Unit V Annotated Bibliography

RCH 8301, Quantitative Research Methods 1

Course Learning Outcomes for Unit V Upon completion of this unit, students should be able to:

6. Create research questions appropriate for a selected research method and design. 6.1 Investigate a research topic, and include appropriate research questions.

7. Formulate hypotheses appropriate for a selected research method and design.

7.1 Design hypotheses that are suitable for a selected research method and design.

Course/Unit Learning Outcomes

Learning Activity

6.1, 7.1

Unit Lesson Chapter 16, pp. 281–299 Chapter 17, pp. 302–315 Unit V Annotated Bibliography

Required Unit Resources Chapter 16: Making Inferences from Sample Data I: The Null Hypothesis Significance Testing Approach, pp. 281–299 Chapter 17: Making Inferences from Sample Data II: The Evidence-Based Approach, pp. 302–315

Unit Lesson

Making Inferences from Sample Data

Working with an entire population is not possible for most researchers, so a sample of the population is typically studied, and a conclusion about the general population is inferred from the results of the research. The textbook outlines the underlying concepts of devising the inferences from sample data using null hypothesis significance testing and the evidence-based approach. In research, the term hypothesis is defined as the predictor statement or assumption, which focuses on providing the concrete overview about the expected happenings as a result of performing the research (Burns & Burns, 2000). In short, hypotheses speculate about the outcome of the research.

The Null Hypothesis Significance Testing (NHST) is one approach to reporting the outcomes of statistical tests. NHST has been the generally accepted method to guide inferences from data analysis (Gliner et al., 2017). Under NHST, a null hypothesis is the tentative statement that negates the existence of association or relationship between the variables; in contrast, an alternative hypothesis signifies the presence of a relationship between the target variables. The null hypothesis is denoted by H0 whereas Ha refers to alternative hypothesis. A null hypothesis is considered non-directional and assumes the existence of difference between variables, but it is not concerned about the direction. Thus, it is considered a two- tailed test. An alternative hypothesis is further categorized as directional and non-directional hypothesis. A directional hypothesis, indicated by H, is termed as a predictor statement

UNIT V STUDY GUIDE

Data Analysis: Making Inferences from Sample Data

Research process sampling from a target population. (Iamnee, n.d.)

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related to the researcher’s perception about the results. Since a directional hypothesis only looks at one direction (i.e., greater than a value or less than a value), it is also referred to as a one-tailed test. Research population is another important concept, which is defined as the focus group of a scientific query (Kumar, 2010). It is further categorized as theoretical and accessible population. Theoretical population is a broader group upon which the research conclusion is generalized. It is also termed as the target population of a research study. Accessible population is the derived subset of the theoretical population who participates in the study and helps the researcher in drawing a conclusion, which can be further applied to that group; this is usually referred to as a study population. When a researcher selects a research topic, he or she must first identify his or her target population. For example, the target population is the entire group that the researcher is intending to research and analyze. A company customer base can be considered as the target population when determining if a new product concept might be successful. The accessible population would then be that portion of the target population to which the researcher has reasonable access. Of the entire company customer base, there is a smaller accessible population who responds to surveys or participates in focus groups. Inferential statistics undertakes the process of making inferences by evaluating the data which has been collected from the population. A Type I error occurs when a researcher rejects the null hypothesis when it is true. Alpha (α) represents the likelihood of making a Type I error, which can be lowered by reducing the value of alpha. In contrast, a Type II error occurs when a researcher fails to reject the null hypothesis when it is not true. The dependency factor of this error is test power, which is referred to as beta (β), and can be avoided by increasing the sample size of the study. Statistical power is the likelihood of rejecting the null hypothesis and accepting the alternative hypothesis when the alternative hypothesis is found to be true. The statistical power can be increased by using a larger sample size, a higher significance level, or larger difference values and opting for a one-tailed directional hypothesis. Statistical decision-making is another vital concept, which is defined as a rational procedure of collecting, analyzing, and interpreting data through the inclusion of statistical techniques and measures to extract the meaningful insights from it and speculate about the population. Researchers often use a power analysis program, such as G*Power, to determine the sample size needed. G*Power is a widely used tool to compute statistical power for many different tests (Faul et al., 2007). Significance testing of a null hypothesis entails numerous criticisms and problems. In reality, the null hypothesis possesses a false nature. The p-value helps determine the significance of the results. A small p- value (typically ≤ 0.05) indicates strong evidence against the null hypothesis, so the null hypothesis would be rejected. A large p-value (> 0.05) indicates weak evidence against the null hypothesis, so the null hypothesis would not be rejected. Similarly, a small p-value depicts unlikeliness of the data under a null hypothesis. A difference between statistical and scientific significance is another aspect. The concept of real error cannot only be based on statistical error due to it being a very small component of it. Lastly, if the p-value is small, it does not validate the probability of being wrong. For example, suppose a pizza delivery restaurant claims their delivery times are 30 minutes or less on average, and we want to test their claim. We would conduct a hypothesis test since we believe the null hypothesis, H0, which is that the delivery time of 30 minutes is incorrect. Your alternative hypothesis (Ha) is that the delivery time is greater than 30 minutes. You randomly sample some delivery times, run the data through statistical analysis software, and identify that the p-value turns out to be 0.013, which is less than 0.05. Since the null hypothesis is typically rejected when the probability is less than 0.05, we conclude that the pizza delivery times are more than 30 minutes on average.

Evidence-Based Approach

The second approach is evidence-based, which entails the formulation process of the research question and its respective design based on multiple aspects, perspectives, and resources. There are three evidence- based methods that help interpret research results, and these methods use confidence intervals, effect sizes, and meta-analysis. The purpose of computing a statistic by extracting a random sample from the population is to obtain the approximation about the population mean (Creswell, 2014). The extent to which the computed sample

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statistic estimates the value of population is always an unanswered question. In such a situation, confidence intervals play a major role in providing a range of values, which ensure the high likelihood of the population parameters. Confidence level forms the basis of the confidence interval, which is usually set at 95% but can be either 90% or 99%. Why is this significant? With the selection of a sample from the same population at different occasions and with the creation of occasional interval estimates, 95% of the cases will contain the true population mean. In other words, it can be stated that the inverse of Alpha is the confidence at 1- alpha level.

Furthermore, effect size of a study refers to the magnitudinal quantification of a phenomenon so as to measure the relative strength of the relationship; in other words, effect size can be defined as a standard measure that depicts the difference between two groups. The greater the difference, the greater the effect size. Standardized effect sizes are “effect sizes that can be computed regardless of the specific measurement scale used in the study” (Gliner et al., 2017, p. 307). This includes the r family of effect size measures, which contains measures of association, and the d family, which contains measures of the differences between groups. Examples of the r family are the Pearson product-moment correlation

coefficient (r), the Spearman rank-order correlation coefficient (rs, which is pronounced as rho), and the Kendall rank-order correlation coefficient (T, which is pronounced as tau). Examples of the d family are Cohen’s d, Glass’s delta (∆), Hedges’s g, and the odds ratio. For effect sizes of the r-family, Cohen (1988) views the values of 0.1, 0.3, and 0.5 as small, medium, and large, respectively. For effect sizes of the d family, the values 0.2, 0.5, and 0.8 represent small, medium, and large effect sizes, respectively (Cohen, 1988). Furthermore, this unit’s textbook readings discuss details regarding the computational formulas and interpretative aspects of the effect sizes for further understanding. Lastly, meta-analysis is topic fit for review as it follows the approach of combining the results from different studies by performing relevant statistical analysis procedures in order to identify the underlying common truth. In short, this unit requires extra attention in order to understand the principles behind each of the statistical concepts, which have been discussed in this unit’s textbook readings. After going through all of the topics, you will be able to obtain a better understanding of the two basic approaches of drawing inferences from the data, which include null hypothesis significance testing and the evidence-based approach. Furthermore, this unit will help you to understand the differences between null and alternative hypotheses, Type I and Type II errors, the problems with null hypothesis significance testing, confidence intervals, effect sizes, and the distinguishing factors among r and d effect sizes. All of the concepts will improve your knowledge base along with giving you a practical insight toward the application of these concepts in research.

References

Burns, R. B., & Burns, R. B. (2000). Introduction to research methods (4th ed.). Sage. Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Lawrence Erlbaum

Associates. Creswell, J. W. (2014). Research design: Qualitative, quantitative, and mixed methods approaches.

SAGE. Faul, F., Erdfelder, E., Lang, A. G., & Buchner, A. (2007). G*Power 3: A flexible statistical power analysis

program for the social, behavioural, and biomedical sciences. Behavior Research Methods, 39(2), 175–191. https://psycnet.apa.org/record/2007-11814-002

Gliner, J. A., Morgan, G. A., & Leech, N. L. (2017). Research methods in applied settings: An integrated

approach to design and analysis (3rd ed.). Routledge.

Illustration of a statistical analysis of people and population. (Lacroix, n.d.)

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Iamnee. (n.d.). Research process sampling from a target population. Infochart, chart (ID 81702930) [Illustration]. Dreamstime. https://www.dreamstime.com/stock-illustration-research-process- sampling-target-population-business-marketing-social-selecting-sample-elements-to-conduct- image81702930

Kumar, R. (2010). Research methodology: A step-by-step guide for beginners. SAGE. Lacroix, A. (n.d.). People analysis (ID 85123566) [Illustration]. Dreamstime.

https://www.dreamstime.com/stock-illustration-people-analysis-statistical-population- image85123566

Learning Activities (Nongraded) Nongraded Learning Activities are provided to aid students in their course of study. You do not have to submit them. If you have questions, contact your instructor for further guidance and information. Review the “Interpretation Questions” and “Application Problems” at the end of Chapters 16 and 17.