Assignment Overview A researcher conducts a test on the effectiveness of a cholesterol treatment on 114 total subjects. Case Assignment Discuss what a hypothesis is. What is null and alternative? Discuss hypothesis testing? How is it carried out? For the data set above, formulate a null and an alternative hypothesis. Without performing the actual calculations or determining statistical significance, explain your procedure for testing to see whether the treatment is effective. DRAWING INFERENCE ABOUT POPULATION MEANS AND PROPORTIONS Required Reading Norman, G., and Streiner, D. (2008). Comparing Two Groups: the t-Test. Biostatistics The Bare Essentials. 3rd Edition. BC Decker Inc. PMPH USA, Ltd. Shelton, CT. eISBN: 9781607950585 pISBN: 9781550093476. Available in Ebrary, accessed via Trident’s online library. Norman, G., and Streiner, D. (2008). Chapter the Twenty First: Tests of Significance for Categorical Frequency Data (pages 235-241). In: Biostatistics The Bare Essentials. 3rd Edition. BC Decker Inc. PMPH USA, Ltd. Shelton, CT. eISBN: 9781607950585 pISBN: 9781550093476. Available in Ebrary, accessed via Trident’s online library. Peat, J. and Barton, B. (2008). Chapter 6: Continuous Data Analyses: Correlation and Regression. Medical Statistics and Critical Appraisal. Wiley. Chichester, England. Available in Ebrary, accessed via Trident’s online library. *Please note that you only need to read the first section on correlation; the section on regression is an advanced topic beyond the scope of this course. DRAWING INFERENCE ABOUT POPULATION MEANS AND PROPORTIONS Modular Learning Outcomes Upon successful completion of this module, the student will be able to satisfy the following outcomes: Case Identify and discuss hypothesis to include null and alternative. Discuss hypothesis testing. SLP Define the possibility for measurement error. Describe how possibility for measurement error can apply to data collection. Discussion Identify the types of variables needed in Chi square, one-sample t-test and paired t-test. Module Overview Now that we’ve covered the logic upon which statistical hypothesis testing is based, we can apply that logic to drawing inference in comparing groups. The t-test is used to assess whether the means of two groups are statistically different from one other. When examining the differences between scores of two groups, we judge the difference between their means relative to the spread or variability of their scores (Trochim, 2006). The t-test is calculated as a ratio; the numerator is the difference between the two means, and the denominator is the variability of groups. In the health sciences, the t-test can be used to compare the effectiveness of a drug versus a placebo, or in a case control study (Norman & Streiner, 2008). The t-test is based on assumption about the normality of the distribution. As such, it is called a parametric test. By contrast, a non-parametric test is one in which there is no assumption made about the nature of the distribution (Norman & Streiner, 2008). Chi Square statistic is non-parametric test used to measure of the difference between observed and expected counts. To compute the chi square statistic, we first calculate the difference between observed and expected counts. Then square the differences from step one. Divide each of the squared difference by the corresponding expected value. Finally, we calculate a sum of all the values in step three to get the chi-square statistic. We end up with a sense of the difference between observed and expected values. Because we have one nominal variable with two or more values and we find out how well a statistical model fits observed data. According to Steinberg (2011), “the goal of a two-variable Chi-square is to determine whether or not the first variable is related to—or independent of—the second variable”. The Chi Square can thus be used as a Test of Independence when we have two nominal variables, each with two or more possible values (Trochim, 2006). As you read the background materials, follow the calculations displayed in contingency tables. Source: Langley, R. 1970. Practical Statistics An important concept in Statistics for continuous data is correlation. Correlation describes how closely two variables are related, or the amount of variability in one measurement explainable by variability in the other measurement (Peat and Barton, 2008). A correlation coefficient of zero indicates a random relationship, and thus the absence of a linear relationship (Peat and Barton, 2008). The Pearson’s Correlation Coefficient (r) is used to measure the association between two continuous variables that are assumed to be normally distributed. As you move forward with studying scientific articles, always keep in mind that use of the word “correlation” is often misused by those unfamiliar with statistics, and by those who wish to confuse the gullible. So, a point that cannot be overemphasized is that correlation indicates the strength of statistical association but it does not, however, imply causation. For philosophical discussions of causation, one should become familiarized with the Bradford Hill Criteria. In more advanced statistics courses, you will have the opportunity to apply the same principles for the purposes of comparing more than two groups. For example, the statistician may employ multiple regression analysis to identify predictors of an outcome variable. Please proceed to the background readings for this module. Sources: Peat, J. and Barton, B. (2008). Medical Statistics and Critical Appraisal. Trochim, W. (2006). The t-test. From: The Research Methods Knowledge Base.