RESEARCH METHOD COHEN ok
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RESEARCH METHOD COHEN ok

RESEARCH METHOD COHEN ok RESEARCH METHOD COHEN ok

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MEASURING ASSOCIATION 531 found and, as we shall see, most coefficients of correlation in social research are around +0.50 or less. The correlation coefficient may be seen then as an indication of the predictability of one variable given the other: it is an indication of covariation. The relationship between two variables can be examined visually by plotting the paired measurements on graph paper with each pair of observations being represented by a point. The resulting arrangement of points is known as a scatterplot and enables us to assess graphically the degree of relationship between the characteristics being measured. Box 24.25 gives some examples of scatterplots in the field of educational research (see http://www.routledge.com/textbooks/ 9780415368780 – Chapter 24, file 24.14.ppt). While correlations are widely used in research, and they are straightforward to calculate and to interpret, the researcher must be aware of four caveats in undertaking correlational analysis: Do not assume that correlations imply causal relationships (i.e. simply because having large hands appears to correlate with having large feet does not imply that having large hands causes one to have large feet). There is a need to be alert to a Type I error – not supporting the null hypothesis when it is in fact true. There is a need to be alert to a Type II error – supporting the null hypothesis when it is in fact not true. Statistical significance must be accompanied by an indication of effect size. In SPSS a typical printout of a correlation coefficient is given in Box 24.26. In this fictitious example using 1,000 cases there are four points to note: The cells of data to the right of the cells containing the figure 1 are the same as the cells to the left of the cells containing the figure 1, i.e. there is a mirror image, and, if very many more variables were being correlated then, in fact, one would have to decide whether to look at only the variables to the right of the cell with the figure 1 (the perfect correlation, since it is one variable being correlated with itself), or to look at the cells to the left of the figure 1. In each cell where one variable is being correlated with a different variable there are three figures: the top figure gives the correlation coefficient, the middle figure gives the significance level, and the lowest figure gives the sample size. SPSS marks with an asterisk those correlations which are statistically significant. All of the correlations are positive, since there are no negative coefficients given. What these tables give us is the magnitude of the correlation (the coefficient), the direction of the correlation (positive and negative), and the significance level. The correlation coefficient can be taken as the effect size. The significance level (as mentioned earlier) is calculated automatically by SPSS, based on the coefficient and the sample size: the greater the sample size, the lower the coefficient of correlation has to be in order to be statistically significant, and, by contrast, the smaller the sample size, the greater the coefficient of correlation has to be in order to be statistically significant. In reporting correlations one has to report the test used, the coefficient, the direction of the correlation (positive or negative), and the significance level (if considered appropriate). For example, one could write: Using the Pearson-product moment correlation, a statistically significant correlation was found between students’ attendance at school and their examination performance (r = 0.87, ρ = 0.035). Those students who attended school the most tended to have the best examination performance, and those who attended the least tended to have the lowest examination performance. Alternatively, there may be occasions when it is important to report when a correlation has not been found, for example: There was no statistically significant correlation found between the amount of time spent on homework and examination performance (r = 0.37, ρ = 0.43). Chapter 24

532 QUANTITATIVE DATA ANALYSIS Box 24.25 Correlation scatterplots Academic achievement Socio-economic status r 0.90 r 0.30 IQ IQ Weight r 00 IQ Absenteeism r 0.30 Visual acuity r 0.90 IQ IQ Source:Tuckman1972 In both of these examples of reporting, exact significance levels have been given, assuming that SPSS has calculated these. An alternative way of reporting the significance levels (as appropriate) are: ρ

532 QUANTITATIVE DATA ANALYSIS<br />

Box 24.25<br />

Correlation scatterplots<br />

Academic<br />

achievement<br />

Socio-economic<br />

status<br />

r 0.90 r 0.30<br />

IQ<br />

IQ<br />

Weight<br />

r 00<br />

IQ<br />

Absenteeism<br />

r 0.30<br />

Visual acuity<br />

r 0.90<br />

IQ<br />

IQ<br />

Source:Tuckman1972<br />

In both of these examples of reporting, exact<br />

significance levels have been given, assuming that<br />

SPSS has calculated these. An alternative way of<br />

reporting the significance levels (as appropriate)<br />

are: ρ

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