but the coefficient for <strong>female group </strong>is slightly higher but it is still insignificant. The reason for this is the number of cases in each group. The sample size for male groups is significantly higher (N = 235) in comparison to female group (N = 30).</p>
<h3>
Statistical Significance for difference between Groups</h3>
<p class="rtejustify">While you now know how to find correlation coefficient in each of the groups, but still we do not know if the difference in relationship between groups is significant. This section describes the procedure that can be used to find out whether the correlations for the two groups are significantly different. Unfortunately, SPSS will not do this step for you, so it is done manually. Step by Step procedure to find out if the relationship is significantly different you can follow the following steps.</p>
<p class="rtejustify">First we will be converting the r values into z scores and then we use an equation to calculate the observed value of z (zobs value). The value obtained will be assessed using a set decision rule to determine the likelihood that the difference in the correlation noted between the two groups could have been due to chance.</p>
<p class="rtejustify">Before calculating the statistical significance you will check certain assumptions.</p>
<ol start="1" type="1">
<li>
It is assumed that the r values for the two groups were obtained from random samples and that the two groups of cases are independent (not the same participants tested twice).</li>
<li>
The distribution of scores for the two groups is assumed to be normal.</li>
<li>
It is also necessary to have at least 20 cases in each of the groups.</li>
</ol>
<p><strong>Convert each of the r values into z values</strong></p>
<p class="rtejustify">First step is to convert the correlation coefficients (r) into the Z scores. From the SPSS output, find the r value (ignore any negative sign out the front) and N for Group 1 (males) and Group 2 (females).</p>
<p>Males r1 =.262 N1 =235</p>
<p>Females r2 =.293 N2 =30</p>
<p>Using the following , find the <em>z </em>value that corresponds with each of the r values.</p>
<p>Males z1 =.266</p>
<p>Females z2 =.304</p>
<p><strong>Put these values into the equation to calculate zobs</strong></p>
<p class="rtejustify">The equation is provided below, put the respective values in the equation and make the necessary calculations.</p>
<p><strong>Determine if the zobs value is statistically significant</strong></p>
<p>If the zobs value that you obtained is between 1.96 and +1.96, this means that there is no statistically significant difference between the two correlation coefficients. We can only reject the null hypothesis (no difference between the two groups) <em>only </em>if your z value is outside these two boundaries. The decision rule therefore is:</p>
<ol start="1" type="1">
<li>
If 1.96 < zobs < 1.96: correlation coefficients are not statistically significantly different.</li>
<li>
If zobs is less than or equal to 1.96 or zobs is greater than or equal to 1.96: coefficients are statistically significantly different.</li>
</ol>
<p>In the example above, zobs value of .206, that is between the boundaries, so we can conclude that there is a no statistically significant difference in the strength of the correlation between ATIB and SI for males and females.</p></div></div></div>
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Sat, 12 Sep 2015 12:49:32 +0000MnE Expert176 at http://mnestudies.comhttp://mnestudies.com/research/pearson-correlation-coefficient-between-groups#commentsWhat is Correlation | Concept of Correlation
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<h2>
Definition</h2>
<p class="rtejustify">Correlation is a measure of relationship between two variables. It has wide application in business and statistics. Correlation analysis is used to describe the strength and direction of the linear relationship between two variables.</p>
<p class="rtejustify">Do the students who spend the most time studying achieve the highest marks in examinations and do those who spend the least time studying get the lowest marks? What we are asking here is whether the variable study time correlates with the variable examination performance. If we found that this was the case then we would say that there is positive correlation between the variables, that is, as a score on one variable increases so the corresponding score on the other variable does the same. Sometimes we find a correlation between two variables where as one goes up the other goes down. This is termed a negative correlation. We are likely to find a negative correlation between smoking and health as the more a person smokes the less healthy that person tends to be.</p>
<h2>
Examples of Correlation</h2>
<ul type="disc">
<li>
Marketing: The marketing manager wants to know if price reduction has any relationship with increasing sales.</li>
<li>
Production: The production department wants to know if the number of defective items produced has anything to do with the age of the machine.</li>
<li>
Human Resource: The HR department wants to know if the productivity of its workers decreases with the number of hours they put in.</li>
<li>
Social Sciences: A social activist wants to know if increasing female literacy has any association with increasing the age of marriage of the girl child.</li>
<li>
Research: An educationist wants to know if enforcing stricter attendance rules relates to students in performing better in their studies.</li>
</ul>
<p class="rtejustify">It is important to note that in correlation we have two different variables for which we use correlation, some hypothesis for which we can use correlation test are written below</p>
<ul type="disc">
<li>
H1: Employee Job Satisfaction is associated with Employee Intention to Quit</li>
<li>
H2: Organizational Learning is related to Innovation Capability</li>
<li>
H3: Advertising is associated with sales of a product</li>
</ul>
<p class="rtejustify">In all the three hypothesis, we must note that there are 2 variables in each of the hypothesis, between whom we need to check for the relationship. On a simple level, the basic question being dealt with by correlation can be answered in one of three possible ways. Within any bivariate data set, it may be the case that the high scores on the first variable tend to be paired with the high scores on the second variable (implying, of course, that low scores on the first variable tend to be paired with low scores on the second variable). I refer to this first possibility as the high-high, low-low case. The second possible answer to the basic correlational question represents the inverse of our first case. In other words, it may be the case that high scores on the first variable tend to be paired with low scores on the second variable (implying, of course, that low scores on the first variable tend to be paired with high scores on the second variable). My shorthand summary phrase for this second possibility is high-low, low-high.</p>
<p class="rtejustify">Finally, it is possible that little systematic tendency exists in the data at all. In other words, it may be the case that some of the high and low scores on the first variable are paired with high scores on the second variable, whereas other high and low scores on the first variable are paired with low scores on the second variable. I refer to this third possibility simply by the three-word phrase little systematic tendency.</p>
<p class="rtejustify">There are a number of different statistics available from SPSS, depending on the level of measurement and the nature of your data. The procedure for obtaining and interpreting a Pearson product-moment correlation coefficient (r) is presented along with Spearman Rank Order Correlation (rho). Pearson r is designed for interval and Ratio level (continuous) variables. It can also be used if you have one continuous variable (e.g. scores on a measure of self-esteem) and one dichotomous variable (e.g. sex: M/F). Spearman rho is designed for use with ordinal level or ranked data and is particularly useful when your data does not meet the criteria for Pearson correlation.</p>
<h2>
Correlation Coefficient</h2>
<p class="rtejustify">The correlation coefficient gives a mathematical value for measuring the strength of the linear relationship between two variables. It can take values from 1 to 1 with:</p>
<ol start="1" type="1">
<li>
+1 representing absolute positive linear relationship (as X increases, Y increases).</li>
<li>
0 representing no linear relationship (X and Y have no pattern).</li>
<li>
1 representing absolute inverse relationship (as X increases, Y decreases).</li>
</ol>
<h2>
Interpretation of Coefficient of Correlation</h2>
<p class="rtejustify">Generally, the coefficient of correlation is interpreted in verbal description. The rule of thumb for interpreting the size of a correlation coefficient is presented below :-</p>
<div align="center">
<table border="1" cellpadding="0" cellspacing="1" width="619">
<tbody>
<tr>
<td width="174">
<p> </p>
<p><strong>Size of Correlation</strong></p>
</td>
<td width="415">
<p><strong>Interpretation</strong></p>
</td>
</tr>
<tr>
<td width="174">
<p>1</p>
</td>
<td width="415">
<p>Perfect Positive/Negative Correlation</p>
</td>
</tr>
<tr>
<td width="174">
<p>+/- .90 to +/- .99</p>
</td>
<td width="415">
<p>Very High Positive/Negative Correlation</p>
</td>
</tr>
<tr>
<td width="174">
<p>+/- .70 to +/- .90</p>
</td>
<td width="415">
<p>High Positive/Negative Correlation</p>
</td>
</tr>
<tr>
<td width="174">
<p>+/- .50 to +/- .70</p>
</td>
<td width="415">
<p>Moderate Positive/Negative Correlation</p>
</td>
</tr>
<tr>
<td width="174">
<p>+/- .30 to +/- .50</p>
</td>
<td width="415">
<p>Low Positive/Negative Correlation</p>
</td>
</tr>
<tr>
<td width="174">
<p>+/- .10 to +/- .30</p>
</td>
<td width="415">
<p>Very low Positive/Negative Correlation</p>
</td>
</tr>
<tr>
<td width="174">
<p>+/- .00 to +/- .10</p>
</td>
<td width="415">
<p>Markedly Low and Negligible Positive/Negative Correlation</p>
</td>
</tr>
</tbody>
</table>
</div>
<p> </p>
<h2>
References:</h2>
<ol start="1" type="1">
<li>
Gaur, A., & Gaur, S. (2009). Statistical Methods for Practice and Research :A guide to data analysis using SPSS (2 ed.). New Delhi: Response Books.</li>
<li>
Huck, S. (2012). Reading Statistics and Research (6 ed.). Boston: Pearson.</li>
<li>
Pallant, J. (2011). SPSS Survival Manual: A step by step guide to data analysis using SPSS (4 ed.). New South Wales: Allen & Unwin.</li>
</ol></div></div></div>
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Mon, 31 Aug 2015 12:09:33 +0000MnE Expert173 at http://mnestudies.comhttp://mnestudies.com/research/what-correlation-concept-correlation#commentsHow to Use Pearson Correlation
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<p class="rtejustify">To illustrate how to use Correlation I would use dataset of <a href="http://www.hrnutshell.com/DownFiles/Islamic.sav"><strong>Islamic.sav</strong></a>. The Questionnaire was designed to evaluate the factors that affect people’s attitude towards Islamic banking. In this example I am interested in assessing the correlation between attitude towards Islamic banking and the Social Influence. If you wish to follow along with this example, you should start SPSS and open the <a href="http://www.hrnutshell.com/DownFiles/Islamic.sav"><strong>Islamic.sav</strong></a> file.</p>
<h2>
Example on Running Pearson Correlation</h2>
<h3>
The Problem:</h3>
<p>Investigate the relationship between Social Influence and attitude to Islamic banking.</p>
<p><strong>Null Hypothesis</strong></p>
<p><strong>H0:</strong>There is no association between Social Influence and Attitude towards Islamic Banking.</p>
<p><strong>HA:</strong>There is an association between Social Influence and Attitude towards Islamic Banking.</p>
<p><strong>Information Required:</strong></p>
<ul type="disc">
<li>
Two continuous variables (In this case, Social Influence and Attitude)</li>
</ul>
<h3>
Assumptions for Pearson Correlation</h3>
<ul type="disc">
<li>
At least two continuous variables (Interval or Ratio) or One Continuous variable and other is dichotomous scale variable</li>
<li>
If there is a dichotomous variable you should, however, have roughly the same number of people or cases in each category of the dichotomous variable.</li>
<li>
Normal distribution for Continuous Variable</li>
</ul>
<h3>
Steps to run Pearson Correlation</h3>
<ol start="1" type="1">
<li class="rtejustify">
Choose <strong>Analyze â†’ Correlate â†’ Bivariate</strong></li>
<li class="rtejustify">
Choose the variables for which the correlation is to be studied from the left-hand side box and move them to the right-hand side box labeled <em>Variables</em>. Once any two variables are transferred to the variables box, the <em>OK </em>button becomes active. We can transfer more than two variables, but for now we will stick to only two.</li>
<li class="rtejustify">
Select the variable <strong>ATIB</strong> (Attitude towards Islamic Banking) and <strong>SI</strong> (Social Influence). Press the Arrow button to the add the variable to the <strong>Variables:</strong> list box</li>
<li class="rtejustify">
There are some default selections at the bottom of the window; these can be changed by clicking on the appropriate boxes. For our purpose, we will use the most commonly used Pearson’s coefficient. <strong>Pearson</strong> checkbox is check from the <strong>Correlation Coefficient</strong> group box</li>
<li class="rtejustify">
Next, while choosing between one-tailed and two-tailed test of significance, we have to see if we are making any directional prediction. The one-tailed test is appropriate if we are making predictions about a positive or negative relationship between the variables; however, the two-tailed test should be used if there is no prediction about the direction of relation between the variables to be tested. In this case we will stick to two-tailed test.</li>
<li class="rtejustify">
Finally <strong>Flag significant correlations </strong>asks SPSS to print an asterisk next to each correlation that is significant at the 0.05 significance level and two asterisks next to each correlation that is significant at the 0.01 significance level.</li>
<li class="rtejustify">
<strong>Press OK</strong></li>
</ol>
<h3>
Output</h3>
<p>The output of the analysis is shown below, the results shows only one table</p>
<h3>
Interpretation of Output</h3>
<p class="rtejustify">For Pearson Correlation, SPSS provides you with a table giving the correlation coefficients between each pair of variables listed, the significance level and the number of cases. The results for Pearson correlation are shown in the section headed <strong>Correlation</strong>.</p>
<p class="rtejustify">The tables shows that a total of 265 respondents. First it is important to consider is the direction of the relationship between the variables. This is identified through a negative sign in front of the correlation coefficient value? A negative sign before the correlation coefficient means that there is a negative correlation between the two variables (i.e. high scores on one are associated with low scores on the other).</p>
<p class="rtejustify">The interpretation of relationship depends how the variables are scored. Checking the Questionnaire, it shows that higher scores on the construct <strong>Attitude towards Islamic Banking </strong>means positive attitude similarly higher scores on Social Influence means greater social influence. This is one of the major areas of confusion for students, so make sure you get this clear in your mind before you interpret the correlation output.</p>
<p class="rtejustify">In the example given here, the Pearson correlation coefficient (.267) indicating a positive correlation between <strong>Social influence</strong> and <strong>Attitude towards Islamic Banking</strong>. The more the social influence on people with regards to Islamic banking, the positive would be the attitude of people towards Islamic banking. To determine the strength of relationship we would use the table 11.1 presented earlier, using the table the correlation matrix shows that there is a Very low Positive between the two variables.</p>
<p class="rtejustify">The Correlation Coefficient can be used to assess how much variance the two variables share.</p>
<p class="rtejustify">This can be done by squaring the r value (multiply it by itself) also called the Coefficient of Determination, to convert this to â€˜percentage of variance’; just multiply by 100 (shift the decimal place two columns to the right).</p>
<p class="rtejustify">In our example we have the coefficient value of .267, two variables that correlate to get the coefficient of determination we square the r value and the result is .0712, and the percentage of variance is 7.12. This shows that Social Influence indicates 7.12% variance in Attitude towards Islamic banking.</p>
<p class="rtejustify">The next thing to consider is the significance level (listed as <strong>Sig. 2 tailed</strong>). This is a frequently misinterpreted area, so care should be exercised here. The level of statistical significance does not indicate how strongly the two variables are associated (this is given by r), but instead it indicates how much confidence we should have in the results obtained. The significance of r is strongly influenced by the size of the sample. In a small sample (e.g. n=30), you may have moderate correlations that do not reach statistical significance at the traditional p<.05 level. In large samples (N=100+), however, very small correlations (e.g. r=.267) as in our case, it may reach statistical significance. While you need to report statistical significance, you should focus on the strength of the relationship and the amount of shared variance (explained earlier).</p>
<h3>
Reporting Pearson Correlation</h3>
<p>Pearson product correlation social influence and attitude towards Islamic banking is very low positive and statistically significant (<em>r </em>= 0.267).</p>
<h3>
Correlation Matrix</h3>
<p class="rtejustify">Correlation is often used to explore the relationship among a group of variables, rather than just two as described above. In this case, it would be awkward to report all the individual correlation coefficients in a paragraph; it would be better to present them in a table also referred to as correlation matrix. SPSS results provide the table that can be made part of the thesis.</p>
<p class="rtejustify">In order to produce a correlation matrix showing relationships between more than two variables, you need to add more than two variable on which the relationships is intended to be studied. For our example we would add the 6 critical factors and attitude towards Islamic banking. Follow the steps mentioned above, add the factors between which the correlation is to be evaluated.</p>
<p class="rtejustify">Press OK, the following correlation matrix is displayed in the output window.</p>
<p class="rtejustify">The output gives correlations for all the pairs of variables and each correlation is produced twice in the matrix. The Correlations are repeated under the number 1 in the diagonal. You can consider the correlation in either of the diagonal. It would be better to present them in a table. One way this could be done is as follows:</p>
<p class="rtejustify">In each cell of the correlation matrix, we get Pearson’s correlation coefficient that shows the strengths of the relationship, which could be evaluated using the table described earlier, the significance is shows through asterisks right next to the correlation coefficient. A Single * shows that correlation is significant at .05 (5%) while ** shows that correlation is significant at .01 (1%). From the output, we can see that the correlation coefficient between ATIB and SI is 0.267 which is very low positive and significant at .01. Similarly the correlation coefficient between ATIB and RC is 0.485 which is and is low positive and significant at .01. Results for correlations between other set of variables can also be interpreted similarly. Coefficient not having the asterisks sign are not significant related and the strength of relationship is almost negligible.</p></div></div></div>
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Sun, 05 Jul 2015 13:02:01 +0000MnE Expert167 at http://mnestudies.comhttp://mnestudies.com/research/how-use-pearson-correlation#comments