0 13 C S L ■2 to , t/i V) o, 2 « 15 ° e c H o 5 £ < s i o ni S"-o C UJ i s C c si 3 j £• •• s ■= If «* -s O ™ o>: ■ ó 3 |i <2 0€ >i 0 v) p>c ,9í o Ä: c «I ■o a i Q íl &s si Ä* O) Z,e íl Ú 2-Š CHAPTER 1 Research Problems, Approaches, and Questions Research Problems The research process begins with «problem. What is a research problem? Kerlinger(l9-8o) formally describes a problem as "...an interrogative sentence or statement that asks: What relation exists between two or more variables?"(p. 16). Note that almost all research studies have more than two variables- Kerlingcr suggests that prior to the problem statement "...tlie scientist will usually experience an obstacle to understanding, a vague unrest about observed and unobserved phenomena, a curiosity as to why something is as it is " (p. 11). Appendix A provides templates to help you phrase your research problem, and provides examples from the higU school and beyond (HSB) data set. Variables A variable has one defining quality. U must be able to vary or have different values. For example, gender is a variable because it has two values, female or male. Age is a variable that has a large number of values. Type of treatment/intervention (or type of curriculum) is a variable if there is more than one treatment or a treatment anil a control group. Number of days to leiirn something or to recover from an ailment, common measures of the effect of a treatment, urc also variables. Similarly, amount of mathematics knowledge is a variable because it can vary (Vom none to a lot. If a concept has one value in a particular study it is not a variable, e.g., ethnic group is not a variable if all participants arc Caucasian. Definition of a variable. We can define the term "variable" as a characteristic of Hie participants or situation of a given study that has different values in that study. In quantitative research, variables are defined operationally and are commonly divided into independent variables (active or attribute), dependent variables, and extraneous variables. Each of Ihcsc topics will be dealt with in the following sections. Operational definitions of variables. An operational definition describes or defines a variable in terms of the operations or techniques used to elicit or measure it. When quantitative researchers describe the variables in their study, they specify what they mean by demonstrating how they measured the variable. Demographic vnriablos like age, gender, or ethnic group are usually measured simply by asking the participant lo choose the appropriate category from u list. Types uf treatment (or curriculum) sire usually dcscrilicd/dcfinal much more extensively so the reader can understand what the rcsciirchcr meant by, for example, a cognitivcly enriching curriculum or sheltered work. Likewise, abstract concepts like mathematics knowledge, self-concept, or mathematics anxiety need to be defined operationally by spelling out in some detail how (hey were measured in a particular study. To do Ulis, tlie investigator may provide sample questions, append the actual instrument, or provide a reference where more information can be found. Independent Variables Active independent variables. This first type of variable is often called a manipulated independent variable. A frequent goal of research is to investigate the effect of a particular mlcrvoniion. An example might be the effect of a new kind of therapy compared to ihc traditional treatment. A second example might be the effect of a new teaching method, such as cooperative learning, on student performance. In Ihc two examples provided above, the variable of interest was something that was given to the participants. Therefore, an active independent variable is a variable, such as a workshop, new curriculum, or other intervention one level of which can be given lo a group of participants, usually within a specified period oMim during the study. In traditional experimental research, independent variables are those that the investigator can manipulate; they presumably cause a change in some resulting behavior, attitude or physiological measure of interest. An independent variable is considered to be manipulated or active when the investigator has the option to give one value to one group (experimental condition), and another value to another group (control condition). However, there are many circumstances, especially in applied research, when we have an active independent variable but this variable ts not direedy manipulated by the instigator. Consider I he situation where (ho investigator is interested in a now type of treatment. In order lo cany out the study, k turns out that rehabilitation center A will be using that treatment. Rehabilitation center It will be using the traditional treatment. The investigator will compare Ihc two centers lo determine if one treatment works belter than the other. Notice that the independent variable is active but has not been manipulated by the investigator. Thus, active independent variables are given to the participants in the study but are not necessarily manipulated by the experimenter. They may be given by a clinic, school, or someone other than the mvesttgator. From the participants- point of view the situation was manipulated. Attribute independent variables. Unlike some authors of research methods books, we do not restrict the term "independent variable" to those variables that arc manipulated or active We define an independent vanablc more broadly to include any predictors, antecedents, txpresumed causes or influences under investigation in (he study. At(ribu(es of the participants as well as aclivc independent vanables fit within this definition. For the social sciences, education and disciplines dealing with special needs populations, attribute independent variables arc especially important. Type of disability or level of disability is often the major focus of a study Disability certainly qualifies as a variable since il can (akc on different values even though Hicy arc not "given" in (he study, hor example, cerebral palsy is different from Down syndrome which is different from spina bifida, yet all arc disabilities. Also, there arc different levels of ihc same disability. People already have defining characteristics or attributes which place them into one of two or more categories. The different disabilities are already present when we begin our study Thus we are also interested in studying a class of variables that cannot be given during the study even by other persons, schools, or clinics. I A variable which cannot he given, yet is a major fucus of the study, is called an nltiibute independent variable (Kcrluigcr, 1986). In other words, Ihc value* of the independent vnrinble are attributes of the pcmtni or the environment that are not manipulated during the study. For example, gender, age, ethnic group, or disability are attnbutcs of a person. Other labels far the independent variable. SPSS use* a variety of terms such as factor (chapters 5,15, 16, 17 and 18). covnrlale (chapter 13), and grouping variable (chapters 14, 15). In other cases (chapters 5,9) SPSS docs not make a distinction between the independent and dependent variable, just labeling them variables. Another common label for an attribute independent variable is a measured variable. However, we prefer nttribule so it is not easily confused with the dependent variable, which is also measured. Sometimes variables such as gender or ethnic group are called moderator or mediating variables because they serve these functions; however, SPSS does not use these terms so we will not either in this book. Type of independent variable and inferences about came and effect. When we analyze dala from a research study, the statistical analysis does not differentiate whether the independent variable is an active independent variable or an attribute independent variable. 1 lowevcr, oven though SPSS and most statistics books use the label independent variable for both active and attribute variables, there is a crucial difference in interpretation A significant change ot difference following manipulation of the active independent variable may reasonably lead Ihc investigator to infer thai tho independent variable caused the change in the dependent variable. However, a significant change or difference between or aiming values of an attribute independent variable should not lead one to the interpretation lliat Ihe attribute independent variable caused the dependent variable to change A major goal of scicnufic research is to be able lo idcnlify a causal relationship between iwo variables. For those in applied disciplines, the need io demonstrate dial a given intervention or treatment causes change in behavior or performance is extremely important. Only the approaches that have an active independent variable (tho randomized experimental and lo a lesser extent Ihc qua«-experimental) can be successful in providing data that allow one lo infer that the independent variable caused the dependent variable. Although studies with attribute independent variables are limited in what can be said about causation, they can lead lo solid conclusions about ihc differences between groups and about associations between variables Furthermore, they are the only available approach if the focus of your research is on attribute- independent variables. The descriptive approach, as wc define it, dots not attempt to iilcnlify relationships. It focuses on describing variables. As implied above, Ihis distinction between active and attribute independent variable« i» important because terms such as «win effect and effect size used by SPSS and most statistics lK*'ks might lead one to believe that if you find a significant difference Ihe independent variable caused tilt difference. These terms ate misleading when the independent variable is an attribute. I 'alues of the independent variable. In defining a variable, we said that it musí havo moro (han one value. When describing the different categories of an independent variable, SPSS uses Ihe woul values. This docs not necessarily imply thai the values arc ordered.' Suppose that an investigator is performing a study to investigate the effect of a treatment. One group of participants is assigned lo the treatment group A second group docs not receive Ihe treatment. The study could be conceptualized as having one independent variable (treatment type), with Iwo values or levels (treatment and no treatment). The independent variable in llii» example would be classified as nn aclivc independent variuhlo. Instead, suppose ihe investigator was interested primarily in comparing two different treatments but decided lo include a third no-tieatmenl group as a control group in the study. The sludy still would be conccpniali/cd aa having one active independent variable (treatment type), but with Ihrec values (the Iwo treatment conditions and Ihe control condition). This variable could be diagrammed as follows; Variable Label Values Value Labels Treatment Woe = Treatment 1 Treatment 2 No treatment (control) As an additional example, consider gender, wliich is an attribute independent variable with two value*, male and female. It could be diagrammed as follows: * 1 - Male Gender 2 - Female Nole lhal in SPSS each variable is given a label; the values, which arc numbers, may also have labels. It is especially important lo know ihe value labels when the variable is nominal; i.e^, when the % -ill*'- -■ "I ihc v.irir.bleartjail no» u4, Ebus, m QOtOfdend Dependent Variables The dependent variable is the presumed outcome or criterion, li is assumed lo measure or assess the effect of the independent variable Dependent variables are oflen leal score», ratings on questionnaires, readings from instrumcnlK (electrocardiogram, galvanic skin response, etc.), or measures »f physical performance. When wc discuss measurement in chapter 3, we are usually referring to the dependent variable. SPSS also uses a number of other terms for the dependent variable The most common is dependent list, used in cases where you can do Ihc same statistic several limes, for a list of dependent variable* In discriminant analysu (chapter 13), ihe dependent variable is called the grouping variable. The term lest variable ix used in several of the chapters on r tests and analysis of variance. 1 Ihe lemu caMgorWf. lewh. group*, or sampln are somtnroci rad kacrenaafnbry wiih (be leim vdues, espKMly In Maüütct boob. Ukesrnc the Krai fetor u oiks used brand of i*kf*oot*l variable. Basic comparative approach. IT» compiirulivc research approach di ffcrs from the experimental and quasi-experimental approaches because the investigator cannot randomly assign participants to groups mid because there is not an active independent variable. Tabic I. I shows lhát, like experiments and quasi-expcriincrus, comparative designs usually have a few levels or categories for the independent variable and make comparisons between groups. Studies that use the comparative approach examine the presumed effect of an attribute independent variable. An example of the comparative approach is a study that compared two groups of children on a series of motor performance tests. The investigators attempted to determine whether the differences between the two groups were due to perceptual or motor processing problems, One group of children, who had motor handicaps, was compared to a second group of children who did not have motor problems. Noiicc that the independent variable in this study was an attribute independent variable with two levels, motor handicapped and not handicapped. Tims, it is not possible for the investigator to randomly assign participants In groups, or "give" the independent variable; the independent variable was not active. The independent variable had only two values '. Chapter 1 • Kesenrcli I'roblciiis, Approaches, and Questions "y or categories so a statistical comparison between Die groups would be performed. It is, of course, possible for comparisons to be made between three or more groups.' Hasič associational approach. Nnw. we would like to consider an approach to research where the independent variable is usually continuous or has several ordered categories, usually five or more. Suppose that the investigator is interested in the relationship between gitledness and sclf-perceived confidence in children. Assume dial the dependent variable is a self-confidence scale for children. The independent variable is gifledness. If giftedness had been divided into high, average, and low groups (a few values or levels), we would have called the research approach comparative because the logical thing to do would be to compare the groups. However, in the typical associational approach, tht independent variable is continuous or has at least five ordered levels or values.' All participants would be in a single group with two continuous variahles— giftedness and self-concept. A correlation coefficient could he performed to determine the strength ofthe relationship between [he two variables. As implied above, it is somewhat arbitrary whether a study is considered to 1ms comparative or associational. For example, a continuous variable such as age can always be divided into a small number of levels such as young and old. However, we make this distinction for two reasons. First, we think it is usually unwise to divide a variable with many ordered levels into a few because information is lost. For example, if Ihc cut point for "old age" was 65. persons 66 and 96 wuuld he lumped together as would persons 21 and 64. Second, different types of statistics are usually used with Hie two approaches (see Fig. 1.1). We think this distinction and the similar one made in the section on research questions will help you decide on an appropriate statistic, which we have found is one of the hardest parts of the research process for students. Hasíc descriptive approach. This approach is different from the other four in that only one variable is considered at a lime so that no relationships arc made. Table 1.1 shows that this lack of comparisons or associations is what distinguishes this approach from (he other four. Of course, the descriptive approach docs not meet any of the other criteria such as random assignment of participants (o groups. Most research studies include sonic descriptive questions (at least to describe Die sample), but do not stop there. It is rare these days for published quantitative research to be purely descriptive; we almost always study several variables and their relationships. However, political polls and consumer surveys are sometimes only interested in describing hov/ voters as a whole react to issues or what products a group of consumers will buy. Exploratory studies of a new topic may just describe what people say or feel about that topic. Most research books use a considerably broader definition for descriptive research. Some use the phrase "descriptive research" to include all research thai is not randomized experimental or 'It in alio pouiblc to compare relatively larije number* of giou]w(c.u,., 5 or 10) if ono ho* enough pur tic i pnu b Hint Ihc gioup si/it. aic adequate, bul tin* in atypical. * ll is po&iiblc, SB we will sec in dinplcu 7 and B, Hi use tlK aisocinltonal approach nnd statistics when one Uns tcwci lhair five ordered values of the variable« and even with unordered nominal vutiablcs, bul (hu in nol typical 7 düpier 1 - Research Problem», Approaches, and Questions i quasi-expcri mental. Others do not .seem to have it clear definition, using descriptive almost as a synonym tor exploratory or sometimes "correlational" research. We think it is clearer and less confusing 10 students to restrict the lain descriptive research to questions and studies thai use only {Inscriptive statistics, such as Averages, percentages, histograms, and frequency distributions, and do nol lest null hypotheses with inferential statistics. Complex Research Approaches It is important to noto that most studies are more complex Hum implied by the above examples. In fact, almost all studies have more than one hypothesis or research question and may utilize more than one of the above approaches. It is common to find a study with one active independent variable (e.g., type of treatment) and one or more attribute independent variables (e.g., gender). This type of study combines the randomized experimental approach (if the participants were randomly assigned 10 groups) and thc-comparativc approach. Most "survey" studies include both the associaiional and comparative approaches. As mentioned above, most studies also have some descriptive questions so it is common for published studies to use three or even more of the approaches. Research Qu es (ions/Hypo theses Next, we divide research questions into three broad types: difference., associaiional, and descriptive. For the difference type of question, wc compare groups or values of the independent variable on their scores on the dependent variable. This type of question typically is used with the randomized experimental, quasi-experimental, and comparative Approaches. For an associaiional question, wc associate or relate the independent und dependent variables. Descriptive questions arc not answered with inferential statistics; they merely describe or summarize data. Basic Difference Versus Associaiional Research Questions or Hypotheses Hypotheses are defined as predictive statements about Ike relationship between variables. Fig. 1.1 shows thai both difference and associational questions/hypotheses have as a general purpose ihe exploration of relationships between variables: This similarity is in agreement with the statement by statisticians that all parametric inferential statistics are relational, and it is consistent with the notion lhal the distinction between the comparative and associational approach is somewhat arbitrary.4 However, we believe that the distinction is educationally useful. Nute that difference and associational questions differ in specific purpose and the kinds of statistics they use to answer the question. ' We use Die leim assocuuional for this type of research question, approacli, and statistics rather tlian relational or correlational I« distinguish them from the general purpose of both difference and associational questions/hypotheses described above. Also wc wanted to distinguish between correlation, as n specific statistical technique, and the broader types of approach, questions, and group of statistics- Chapter 1 - Research Problems, Approaches, and Questions Genera] Purpose S pee I fir Approach Specific Purpose Riplore 11*1 a t in null tp* rietwcen Variables K 4 mil) in lint V.i pu Im coin I, Aiiiirialliinil Qimil-BilJCilinciilal, anil Comparative Compare Groups fiivl Aiiwialiuiis. Relate Variables, Mike Predictions DcKtiption (Only) |U trlplivc Suiinnjiiic Dii la 1 Type of Qncstlon/Ilypollirvls IHIliiiut.' AvMxrlitionil Descriptive CeneriilTypcur.Nliittvlic nUTucntc liifrKiitlal StaHfHct (e.*,,* ten, ANOVA) AiMdalUmal Descriptive Statistic* liifiiuillil St j l Ink» («.(., Iii-.IOH« ums. (ca., coitelailon. iiwwi*. percentages, multiple icgrcsiton) ľ°* plot») Fig. 1.1. Schematic diagram showing how f he purpose, approach and type of research question correspond to the general type of statistic used in a study. Table 1.2 provides the general format and one example of a basic difference hypothesis and of a basic associaiional hypothesis. Research questions arc similar lo hypotheses, but they are stated in question formal. We think il is advisable to use the question format when one docs nol have a clear directional prediction and for tho descriptive approach. More details and cxaniplcs arc given in Appendix A. ■■ p ä 0 ■Q C t. O . I/I Ü1 Q. Q) w 15 o* c w o w c < 2 E s i 8-5 C UJ \i »a Q; = J5 ^.. M -í 1 »■= o> S o.a *M 5 P 0£ > § 0 « cnc ů> 5 S W Ojg ■c í §e í* < C §1 Chapter I - Research Problems, Approaches, and Questions i Tabic 1.2. Examples of Basic Difference and Associational Hypotheses 1. Difference (group comparison) Hypothesis • For Ulis type of hypothesis, Ihc levels or values of the independent variable (e.g.. gender) are used to divide the participants into groiips {male and female) which are then compared to see if they differ in respect to the^avcrage scores on the dependent variable (e.g., empathy). • An example of a directional research hypothesis is: Women will score higher than men on empathy scores. In other words, the average empathy scores of the women will be significantly higher than ihc average empathy scores for men. 2. Associational (relational) Hypothesis • For this type of hypothesis, the scores on the independent variable (e.g., self-esteem) arc associated with or related to the dependent variable (e.g., empathy). It is often arbitrary which variable is considered the independent variable but most researchers have an idea about whai they think is the predictor (independent) and what is the outcome (dependent) variable. • An example of a directional research hypothesis is: There will be a positive association (relation) between self-esteem scores and empathy scores. In other words, those persons who arc high on self-esteem will tend to have high empathy, those with low self-esteem will lend also to have low empathy, and those in the middle on the independent variable will tend to be in ihc middle on ihc dependent variable. Six Types of Research Questions Table 1.3 expands our overview of research questions to include both basic and complex questions of each of ihc three types: descriptive, difference, anil associaiional. nie tabic also includes references to the tables in chapters 3 and 7, designed to help you select an appropriate Statistic and examples of the types of statistics that we include under each of the six types of questions. Appendix A and the last section in tlus chapter provide examples of research questions for each of the six types. We use the terms basic and complex because the more common names, univariate and multivariate, are not used consistently in die literature. Note mal some complex descriptive statistics (e.g., a cross-tabulation table) could be tested for significance with inferential statistics; if they were so tested they would no longer be considered descriptive. We think that most qualitarive/constructivist researchers ask complex descriptive questions because they consider more than one variľble/concept at a lime but do not use inferential/hypothesis testing statistics. Furthermore, complex descriptive statistics arc used to check reliability {e.g., Cronbach's alpha) and to reduce the number of variables (e.g.t factor analysis). CliapicT 1 - Researcft Problems, Approaches, and Questions Table 1.3. Summary of Types of Research Questions Type of Research Questions (Number of Variables) Statistics (Example) !) Basic Descriptive Questions- 1 variable 2) Complex Descriptive Questions — 2 or more variables, but no use of inferential statistics See Table 3.2 (mean, standard deviation, frequency distribution) (box plols, cross-tabulation tables, factor analysis, measures of reliability) 3) Basic Difference Questions-1 independent and I dependent variable. Independent variable usually has a few values (ordered or not). Table 7.1 (f test, one-way AN0VA) 4) Complex Difference Question ■ 3 or more variables. Usually 2 or a few independent variables and 1 or more dependent variables considered together. Table 7.3 (factorial ANOVA, MÁNOVA) :>) Basic Associational Questions 1 independent variable Table 7.2 and 1 dependent variable. Usually at least 5 ordered values (correlation tested for for both variables. Often they are continuous. significance) 6) Complex Associaiional Questions - 2 or more Table 7.4 independent variables and 1 or more dependent variables. (multiple regression) Usually 5+ ordered values for all variables but some or all can be dichoiomous variables. Difference versus associaiional inferential statistics. We think it is educationally useful, although not common in statistics books, to divide inferential statistics into two types corresponding to difference and associational hypotheses/questions. Difference inferential statistics are used for the experimental, quasi-experimenlal, and comparative approaches, which test for differences between groups (e.g., using analysis of variance). Associational inferential statistics test for associations or relationships between variables and use corrclalion or multiple regression analysis.* Wc will utilize this contrast between difference and associational inferential statistics in chapter 7 and later in this book. * We realize that all parametric inferential statistics ate relational so iliis dichotomy of using one type of data analysis procedure to test for differences (when there are a few values oi levels of the independent variables) and another type of data analyvis procedure ic> test for associations {when there are continuous independent variables) is 5omewb.it artificial. Botb continuous and categorical independent variables can be used in a general line« model