File Name: applied statistics analysis of variance and regression .zip
Parametric Data Analysis. When we wish to know whether the means of two groups one independent variable e. In order to calculate a t test, we need to know the mean, standard deviation, and number of subjects in each of the two groups. It is the number of subjects minus the number of groups always 2 groups with a t-test. You may wish to review the instructor notes for t tests.
If the independent variable e. The first number is the number of groups minus 1. The second number is the total number of subjects minus the number of groups. Because we had subject and 3 groups, it is ]. ANOVAs can have more than one independent variable. A two-way ANOVA has three research questions: One for each of the two independent variables and one for the interaction of the two independent variables.
Do males and females differ on their opinion about a tax cut? Is there an interaction between gender and political party affiliation regarding opinions about a tax cut? A two-way ANOVA has three null hypotheses, three alternative hypotheses and three answers to the research question. The answers to the research questions are similar to the answer provided for the one-way ANOVA, only there are three of them.
Sometimes we have several independent variables and several dependent variables. Sometimes we wish to know if there is a relationship between two variables.
A simple correlation measures the relationship between two variables. The variables have equal status and are not considered independent variables or dependent variables.
While other types of relationships with other types of variables exist, we will not cover them in this class. A canonical correlation measures the relationship between sets of multiple variables this is multivariate statistic and is beyond the scope of this discussion. An extension of the simple correlation is regression. In regression, one or more variables predictors are used to predict an outcome criterion.
Data for several hundred students would be fed into a regression statistics program and the statistics program would determine how well the predictor variables high school GPA, SAT scores, and college major were related to the criterion variable college GPA. Not all of the variables entered may be significant predictors. R 2 tells how much of the variation in the criterion e.
For example, someone with a high school GPA of 4. Universities often use regression when selecting students for enrollment. I have created a sample SPSS regression printout with interpretation if you wish to explore this topic further. You will not be responsible for reading or interpreting the SPSS printout.
We might count the incidents of something and compare what our actual data showed with what we would expect. Suppose we surveyed 27 people regarding whether they preferred red, blue, or yellow as a color. If there were no preference, we would expect that 9 would select red, 9 would select blue, and 9 would select yellow. We use a chi-square to compare what we observe actual with what we expect.
If our sample indicated that 2 liked red, 20 liked blue, and 5 liked yellow, we might be rather confident that more people prefer blue. If our sample indicated that 8 liked read, 10 liked blue, and 9 liked yellow, we might not be very confident that blue is generally favored. Chi-square helps us make decisions about whether the observed outcome differs significantly from the expected outcome.
Just as t-tests tell us how confident we can be about saying that there are differences between the means of two groups, the chi-square tells us how confident we can be about saying that our observed results differ from expected results. Each of the stats produces a test statistic e.
Ultimately, we are interested in whether p is less than or greater than. It all boils down the the value of p. Thanks to improvements in computing power, data analysis has moved beyond simply comparing one or two variables into creating models with sets of variables. Structural Equation Modeling SEM analyzes paths between variables and tests the direct and indirect relationships between variables as well as the fit of the entire model of paths or relationships.
For example, a researcher could measure the relationship between IQ and school achievment, while also including other variables such as motivation, family education level, and previous achievement. The example below shows the relationships between various factors and enjoyment of school. When a line connects to variable, there is a relationship.
If two variable are not related, they are not connected by a line. The strengths of the relationships are indicated on the lines. See D. Often the educational data we collect violates the important assumption of independence that is required for the simpler statistical procedures. Students are often grouped nested in classrooms. Those classrooms are grouped nested in schools. The schools are grouped nested in districts. This nesting violates the assumption of independence.
HLM allows researchers to measure the effect of the classroom, as well as the effect of attending a particular school, as well as measuring the effect of being a student in a given district on some selected variable, such as mathematics achievement.
For more information on HLM, see D. Del Siegle www. UConn A-Z. Investigating Relationships Simple Correlation Sometimes we wish to know if there is a relationship between two variables.
Regression An extension of the simple correlation is regression. Non Parametric Data Analysis Chi-Square We might count the incidents of something and compare what our actual data showed with what we would expect. In Summary Each of the stats produces a test statistic e. Model Building Thanks to improvements in computing power, data analysis has moved beyond simply comparing one or two variables into creating models with sets of variables.
Applied Statistical Methods covers the fundamental understanding of statistical methods necessary to deal with a wide variety of practical problems. This chapter text presents the topics covered in a manner that stresses clarity of understanding, interpretation, and method of application. The introductory chapter illustrates the importance of statistical analysis. The next chapters introduce the methods of data summarization, including frequency distributions, cumulative frequency distributions, and measures of central tendency and variability. These topics are followed by discussions of the fundamental principles of probability, the concepts of sample spaces, outcomes, events, probability, independence of events, and the characterization of discrete and continuous random variables. Other chapters explore the distribution of several important statistics; statistical tests of hypotheses; point and interval estimation; and simple linear regression. The concluding chapters review the elements of single- and two-factor analysis of variance and the design of analysis of variance experiments.
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