Probability and Statistics - Assignment Example

Answer to Problems Briefly describe your area of research interest 3 sentences is sufficient). I am a thinking of a research on the relationship between self-esteem and materialism. I wish to explore if there is a link between how a person would think highly or lowly about himself and whether his or her highest goals would revolve on material goals or the acquisition of material things. 2. List 4 variables that you might assess in a research project related to your research area. List one for each type of measurement scale: Nominal, ordinal, interval, and ratio. If you cannot think of a variable for each measurement scale, explain why the task is difficult. With regard to self-esteem, the possible variables are how one would value himself in relation to others and how one would value himself or herself in a scale of 1 to 10. Both of these variables are ordinal. Meanwhile, materialism can be operationalized as life goals wherein the possible variables are the most important goals (which can be categorized into material and non-material like strengthening of relationships with relatives, friends or loved ones) and career plan (which can be categorized between material oriented and non-material oriented). These variables can be transformed into nominal variables. For instance, a career plan leading business-related courses can be classified as material-oriented or materialist while a course leading to medicine can be categorized as non-material-oriented or non-materialist. These are imprecise but they can serve the research purpose. 3. Create one alternate hypothesis and its associated null hypothesis related to your research area. Null Hypothesis: self-esteem is associated with materialism. Alternate Hypothesis: There is no relationship between self-esteem and materialism. 4. Briefly describe whether you think your area of interest is more conducive to experimental or correlational research. What are the costs/benefits of each as it relates to your research area? I think it is appropriate to use correlational research for my topic as I can cover more people. At the same time, I believe a correlational research need not be expensive. I can do a sample survey within a fairly manageable population. In contrast, I will have to do a lot of persuasion to convince someone to participate in an experimental research. 5. Reliability vs. Validity. Considering your area of research interest, discuss the importance of reliability and validity. Can you have one without the other? Why or why not? I think both reliability and validity are important issues. In the case of my research of interest, reliability can pertain to whether the same findings can be obtained if persons other than me conduct the measure or research. I believe that so long as unbiased and scientific research methods are used, there should be no problem with regard to reliability. The research can be done in a transparent manner, with others even watching so long as confidentiality of information between the researcher and respondents are assured and protected. There are definite formulas on how correlation coefficients can be computed and there are also definite formulas on how the significance can also be computed or assessed. Thus, provided a research follows the protocols religiously, there should be problem of reliability. Each of us should be getting the same values provided we have the same sample and we observe full randomness in sampling. Validity can be a problem. This because a course or a career may be associated with non-materialist inclination but the motive for the selecting the said career may actually be materialistic. For example, I may want to be a doctor but money rather than having the ability to take care of someone may be the more important consideration why I am seeking to be a doctor. Thus, validity is a problem in my intended research. Recognizing this, I will have to recognize this problem as a limitation in my research and factor in this limitation in the interpretation of my data. I will have to be explicit in stating the limitation of my research. At the same time, it will be helpful if conceptual relationships are also expressed in operational relationships. The variable chosen for a concept may not have a good fit. A career plan, for example, that is believed to be materialistic may not be materialistic because people may have different objectives in pursuing a course. A doctor, for example, may have chosen his or her career out of altruism but it is also possible that a doctor did the same out of materialism. 6. Sample vs. Population. Considering your area of research interest, describe the difference between a sample and population. Why is it important to understand the difference between a sample and population in a statistics course? The sample and the population usually comes up in an inferential statistics contexts (Urdan, 2005, pp. 2-3). In an inferential statistics, we use a sample to describe population characteristics or relationships. In studying a population, we have two choices: use inferential statistics or use complete enumeration of data to derive population characteristics or relationships from a sample. Using a sample to describe population characteristics and relationship is usually employed when getting the population data or enumeration of data of the population is too costly. 7. Measures of Central Tendency The Excel-computed mean is 126.25, Excel-computed median is 115, and the Excel-computed mode is 115. Usually, it is best to use the mean as a measure of central tendency for the ratio data because each and every information from the data set is factored in the mean. However, the availability of information on the median also provides a useful information on the data set. We can say, for example, that the median divides the data set into two equal parts: half of the data set lies above the median while the other half lies below the median. 8. Measures of Dispersion. For the data set above, calculate the range, the interquartile range, the variance, and the standard deviation. What do these measures tell you about the spreadsheet of the data? The range for the entire data set is from 100 to 275. For the first quartile, the range is from 100 to 106.5. The second quartile range is 106.5 to 115. The third quartile range is from 115 to 117. Finally, the fourth quartile range is from 117 to 275. The quartile data indicate that we have a long-tail to the right or higher values of the distribution. Thus, the quartile information indicates that the distribution is positively skewed. The standard deviation of the distribution is 47.2 while the sample variane is 2,224.5, indicating high dispersion. Thus, the distribution is non-homogenous and highly variable and positively skewed. All measures were estimated using Excel. 9. Descriptive Statistics. Why is it important to perform basic descriptive statistics prior to conducting inferential statistical tests? It is best to do a descriptive statistics prior to an inferential statistics because a homogenous data will most likely report non-significant relationship even if there are in fact significant relationships between variables. At the same time, a relatively homogenous data would most likely report, a more “precise” estimate of the mean in the sense that the population can be found plus or minus a small range to the right or to the left of the sample mean. 10. Statistical Significance. Revisit the hypotheses you created above in #5. If you conducted a statistical test based on these hypotheses and found a statistically significant result, what would that mean from both a statistical and practical standpoint? (Be sure to use the phrases null hypothesis and “effect size” in your answer). The use of large sample sizes would make the data on significance or lack of significance of statistics more reliable and valid. Thus, sample size affect or has an effect on the reliability and validity of findings. From a statistical and practical standpoint, it is best to use higher sample sizes. However, this does not mean that our samples have to very large in order to have reliable and valid results. For examples, there are several formulas that can be used to estimate the population mean based on a “target error” and confidence level. 11. Type I and Type II Error. The concept of Type I and Type II Error is critical and will come into play not only with each and every statistical test you perform, but when you are asked to conduct an a priori power analysis for your Dissertation Proposal. Considering your answer to #10, discuss the implications of making both a Type I and Type II error. According to Walpole et al. (2007, pp. 324-325), Type I error is rejecting the null hypothesis when the null hypothesis is in fact true while type II is accepting the null hypothesis when it is in fact false. The implication of having any one of the two errors will be unfortunate for any study involving statistics because the researcher is misled into an incorrect conclusion. The use of larger sample sizes will make a study more reliable and will help in minimizing or perhaps even eliminating the possibility of a Type I or Type II error. 12. After completing Activity #1, are there any areas of concern you have that you would like to share with your mentor? None at this point but a review on the subject would be best. Work Cited Walpole, R., Myers, R., Myer, S., and Ye, K. (2007). Probability and Statistics for Engineers and Scientists. 8th ed. London: Pearson Education Ltd. Urdan, T. (2005). Statistics in Plain English. 2nd ed. London: Lawrence Erlbaum Associates, 2005. Read More