The controlled crosstabular analysis is also referred to by the phrase "the elaboration method". While we will have gone over this in class, you may want to look that phrase up in a couple of methods texts for a more in depth discussion.
The first thing you have to do is choose which of the two hypotheses you tested is your primary hypothesis (HINT: it is most likely the hypothesis tested in crosstab 1.
You are then going to control the relationship between the variables in your primary hypothesis by looking at the relationship between your independent variable and your dependent variable at every level of your control variable. What this means is that the computer builds a crosstab table to examine the relationship between your IV and DB for each responce category of the control variable. For example, if I were interested in the relationship between political party (PARTYID) and frequency of sexual relations (SEXFREQ) and I controlled that relationship by sex. SPSS would build a table crossing PARTYID and SEXFREQ for males and another table crossing PARTYID and SEXFREQ for females. If I had controlled by AGE instead, SPSS would have built a table crossing PARTYID and SEXFREQ for each age category. Each of these separate tables will have its own chi-square statistics and its own lambda and/or gamma statistics (if you asked SPSS to calculate statistics).
Now, for the write up there are just about 5 different variations for the controlled crosstab write-up. You will need to see which one fits your situation. One of the major factors in deciding which variation you use will be the relationship you originally observed between your IV and DV in your earlier crosstabular analysis. Here we go:
The first two cases occur when your initial crosstabular analysis weren't significant.
If the original crosstabular analysis relating your independent variable and dependent variable WAS NOT SIGNIFICANT and you look at each crosstab table for every level of your control variable and they are still not significant, you can then say: "My original relationship was not significant and when controlled by my control variable, Z, the relationship remained non-significant.".
If the original crosstabular analysis relating your independent variable and dependent variable WAS NOT SIGNIFICANT and you look at each crosstab table for every level of your control variable and one or more of the tables IS SIGNIFICANT, then you can say: "My original relationship was not significant; however, controlling by Z revealed a suppressed relationship between X and Y".
The next three cases occur when your initial crosstabular relationship was significant.
If the original crosstabular analysis relating your independent variable to your dependent variable WAS SIGNIFICANT and you look at each crosstab table for every level of your control variable and ALL of the tables STILL SHOW A SIGNIFICANT RELATIONSHIP, then you can say: "My original relationship was significant and when controlled by Z remains significant. The relationship between X and Y is not caused by the influence of Z".
If the original crosstabular analysis relating your independent variable and dependent variable WAS SIGNIFICANT and you look at each crosstab table for every level of your control variable and ALL of the crosstab tables ARE NOT SIGNIFICANT, then you can say: "My original relationship was significant, but controlling for Z, the relationship now appears to be spurious. Z appears to be responsible for the observed relationships between X and Y."
Lastly, we have the tricky one--the mixed case. This case is, of course, what most of you are likely to see when you look at your controlled crosstabular analysis. IF the original crosstab comparing your independent variable and dependent variable WAS SIGNIFICANT and you look at each crosstab table for every level of your control variable and see that SOME of the tables ARE SIGNIFICANT and SOME ARE NOT SIGNIFICANT, then you will need to make a judgment call. Here's the judgment:
Were there enough respondents in each of the controlled crosstab tables?
WHY IS THIS THE IMPORTANT JUDGMENT CALL? We know that as your N in a crosstab table increases that smaller differences are more likely to be considered statistically significant. It is possible that your data still exhibits the same patterns (in the percentages) that you saw in your earlier crosstab , but since your sample is divided across several tables it won't be statistically significant.
IF you believe that the table does show the same pattern, but fails to be significant due to a small number of respondents. You may argue that. If you can argue that for all the controlled crosstab tables that aren't significant (if there aren't too many), then you could state that "It appears that the relationship between X and Y persists when one looks at the patterns in the column percentages; however, some of the controlled crosstab tables are not statistically significant. Still, I would argue against calling this a spurious relationship. My reading is that the relationship between X and Y is not truly caused by Z."
OTHERWISE, you will need to argue that the control variable mediates the relationship. That is, the control variable really helps delineate in which situations the relationship holds. For instance, you might find that your relationship between X and Y holds for whites but not for blacks or holds for males but not for females. This can be very important information. In this case you will need to report the significant relationships like you did in Crosstab 1.
Before designing a quantitative research study, you must decide whether it will be descriptive or experimental because this will dictate how you gather, analyze, and interpret the results. A descriptive study is governed by the following rules: subjects are generally measured once; the intention is to only establish associations between variables; and, the study may include a sample population of hundreds or thousands of subjects to ensure that a valid estimate of a generalized relationship between variables has been obtained. An experimental design includes subjects measured before and after a particular treatment, the sample population may be very small and purposefully chosen, and it is intended to establish causality between variables.
The introduction to a quantitative study is usually written in the present tense and from the third person point of view. It covers the following information:
- Identifies the research problem -- as with any academic study, you must state clearly and concisely the research problem being investigated.
- Reviews the literature -- review scholarship on the topic, synthesizing key themes and, if necessary, noting studies that have used similar methods of inquiry and analysis. Note where key gaps exist and how your study helps to fill these gaps or clarifies existing knowledge.
- Describes the theoretical framework -- provide an outline of the theory or hypothesis underpinning your study. If necessary, define unfamiliar or complex terms, concepts, or ideas and provide the appropriate background information to place the research problem in proper context [e.g., historical, cultural, economic, etc.].
The methods section of a quantitative study should describe how each objective of your study will be achieved. Be sure to provide enough detail to enable the reader can make an informed assessment of the methods being used to obtain results associated with the research problem. The methods section should be presented in the past tense.
- Study population and sampling -- where did the data come from; how robust is it; note where gaps exist or what was excluded. Note the procedures used for their selection;
- Data collection – describe the tools and methods used to collect information and identify the variables being measured; describe the methods used to obtain the data; and, note if the data was pre-existing [i.e., government data] or you gathered it yourself. If you gathered it yourself, describe what type of instrument you used and why. Note that no data set is perfect--describe any limitations in methods of gathering data.
- Data analysis -- describe the procedures for processing and analyzing the data. If appropriate, describe the specific instruments of analysis used to study each research objective, including mathematical techniques and the type of computer software used to manipulate the data.
The finding of your study should be written objectively and in a succinct and precise format. In quantitative studies, it is common to use graphs, tables, charts, and other non-textual elements to help the reader understand the data. Make sure that non-textual elements do not stand in isolation from the text but are being used to supplement the overall description of the results and to help clarify key points being made. Further information about how to effectively present data using charts and graphs can be found here.
- Statistical analysis -- how did you analyze the data? What were the key findings from the data? The findings should be present in a logical, sequential order. Describe but do not interpret these trends or negative results; save that for the discussion section. The results should be presented in the past tense.
Discussions should be analytic, logical, and comprehensive. The discussion should meld together your findings in relation to those identified in the literature review, and placed within the context of the theoretical framework underpinning the study. The discussion should be presented in the present tense.
- Interpretation of results -- reiterate the research problem being investigated and compare and contrast the findings with the research questions underlying the study. Did they affirm predicted outcomes or did the data refute it?
- Description of trends, comparison of groups, or relationships among variables -- describe any trends that emerged from your analysis and explain all unanticipated and statistical insignificant findings.
- Discussion of implications – what is the meaning of your results? Highlight key findings based on the overall results and note findings that you believe are important. How have the results helped fill gaps in understanding the research problem?
- Limitations -- describe any limitations or unavoidable bias in your study and, if necessary, note why these limitations did not inhibit effective interpretation of the results.
End your study by to summarizing the topic and provide a final comment and assessment of the study.
- Summary of findings – synthesize the answers to your research questions. Do not report any statistical data here; just provide a narrative summary of the key findings and describe what was learned that you did not know before conducting the study.
- Recommendations – if appropriate to the aim of the assignment, tie key findings with policy recommendations or actions to be taken in practice.
- Future research – note the need for future research linked to your study’s limitations or to any remaining gaps in the literature that were not addressed in your study.
Black, Thomas R. Doing Quantitative Research in the Social Sciences: An Integrated Approach to Research Design, Measurement and Statistics. London: Sage, 1999; Gay,L. R. and Peter Airasain. Educational Research: Competencies for Analysis and Applications. 7th edition. Upper Saddle River, NJ: Merril Prentice Hall, 2003; Hector, Anestine. An Overview of Quantitative Research in Composition and TESOL. Department of English, Indiana University of Pennsylvania; Hopkins, Will G. “Quantitative Research Design.” Sportscience 4, 1 (2000); "A Strategy for Writing Up Research Results. The Structure, Format, Content, and Style of a Journal-Style Scientific Paper." Department of Biology. Bates College; Nenty, H. Johnson. "Writing a Quantitative Research Thesis." International Journal of Educational Science 1 (2009): 19-32; Ouyang, Ronghua (John). Basic Inquiry of Quantitative Research. Kennesaw State University.