Find all (loop-free) nonisomorphic undirected graphs with four vertices. How man

Question

Find all (loop-free) nonisomorphic undirected graphs with four vertices. How many of these graphs are connected? is there anyway to get an answer without taking it from 'http://www.math.washington.edu/~dumitriu/sol_hw4.pdf'

Explanation / Answer

Nonexperimental research is research that lacks manipulation of the independent variable by the researcher; the researcher studies what naturally occurs or has already occurred; and the researcher studies how variables are related. Despite its limitations for studying cause and effect (compared to strong experimental research), nonexperimental research is very important in education. Steps in Nonexperimental Research The pretty much the same as they were in experimental research; however, there are some new considerations to think about if you want to be able to make any cause and effect claims at all (i.e., that an IV--->DV). Determine the research problem and hypotheses to be tested. Note: it is important to have or develop a theory to test in nonexperimental research if you are interested in making any claims of cause and effect. This can include identifying mediating and moderating variables (see Table 2.2 on page 36 for definitions of these two terms). Select the variables to be used in the study. Note: in nonexperimental research you will need to include some control variables (i.e., variables in addition to your IV and DV that measure key extraneous variables). This will help you to help rule out some alternative explanations. Collect the data. Note: longitudinal data (i.e., collection of data at more than one time point) is helpful in nonexperimental research to establish the time ordering of your IV and DV if you are interested in cause and effect. Analyze the data. Note: statistical control techniques will be needed because of the problem of alternative explanations in nonexperimental research. Interpret the results. Note: conclusions of cause and effect will be much weaker in nonexperimental research as compared to strong experimental and quasi-experimental research because the researcher cannot manipulate the independent variable in nonexperimental research. When examining or conducting nonexperimental research, it is important to watch out for the post hoc fallacy (i.e., arguing, after the fact, that A must have caused B simply because you have observed in the past that A preceded B). By the way, post hoc or inductive reasoning is fine (i.e., looking at your data and developing ideas to examine in future research), but you must always watch out for the fallacy just mentioned and you must remember to empirically test any hypotheses that you develop after the fact so that you can check to see whether your hypothesis holds true with new data. In other words, after generating a hypothesis, you must test it. (This last point goes back to Figure 1.1 on page 18 showing the research wheel.) Independent Variables in Nonexperimental Research This includes variables that cannot be manipulated, should not be manipulated, or were not manipulated. Here are some examples of categorical independent variables (IVs) that cannot be manipulated—gender, parenting style, learning style, ethnicity, retention in grade, personality type, drug use. Here are some examples of quantitative IVs that cannot be manipulated—intelligence, age, GPA, any personality trait that is operationalized as a quantitative variable (e.g., level of self-esteem). It is generally recommended that researchers should not turn quantitative independent variables into categorical variables. Simple Cases of Causal-Comparative and Correlational Research Although the terms causal-comparative research and correlational research are dated, it is still useful to think about the simple cases of these (i.e., studies with only two variables). There are four major points in this section: In the simple case of causal-comparative research you have one categorical IV (e.g., gender) and one quantitative DV (e.g., performance on a math test). · The researcher checks to see if the observed difference between the groups is statistically significant (i.e., not just due to chance) using a "t-test" or an "ANOVA" (these are statistical tests discussed in a later chapter; they tell you if the difference between the means is statistically significant; they are discussed in chapter 16). In the simple case of correlational research you have one quantitative IV (e.g., level of motivation) and one quantitative DV (performance on math test). · The researcher checks to see if the observed correlation is statistically significant (i.e., not due to chance) using the "t-test for correlation coefficients" (it tells you if the relationship is statistically significant; it is discussed in chapter 16). · Remember that the commonly used correlation coefficient (i.e., the Pearson correlation) only detects linear relationships. 3. It is essential that you remember this point: Both of the simple cases of nonexperimental research are seriously flawed if you are interested in concluding that an observed relationship is a causal relationship. · That's because "observing a relationship between two variables is not sufficient grounds for concluding that the relationship is a causal relationship." (Remember this important point!) 4. You can improve on the simple cases by controlling for extraneous variables and designing longitudinal studies (discussed below). · And once you move on to these improved nonexperimental designs, you should drop the “correlational” and “causal-comparative” terminology and, instead, talk about the design in terms of the research objective and the time dimension (which is discussed below, and summarized in Table 11.3)

Related Questions

Navigate

• Browse (All)
• Browse F
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.