T-tests and Statistical Procedure - Coursework Example

T-tests and Statistical Procedure Question 1: Suppose you are interested in a research question that requires examination of more than one independent variable. Would the use of several t-tests be an appropriate statistical procedure? If not, what type of test would you use? Why? Answer: T-tests are used to compare means in different groups in order to make conclusions about the samples. T-tests can even be used when the sample size is small, as long as the data is normally distributed in each. The use of multiple t-tests will not be the most appropriate statistical procedure for the problem at hand. Plonsky (1997) stated that doing multiple two-sample t-tests may increase the chance of having errors in the results and it will also be difficult to do so many t-tests. There is an appropriate method for the analysis of more than one independent variable; Analysis of Variance. Plonsky (1997) stated that it saves the user’s time from doing multiple tests to analyze the effect of each independent variable with the every dependent variable individually. Analysis of Variance (ANOVA) is used for observation and analysis purposes when there are more than one independent variables. It provides a whole picture of the data sets since many samples can be compared with each other at the same time. Doncaster explained some uses of ANOVA: It is very useful in the process of inverse design, where any variable can take the place of an independent variable. It is also used when alternatives are being analyzed for a solution. It is used in the analysis of concepts that might have some effect due to changing scenarios. Question 2: Explain the error term for the analysis of variance? Answer: Analysis of variance can be defined as the set of statistical models that provides a statistical test of whether there exists any equality in the means of several groups. An error term is an important element in the statistical model of analysis of variance. Doncaster stated that error can be defined as the amount by which a result is different from the one that was expected by the model. In Analysis of Variance, the errors are not dependant on each other and are found to be normally distributed in the sample means. The error in ANOVA indicates the variance in the dependent measure that is not considered by the independent measure. Statistics Studio Classroom explained in one of their lectures that it is sometimes defined as the “noise” in the data, which is unexplainable in nature. One of assumptions in the analysis of variance is that the error term is an independent, random variable that has a mean 0 and constant variance. It is also assumed that it is normally distributed. The statistical model of analysis of variance is: Y = X + Where Y is the dependent variable X is the independent variable is the error term Gelman (2005) discussed that there are complicated ANOVA models for complicated designs and designs tend to get more complex when there are multiple error terms. Question 3: What distinguishes qualitative research methods from those categorized as quantitative methods? What types of questions can qualitative research address that cannot be addressed by quantitative research? Answer: One of the articles at E-articles stated that qualitative research is a subjective form of research. The researchers of this method will try to analyze and understand the behavior of his subjects and the reasons that might cause that kind of behavior. The qualitative method not only investigates the matter with “what, where, when” questions but also analyzes “why and how”. For this purpose, a small set of people who are attentive in the process, prove to be better samples rather than large ones. Neill (2006) explained that the main types of data collection techniques that are witnessed in a qualitative research are by interviewing the subjects, written description of their experiences and through observing the subject. The contact with the small sample tends to leave a lasting impression since they are very small in number. Researchers spend time with the subjects to analyze their behaviors. They tend to get attached to their research; therefore a biased approach might be present in the analysis. The article further stated that quantitative research methods are more focused on the generation of statistics from large samples, by the aid of questionnaires or interviews. This type of research survey reaches many people but the contact is very quick as compared to the qualitative research method. The data collected in quantitative methods is absolute and numeric in nature; therefore it can be analyzed in an unbiased fashion. Question 4: Distinguish between descriptive, relational, and causal questions. Explain when each should and should not be used? Answer: Grashaw (2009) stated that descriptive questions are used to evaluate the result as it happens. With the aid of descriptive questions, the researcher tries to understand the events that are occurring at that time and how these might have some relation with other factors. Descriptive questions are suitable when simple data collection is required for the events or measurements that are taking place at that certain time. However, if results are required regarding certain variables, such as culture, origin, race, then descriptive questions will not be very suitable. Descriptive questions and thus research does not try to test the relation or influence of one variable with the other. Grashaw (2009) further explained that relational questions are used to find the relationship between number of variables. These questions might be based on culture, race, gender etc. For example; if there is a research regarding the different opinions of men and women about the education standard in the country then we will be analyzing the relationship between the gender and how they feel about the plan. Whereas a causal study will describe the cause and effect of a certain matter and then analyze the relation to each other (which shall be discussed further in detail). Relational questions are suitable for analyzing the cause and effect relationship. However, it does not produce good results if a general opinion from people is required. Grashaw (2009) described causal questions in the following manner; they are used to determine if one or more variables cause or effect any number of outcome variables. Causal questions seek to find the connection between one thing that might cause the other. It helps in establishing a direct cause and effect relationship. Causal questions can be used to forecast and understand behaviour of the subject and analyze what causes them to behave the way they do. References Doncaster, P., C., Terminology of Analysis of Variance, http://www.soton.ac.uk/~cpd/term.html, E-articles, Qualitative versus Quantitative Research, http://e-articles.info/e/a/title/THE-DIFFERENCE-BETWEEN-QUALITATIVE-AND-QUANTITATIVE-RESEARCH/ Grashaw, K., (2009), Distinguishing between descriptive, relational, and causal questions, Grashaw and Co., http://www.grashaw.com/index.php?option=com_content&view=article&id=121:distinguishing-between-descriptive-relational-and-causal-questions-when-should-each-be-used-or-not-used&catid=43:research-methods&Itemid=56 Gelman, A., (2005), Analysis of variance, http://www.stat.columbia.edu/~gelman/research/unpublished/econanova.pdf Neill, J., (2006), Analysis of Professional Literature Class 6: Qualitative Research I, Wilderdom, http://wilderdom.com/OEcourses/PROFLIT/Class6Qualitative1.htm Plonsky, M., (1997), Analysis of Variance, University of Wisconsin, http://www.uwsp.edu/psych/stat/12/anova-1w.htm#I Statistics Studio Classroom, Experiments with a Single-Factor: The Analysis of Variance, Calpoly, http://statweb.calpoly.edu/rsmidt/stat323/03%20Single%20Factor%20Models%20323.doc. 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