Unit VII Research Discussion

RCH 8301, Quantitative Research Methods 1

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

6. Create research questions appropriate for a selected research method and design. 6.1 Justify appropriate research questions for a specific research topic.

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

7.1 Explain the hypotheses that were selected for a specific research method and design.

Course/Unit Learning Outcomes

Learning Activity

6.1, 7.1

Unit Lesson Chapter 21, pp. 369–382 Chapter 22, pp. 386–409 Unit VII Reflection Paper

Required Unit Resources Chapter 21: Analysis and Interpretation of Basic Associational Research Questions, pp. 369–382 Chapter 22: Analysis and Interpretation of Complex Research Questions, pp. 386–409

Unit Lesson

Basic Associational Research Questions

In this unit, we focus on various types of research questions, which can be divided into three categories: descriptive, difference, and associational. According to Leech et al. (2015), associational research questions refer to the questions in which two or more variables have a relationship. The associations in this type of hypothesis or research question show that the score on the dependent variable is associated with that of the independent variable. Moreover, the basic associational research questions must have one independent variable while the other variable is dependent (Leech et al., 2015). These questions, therefore, consider an approach where there is an attempt to see how the two (or more) variables relate (covary) or, in some instances, show how one variable enables the researcher to predict the other variable that is being investigated. Importantly, in associational research questions, the type of statistics used in the analysis is specific. Using a schematic diagram, such as the one shown below, the statistics used in the analysis and interpretation follows the purpose and the general type of statistics adopted.

UNIT VII STUDY GUIDE

Data Analysis and Interpretation

RCH 8301, Quantitative Research Methods 2

UNIT x STUDY GUIDE

Title

In the analysis and interpretation of the associational research questions, the nature of variables plays an integral role in the choice and usage of the parametric statistics with associational designs as well as statistical significance, effect size, correlation matrix, and confidence intervals for correlations. There are numerous parametric statistics that are used in the analysis and thereby guide the interpretation of the analysis in a research study. As a result, there is a rationale for using these parametric statistics with respect to associational research questions. In the schematic diagram above, it is evident that the choice of associational inferential statistical techniques, such as regression and correlation, are chosen based on the test that needs to be conducted in order to establish the associations between the variables. In order to choose a parametric statistic with associational designs, there is a need to have a clear data analysis plan for the associational research questions. It is also important to understand the variables before data collection. This understanding will help guide the researcher in selecting the correct statistical test. Since parametric statistics are often used when values of ratio-level or interval-level variables are normal (i.e., are normally distributed or portray a bell-shaped curve), then defining the parameters of data becomes a key rationale when choosing the technique for analysis and interpretation of the results. Furthermore, when using parametric statistics to analyze data or variables in an associational research question, where the data are normally distributed, it is important that additional considerations be adopted. These include the level of significance and effect size. For the level of significance, the p-value, which is simply the probability of getting observed data through chance, is a primary concern. Three assumptions made in testing are that the sample must be randomly selected from the population, the variables under study are independent of each other, and the data must be normally distributed.

Tests of Association

The additional considerations in the analysis and interpretation of associational research questions, especially upon choosing a parametric statistic to use, are also important in appreciating the research. For example, the Pearson product-moment correlation (r) is useful in determining the strength of the relationship between two continuous variables, whereas a result from an analysis is said to have statistical significance only when the p-value of the result is at least extreme (Gliner et al., 2017). In the interpretation of the p-value, the value is compared against the pre-specified significance level (mostly set at 95% or 0.05). Thus, the p-value

To explore the relationship (covariance) between variables

General purpose

To find the strength of related or associations in variables

Specific purpose

Associational research questions

Type of research question

Associational inferential statistics, such as multiple regression and correlation among others

General type of statistics

RCH 8301, Quantitative Research Methods 3

UNIT x STUDY GUIDE

Title

represents that the relationship observed did not occur merely by chance. If the defined, pre-specified significance level is defined as α, which is given as the probability of rejecting the null hypothesis, and if the p- value of the test is less than α, the result is statistically significant. In that instance, the null hypothesis will be rejected, and the alternative hypothesis would be accepted. Therefore, the correlation between the variables is tested for the significance levels in relation to the results. Additionally, in the case of associational research questions, basic testing is done for the specified significance levels as opposed to the multiple regression testing for the complex associational questions. A correlation coefficient measures the direction and strength of a linear relationship between two variables and indicates the extent to which dots in a scatterplot form a straight line. This implies that we can usually estimate correlations pretty accurately from nothing more than scatterplots.

There is a need to appreciate the use of nonparametric associational statistics that can be used. The use of statistics, such as the Spearman rank-order correlation (rs) and Kendall rank-order correlation coefficient (tau or Τ), requires that one consider various assumptions, especially in assessing the statistical associations within the ranks of the variables or data. For the Spearman coefficient, the two variables are measured on an ordinal, ratio, or interval scale, and there is the monotonic relationship between the variables measured. Both Spearman and Kendall methods work on the same assumption, though the latter is used with smaller sample sizes compared to the former (Gliner et al., 2017). A positive correlation between variables’ ranks means that both of the variables in the study are increasing, while a negative correlation between the variables’ ranks implies that the increase of one variable results in a decrease of the second variable. When associational designs are used to examine categorical variables, tests (e.g., chi-square [X2]), should be considered. The interpretation of a chi- square statistic requires the understanding of the degrees of freedom (df) in the test statistic. The df is

calculated by subtracting the number of parameters under examination from the sample size and indicates the number of independent variables that have an effect of varying in the analysis without having any constraints. When hypothesis tests use the chi-square test to calculate the independence and statistically significant relationship amongst variables, then the calculated value exceeds the critical value in the chi- square; the null hypothesis is then rejected, and the relationship between variables is established. Overall, the use of correlation coefficients can be misleading, especially where the correlation of two variables is recorded repeatedly over a period. Therefore, to minimize such effects, time trends are removed from the data prior to measuring the correlation and interpretations of the output. In associational research design, there is also the need to interpret the outputs of both correlation and simple linear regression with care.

Complex Research Questions

The analysis and interpretation of complex questions require an understanding of the two-factor between- group analysis of variance (ANOVA) and the analysis of two-factor designs. Unlike the basic associational research questions, complex research questions often require the use of multiple variables. Thus, in the factorial ANOVA, logistic regression, and discriminant analysis, there are at least two independent variables and one dependent variable (Leech et al., 2015). The rationale for adding more independent variables in the research design is to determine the effect of one independent variable’s reliance on other independent variables. In the ANOVA source table, which displays the output from the test, main effects and interaction effects can be shown. These effects differ in terms of their assumptions and nature. For example, the main effect refers to the effect of an independent variable on the dependent variable, where the effects of the other independent variables are ignored. Thus, it is correct to assume that there is only one main effect for any given

Scatterplots provide a visual representation of a relationship between two variables. (Lacroix, n.d.)

RCH 8301, Quantitative Research Methods 4

UNIT x STUDY GUIDE

Title

independent variable in the research. On the other hand, interaction effects are achieved where the effect of one variable differs with a change in the level of the other variable (usually the second variable). Thus, the main effect involves only independent variables—one at a time, and the interaction is ignored. On the other hand, the interaction effect (the effect that one variable has on the second) occurs when the effect of a variable depends on the other, which indicates that a third variable causes the influence in the relationship between the independent and dependent variables.

References

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. Lacroix, A. (n.d.). Correlation (ID 28959089) [Photograph]. Dreamstime.

https://www.dreamstime.com/royalty-free-stock-images-correlation-image28959089 Leech, N. L., Barrett, K. C., & Morgan, G. A. (2015). IBM SPSS for intermediate statistics: Use and

interpretation (5th ed.). Routledge.

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 21 and 22.