MAT-250ASession 1

What are Statistics?

RATIONALE BEHIND STATISTICS

• This lesson is designed to help you build models that will help you apply the scientific method to problems while strengthening your ability to objectively analyze data. You might also have a need to conduct research in your present position, so I hope you will be able to use these tools in the near future. In any situation in which you want to make a sound decision, inferential statistics empowers you to control for random chance while making inferences to larger populations. By failing to control for random chance, numbers may suggest one thing when they in fact mean something else. The results of inferential statistics tests are based on probability of errors, so, based on a probability statement like p< .05, we can be over 95 percent confident that the result of the test was notcaused by random chance. On the other hand, a pstatement for a test that looks like this (p> .05) is insignificant, which means we cannot rule out chance in causing the numbers.

TYPES OF RESEARCH METHODS

• Research conducted for the local folk is called “action research,” which is a form of applied research. Action research is not designed for large external audiences such as those who read professional journals. Action researchis geared more to the needs of local folk such as faculty committees, counseling boards, and trustee members. To be solid, however, action research needs to have the same component parts (i.e., introduction; literature review, methods, analysis and conclusions) that larger studies feature. In short, they must be rigorous.

Applied and Theoretical Research

• Applied research in general is used to test theory or address a problem associated with a particular situation. The results of this type of research can be published if it is good enough. Case studies could also fall into the applied category.
• Theoretical research is typically exploratoryin nature and attempts to establish an understanding of relationships among variables. This type of research is ground-breaking and invites further study to test its tentative conclusions. To some extent all research should invite further study. Theoretical studies require lots of model building and narrative, so they are typically qualitative in nature. Case studies can also be used in theoretical research, but they are not as likely to be based on theory alone.

Quantitative Really Means Deduction

• Most studies that are appliedor experimental use a deductiveapproach designed to answer specific questions. We are always interested in knowing whether or not there is a difference or a similarity among numbers. In a deductive study, a researcher tests a hypothesis. There are two kinds of hypotheses: nulland alternate(aka alternative and research hypotheses). These are quantitative studies.

Induction and Deduction

• Induction is looking at many pieces of evidence to arrive at a larger conclusion. Qualitative studies certainly follow an inductive trajectory.
• These kinds of studies require voluminous writing (narrative) in developing the theory and showing its potentiality to the situation at hand.
• These kinds of studies, however, may still require the use of statistical analyses.
• EdD dissertation was 80 pages long, but it had five stats tests.
• PhD dissertation was 302 pages long, but it still had a lot of numbers; some of them were evaluated with a statistical test (a chi square statistic).
• Barry Vann’s historical geography book, In Search of Ulster Scots Land, also used lots of numbers and a statistical test, so use numbers when they are needed to objectively make inferences about cause and effect relationships, or to measure differences and similarities. Remember in the vast majority of cases, interferential statistics tests ask one of two questions: is there a difference (causal-comparative), or is there a similarity (correlational) between or among groups?
• Deduction, on the other hand, starts with a hypothesis (an educated guess) and then uses a logical system to test it. Deduction is nearly always quantitative and dependent on inferential statistics tests.

Use Numbers and Tests when Needed

• The bottom line is this:
• Statistical tests are tools that add to a study’s objectivity.
• They are not the “end all.” Don’t worship them.
• Don’t be afraid of them either!
• Use them to clarify conclusions and frame future studies.

Collecting Data

• Data can be found in many places, but sometimes we have to create our own survey forms.
• Survey forms need to be validand reliable.
• What do these terms mean? Valid means that the survey measures what it purports to measure, and reliable means that the survey or instrument is consistent.

Descriptive vs Inferential Statistics

• Descriptive statistics, as the name implies, describes a distribution of scores. They include the mean, median, mode, variance, standard deviation, and range. If they are drawn from a sample of a population, they offer little inference about the larger population; they do not control for random chance. For those two important functions, we turn to inferential statistical tests. These tests look for differences or similarities in data sets; they control for random chance, and the generalize or make inferences to larger populations.

Inferential Tests

• Matched pairs (aka correlated samples t-tests, tstat)
• Independent samples t-tests (difference in means, tstat)
• ANOVA (Analysis of Variance) (differences among 3 or more group means, Fstat)
• Correlation (measures the strength of similarities among groups, rstat)
• Regression (similarities in means or some other number, rstat)
• With these seven tests, it is possible to analyze many problems one is likely to face in his or her career. There are certainly more advanced tests out there, but they follow the same logic as these tried and tested methods.