Module Problem- Drawing Inferences about Population Means and Proportions! Upon successful completion of this module, you will be able to satisfy the following outcomes:
• Case
o Discuss the procedure for hypothesis testing.
• SLP
o Define the possibility for measurement error and describe how possibility for measurement error can apply to data collection.
• Discussion
o 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.
Respond to the following question utilizing the required and recommended module readings:
• Identify the types of variables you would need to conduct:
o a Chi-square (for students whose last name begins with A-H)
o one-sample t-test (for students whose last name begins with I-P)
o paired t-test (for students whose last name begins with Q-Z)
• Be sure to explain the number of dependent and independent variables, and the types of dependent variables necessary for the statistical analysis.
• Provide a health-related example (or use a peer-reviewed article that used the statistical analysis) to explain your answer.
Reference:
Cook, A., Netuveli, G., & Sheikh, A. (2004). Chapters 5: Study design, Chapter 6: Combining students, Chapter 7: Managing data. In Basic skills in statistics: A guide for healthcare professionals(pp. 53-86). London, GBR: Class Publishing. eISBN: 9781859591291.
Norman, G. R., &Streiner, D. L. (2014). Section the second: Analysis of variance. Chapter 7: Comparing two groups. In Biostatistics: The bare essentials [4th ed., e-Book]. Shelton, Connecticut: PMPH-USA, Ltd. eISBN-13: 978-1-60795-279-4. Available in the Trident Online Library EBSCO eBook Collection.
Norman, G. R., &Streiner, D. L. (2014). Section the third: Regression and correlation. Chapter 13: Simple regression and correlation. In Biostatistics: The bare essentials [4th ed., e-Book]. Shelton, Connecticut: PMPH-USA, Ltd. eISBN-13: 978-1-60795-279-4. Available in the Trident Online Library EBSCO eBook Collection.
Norman, G. R., &Streiner, D. L. (2014). Section the fourth: Non-parametric statistics. Chapter 21: Tests of significance for categorical frequency data. In Biostatistics: The bare essentials [4th ed., e-Book]. Shelton, Connecticut: PMPH-USA, Ltd. eISBN-13: 978-1-60795-279-4. Available in the Trident Online Library EBSCO eBook Collection.
Bozeman Science (2011, November 13). Chi-squared test [video file].
Calvert, J. (2005). 2 by 2 contingency tables.
McDonald, J. (2009). Chi-square test for goodness-of-fit. In Handbook of biological statistics [2nd ed.]. Sparky House Publishing: Baltimore, Maryland.
McDonald, J. (2009). Chi-square test of independence. In Handbook of biological statistics [2nd ed.]. Sparky House Publishing: Baltimore, Maryland.
Trochim, W. (2006). The t-test. Research Methods Knowledge Base.