Speaker 1: Welcome to this overview of quantitative research methods. This tutorial will give you the big picture of quantitative research and introduce key concepts that will help you determine if quantitative methods are appropriate for your project study. First, what is educational research? Educational research is a process of scholarly inquiry designed to investigate the process of instruction and learning, the behaviors, perceptions, and attributes of students and teachers, the impact of institutional processes and policies, and all other areas of the educational process. The research design may be quantitative, qualitative, or a mixed methods design. The focus of this overview is quantitative methods. The general purpose of quantitative research is to explain, predict, investigate relationships, describe current conditions, or to examine possible impacts or influences on designated outcomes. Quantitative research differs from qualitative research in several ways. It works to achieve different goals and uses different methods and design. This table illustrates some of the key differences. Qualitative research generally uses a small sample to explore and describe experiences through the use of thick, rich descriptions of detailed data in an attempt to understand and interpret human perspectives. It is less interested in generalizing to the population as a whole. For example, when studying bullying, a qualitative researcher might learn about the experience of the victims and the experience of the bully by interviewing both bullies and victims and observing them on the playground. Quantitative studies generally use large samples to test numerical data by comparing or finding correlations among sample attributes so that the findings can be generalized to the population. If quantitative researchers were studying bullying, they might measure the effects of a bully on the victim by comparing students who are victims and students who are not victims of bullying using an attitudinal survey. In conducting quantitative research, the researcher first identifies the problem. For Ed.D. research, this problem represents a gap in practice. For Ph.D. research, this problem represents a gap in the literature. In either case, the problem needs to be of importance in the professional field. Next, the researcher establishes the purpose of the study. Why do you want to do the study, and what do you intend to accomplish? This is followed by research questions which help to focus the study. Once the study is focused, the researcher needs to review both seminal works and current peer-reviewed primary sources. Based on the research question and on a review of prior research, a hypothesis is created that predicts the relationship between the study's variables. Next, the researcher chooses a study design and methods to test the hypothesis. These choices should be informed by a review of methodological approaches used to address similar questions in prior research. Finally, appropriate analytical methods are used to analyze the data, allowing the researcher to draw conclusions and inferences about the data, and answer the research question that was originally posed. In quantitative research, research questions are typically descriptive, relational, or causal. Descriptive questions constrain the researcher to describing what currently exists. With a descriptive research question, one can examine perceptions or attitudes as well as more concrete variables such as achievement. For example, one might describe a population of learners by gathering data on their age, gender, socioeconomic status, and attributes towards their learning experiences. Relational questions examine the relationship between two or more variables. The X variable has some linear relationship to the Y variable. Causal inferences cannot be made from this type of research. For example, one could study the relationship between students' study habits and achievements. One might find that students using certain kinds of study strategies demonstrate greater learning, but one could not state conclusively that using certain study strategies will lead to or cause higher achievement. Causal questions, on the other hand, are designed to allow the researcher to draw a causal inference. A causal question seeks to determine if a treatment variable in a program had an effect on one or more outcome variables. In other words, the X variable influences the Y variable. For example, one could design a study that answered the question of whether a particular instructional approach caused students to learn more. The research question serves as a basis for posing a hypothesis, a predicted answer to the research question that incorporates operational definitions of the study's variables and is rooted in the literature. An operational definition matches a concept with a method of measurement, identifying how the concept will be quantified. For example, in a study of instructional strategies, the hypothesis might be that students of teachers who use Strategy X will exhibit greater learning than students of teachers who do not. In this study, one would need to operationalize learning by identifying a test or instrument that would measure learning. This approach allows the researcher to create a testable hypothesis. Relational and causal research relies on the creation of a null hypothesis, a version of the research hypothesis that predicts no relationship between variables or no effect of one variable on another. When writing the hypothesis for a quantitative question, the null hypothesis and the research or alternative hypothesis use parallel sentence structure. In this example, the null hypothesis states that there will be no statistical difference between groups, while the research or alternative hypothesis states that there will be a statistical difference between groups. Note also that both hypothesis statements operationalize the critical thinking skills variable by identifying the measurement instrument to be used. Once the research questions and hypotheses are solidified, the researcher must select a design that will create a situation in which the hypotheses can be tested and the research questions answered. Ideally, the research design will isolate the study's variables and control for intervening variables so that one can be certain of the relationships being tested. In educational research, however, it is extremely difficult to establish sufficient controls in the complex social settings being studied. In our example of investigating the impact of a certain instructional strategy in the classroom on student achievement, each day the teacher uses a specific instructional strategy. After school, some of the students in her class receive tutoring. Other students have parents that are very involved in their child's academic progress and provide learning experiences in the home. These students may do better because they received extra help, not because the teacher's instructional strategy is more effective. Unless the researcher can control for the intervening variable of extra help, it will be impossible to effectively test the study's hypothesis. Quantitative research designs can fall into two broad categories, experimental and quasi-experimental. Classic experimental designs are those that randomly assign subjects to either a control or treatment comparison group. The researcher can then compare the treatment group to the control group to test for an intervention's effect, known as a between-subject design. It is important to note that the control group may receive a standard treatment or may receive a treatment of any kind. Quasi-experimental designs do not randomly assign subjects to groups, but rather take advantage of existing groups. A researcher can still have a control and comparison group, but assignment to the groups is not random. The use of a control group is not required. However, the researcher may choose a design in which a single group is pre- and post-tested, known as a within-subjects design. Or a single group may receive only a post-test. Since quasi-experimental designs lack random assignment, the researcher should be aware of the threats to validity. Educational research often attempts to measure abstract variables such as attitudes, beliefs, and feelings. Surveys can capture data about these hard-to-measure variables, as well as other self-reported information such as demographic factors. A survey is an instrument used to collect verifiable information from a sample population. In quantitative research, surveys typically include questions that ask respondents to choose a rating from a scale, select one or more items from a list, or other responses that result in numerical data. Studies that use surveys or tests need to include strategies that establish the validity of the instrument used. There are many types of validity that need to be addressed. Face validity. Does the test appear at face value to measure what it is supposed to measure? Content validity. Content validity includes both item validity and sampling validity. Item validity ensures that the individual test items deal only with the subject being addressed. Sampling validity ensures that the range of item topics is appropriate to the subject being studied. For example, item validity might be high, but if all the items only deal with one aspect of the subjects, then sampling validity is low. Content validity can be established by having experts in the field review the test. Concurrent validity. Does a new test correlate with an older, established test that measures the same thing? Predictive validity. Does the test correlate with another related measure? For example, GRE tests are used at many colleges because these schools believe that a good grade on this test increases the probability that the student will do well at the college. Linear regression can establish the predictive validity of a test. Construct validity. Does the test measure the construct it is intended to measure? Establishing construct validity can be a difficult task when the constructs being measured are abstract. But it can be established by conducting a number of studies in which you test hypotheses regarding the construct, or by completing a factor analysis to ensure that you have the number of constructs that you say you have. In addition to ensuring the validity of instruments, the quantitative researcher needs to establish their reliability as well. Strategies for establishing reliability include Test retest. Correlates scores from two different administrations of the same test. Alternate forms. Correlates scores from administrations of two different forms of the same test. Split half reliability. Treats each half of one test or survey as a separate administration and correlates the results from each. Internal consistency. Uses Cronbach's coefficient alpha to calculate the average of all possible split halves. Quantitative research almost always relies on a sample that is intended to be representative of a larger population. There are two basic sampling strategies, random and non-random, and a number of specific strategies within each of these approaches. This table provides examples of each of the major strategies. The next section of this tutorial provides an overview of the procedures in conducting quantitative data analysis. There are specific procedures for conducting the data collection, preparing for and analyzing data, presenting the findings, and connecting to the body of existing research. This process ensures that the research is conducted as a systematic investigation that leads to credible results. Data comes in various sizes and shapes, and it is important to know about these so that the proper analysis can be used on the data. In 1946, S.S. Stevens first described the properties of measurement systems that allowed decisions about the type of measurement and about the attributes of objects that are preserved in numbers. These four types of data are referred to as nominal, ordinal, interval, and ratio. First, let's examine nominal data. With nominal data, there is no number value that indicates quantity. Instead, a number has been assigned to represent a certain attribute, like the number 1 to represent male and the number 2 to represent female. In other words, the number is just a label. You could also assign numbers to represent race, religion, or any other categorical information. Nominal data only denotes group membership. With ordinal data, there is again no indication of quantity. Rather, a number is assigned for ranking order. For example, satisfaction surveys often ask respondents to rank order their level of satisfaction with services or programs. The next level of measurement is interval data. With interval data, there are equal distances between two values, but there is no natural zero. A common example is the Fahrenheit temperature scale. Differences between the temperature measurements make sense, but ratios do not. For instance, 20 degrees Fahrenheit is not twice as hot as 10 degrees Fahrenheit. You can add and subtract interval level data, but they cannot be divided or multiplied. Finally, we have ratio data. Ratio is the same as interval, however ratios, means, averages, and other numerical formulas are all possible and make sense. Zero has a logical meaning, which shows the absence of, or having none of. Examples of ratio data are height, weight, speed, or any quantities based on a scale with a natural zero. In summary, nominal data can only be counted. Ordinal data can be counted and ranked. Interval data can also be added and subtracted, and ratio data can also be used in ratios and other calculations. Determining what type of data you have is one of the most important aspects of quantitative analysis. Depending on the research question, hypotheses, and research design, the researcher may choose to use descriptive and or inferential statistics to begin to analyze the data. Descriptive statistics are best illustrated when viewed through the lens of America's pastimes. Sports, weather, economy, stock market, and even our retirement portfolio are presented in a descriptive analysis. Basic terminology for descriptive statistics are terms that we are most familiar in this discipline. Frequency, mean, median, mode, range, variance, and standard deviation. Simply put, you are describing the data. Some of the most common graphic representations of data are bar graphs, pie graphs, histograms, and box and whisker graphs. Attempting to reach conclusions and make causal inferences beyond graphic representations or descriptive analyses is referred to as inferential statistics. In other words, examining the college enrollment of the past decade in a certain geographical region would assist in estimating what the enrollment for the next year might be. Frequently in education, the means of two or more groups are compared. When comparing means to assist in answering a research question, one can use a within-group, between-groups, or mixed-subject design. In a within-group design, the researcher compares measures of the same subjects across time, therefore within-group, or under different treatment conditions. This can also be referred to as a dependent-group design. The most basic example of this type of quasi-experimental design would be if a researcher conducted a pretest of a group of students, subjected them to a treatment, and then conducted a post-test. The group has been measured at different points in time. In a between-group design, subjects are assigned to one of the two or more groups. For example, Control, Treatment 1, Treatment 2. Ideally, the sampling and assignment to groups would be random, which would make this an experimental design. The researcher can then compare the means of the treatment group to the control group. When comparing two groups, the researcher can gain insight into the effects of the treatment. In a mixed-subjects design, the researcher is testing for significant differences between two or more independent groups while subjecting them to repeated measures. Choosing a statistical test to compare groups depends on the number of groups, whether the data are nominal, ordinal, or interval, and whether the data meet the assumptions for parametric tests. Nonparametric tests are typically used with nominal and ordinal data, while parametric tests use interval and ratio-level data. In addition to this, some further assumptions are made for parametric tests that the data are normally distributed in the population, that participant selection is independent, and the selection of one person does not determine the selection of another, and that the variances of the groups being compared are equal. The assumption of independent participant selection cannot be violated, but the others are more flexible. The t-test assesses whether the means of two groups are statistically different from each other. This analysis is appropriate whenever you want to compare the means of two groups, and especially appropriate as the method of analysis for a quasi-experimental design. When choosing a t-test, the assumptions are that the data are parametric. The analysis of variance, or ANOVA, assesses whether the means of more than two groups are statistically different from each other. When choosing an ANOVA, the assumptions are that the data are parametric. The chi-square test can be used when you have non-parametric data and want to compare differences between groups. The Kruskal-Wallis test can be used when there are more than two groups and the data are non-parametric. Correlation analysis is a set of statistical tests to determine whether there are linear relationships between two or more sets of variables from the same list of items or individuals, for example, achievement and performance of students. The tests provide a statistical yes or no as to whether a significant relationship or correlation exists between the variables. A correlation test consists of calculating a correlation coefficient between two variables. Again, there are parametric and non-parametric choices based on the assumptions of the data. Pearson R correlation is widely used in statistics to measure the strength of the relationship between linearly related variables. Spearman-Rank correlation is a non-parametric test that is used to measure the degree of association between two variables. Spearman-Rank correlation test does not assume any assumptions about the distribution. Spearman-Rank correlation test is used when the Pearson test gives misleading results. Often a Kendall-Taw is also included in this list of non-parametric correlation tests to examine the strength of the relationship if there are less than 20 rankings. Linear regression and correlation are similar and often confused. Sometimes your methodologist will encourage you to examine both the calculations. Calculate linear correlation if you measured both variables, x and y. Make sure to use the Pearson parametric correlation coefficient if you are certain you are not violating the test assumptions. Otherwise, choose the Spearman non-parametric correlation coefficient. If either variable has been manipulated using an intervention, do not calculate a correlation. While linear regression does indicate the nature of the relationship between two variables, like correlation, it can also be used to make predictions because one variable is considered explanatory while the other is considered a dependent variable. Establishing validity is a critical part of quantitative research. As with the nature of quantitative research, there is a defined approach or process for establishing validity. This also allows for the findings transferability. For a study to be valid, the evidence must support the interpretations of the data, the data must be accurate, and their use in drawing conclusions must be logical and appropriate. Construct validity concerns whether what you did for the program was what you wanted to do, or whether what you observed was what you wanted to observe. Construct validity concerns whether the operationalization of your variables are related to the theoretical concepts you are trying to measure. Are you actually measuring what you want to measure? Internal validity means that you have evidence that what you did in the study, i.e., the program, caused what you observed, i.e., the outcome, to happen. Conclusion validity is the degree to which conclusions drawn about relationships in the data are reasonable. External validity concerns the process of generalizing, or the degree to which the conclusions in your study would hold for other persons in other places and at other times. Establishing reliability and validity to your study is one of the most critical elements of the research process. Once you have decided to embark upon the process of conducting a quantitative study, use the following steps to get started. First, review research studies that have been conducted on your topic to determine what methods were used. Consider the strengths and weaknesses of the various data collection and analysis methods. Next, review the literature on quantitative research methods. Every aspect of your research has a body of literature associated with it. Just as you would not confine yourself to your course textbooks for your review of research on your topic, you should not limit yourself to your course texts for your review of methodological literature. Read broadly and deeply from the scholarly literature to gain expertise in quantitative research. Additional self-paced tutorials have been developed on different methodologies and techniques associated with quantitative research. Make sure that you complete all of the self-paced tutorials and review them as often as needed. You will then be prepared to complete a literature review of the specific methodologies and techniques that you will use in your study. Thank you for watching.