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The Concept of Statistical Significance Testing, this online article should help you to better understand the concept of statistical significance, the meaning of probability, the concept of significance testing, and the ways results can be misinterpreted Hypotheses provides a brief, clear and well illustrated discussion of hypothesis testing Hypothesis Testing describes factors related to testing the null and alternative hypotheses, including selection of the proper statistical test, consideration of significance levels, and one-sided to two-sided tests, and one sample or two sample tests Significance Tests: Hypothesis Testing discusses confidence intervals in estimating a population mean; provides a useful discussion of terminology involved in conducting a test of significance Statistical Sampling Terms, a nicely presented and illustrated discussion of the process of estimating a mean for a population; also includes definitions of terms and concepts used in the process
Coefficient of correlation For continuous variables, those measured at the interval or ratio levels, the appropriate measure of association is Pearson's coefficient of correlation that is represented by the letter r. Correlation analysis can also be used with data measured at the ordinal level. When one or either variable is measured at the ordinal level, the raw data can be coded to reflect increasing values for each category of the ordinal variable. For example, the category of "strongly disagree' for an item can be coded with increasing values assigned from "strong disagree," codes as "1," "disagree" as "2," "uncertain" as "3," "disagree" as "4," and "strongly agree" as "5." Other items used in a set to measure a variable would be coded in the same way. For detailed discussion of this method of developing scores, go to Chapter 7, "Constructing Composite Measures, Scales and Indexes." Similar codes can be applied to any set of ordered responses. The resulting scores can be used in correlational or other statistical analyses with another variable in ordinal, interval or ratio form. Conducting statistical analyses with coded ordinal variables, however, assumes that the intervals represented by each category of the ordinal variable are equal. In coding, we assume, for example, that the difference between for the value assigned to "strongly agree" and "agree' is the same as that for the between "uncertain" and "disagree" or between differences between two adjacent categories. This assumption can not be verified. In fact, differences in what these words mean to various respondents may be quite different. Further, the distribution of coded responses may not meet the requirements for certain statistical tests. If you chose to conduct statistical analyses with coded ordinal data, you need to be aware of these limitations. Nevertheless, statistical analysis with coded ordinal variables can give you an idea of association among yourr ordinal, interval and ratio variables. Represented as scatter plots An easy way to understand the coefficient of correlation is to visualize the relationship between two variables. One way to do this is to show the relationship in the form of a scatter plot. We described this technique previously in Chapter 3, but repeat it so you can see its application to understanding correlation. To illustrate, let's say you obtained the following data for the years of schooling and number of babies born to a sample of 10 women. (In actual research, a larger sample would be used. We are using only 10 cases to keep the illustration simple). With two scores, one for schooling and one for fertility, the data could be listed as shown in Table 19.4. |