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# Statistics Tutorial

## What happened?

❶Also pay attention to the linkage between the concepts in your theory and in the way you operationalize those concepts in formulating your hypotheses.

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When conducting experiments , a critical part is to test hypotheses against each other. Thus, it is an important part of the statistics tutorial for the scientific method. Hypothesis testing is conducted by formulating an alternative hypothesis which is tested against the null hypothesis , the common view.

The hypotheses are tested statistically against each other. The researcher can work out a confidence interval , which defines the limits when you will regard a result as supporting the null hypothesis and when the alternative research hypothesis is supported.

This means that not all differences between the experimental group and the control group can be accepted as supporting the alternative hypothesis - the result need to differ significantly statistically for the researcher to accept the alternative hypothesis.

This is done using a significance test another article. Caution though, data dredging , data snooping or fishing for data without later testing your hypothesis in a controlled experiment may lead you to conclude on cause and effect even though there is no relationship to the truth.

Depending on the hypothesis, you will have to choose between one-tailed and two tailed tests. Sometimes the control group is replaced with experimental probability - often if the research treats a phenomenon which is ethically problematic , economically too costly or overly time-consuming, then the true experimental design is replaced by a quasi-experimental approach.

Often there is a publication bias when the researcher finds the alternative hypothesis correct, rather than having a "null result", concluding that the null hypothesis provides the best explanation.

If applied correctly, statistics can be used to understand cause and effect between research variables. It may also help identify third variables, although statistics can also be used to manipulate and cover up third variables if the person presenting the numbers does not have honest intentions or sufficient knowledge with their results.

Misuse of statistics is a common phenomenon, and will probably continue as long as people have intentions about trying to influence others. Proper statistical treatment of experimental data can thus help avoid unethical use of statistics. Philosophy of statistics involves justifying proper use of statistics, ensuring statistical validity and establishing the ethics in statistics. Here is another great statistics tutorial which integrates statistics and the scientific method.

Statistical tests make use of data from samples. These results are then generalized to the general population. How can we know that it reflects the correct conclusion?

Contrary to what some might believe, errors in research are an essential part of significance testing. Ironically, the possibility of a research error is what makes the research scientific in the first place. If a hypothesis cannot be falsified e. If a hypothesis is testable, to be open to the possibility of going wrong. Statistically this opens up the possibility of getting experimental errors in your results due to random errors or other problems with the research. ROC Curves are used to calculate sensitivity between true positives and false positives.

This will help them to understand the nature of what they are studying. The goal of predictions is to understand causes. Correlation does not necessarily mean causation. Regression analysis and other modeling tools. In research it is often used to test differences between two groups e. Analysis of Variance can also be applied to more than two groups.

The watchword for this type of writing is structure. The format of your paper should reveal the structure of your thinking.

Devices such as paragraphing, headings, indentation, and enumeration actually help your reader see the major points you want to make. If you tend to string sentences together without organizing your thoughts into paragraphs, you are not helping him or her make sense of your writing.

As a rule of thumb, if you type a full page double spaced without indenting for a new paragraph, you almos tcertainly have run one thought into another and have missed an opportunity to differentiate your ideas.

Headings can convey the major topics discussed in your paper. A research report see the Lacy article on analysis of variance typically contains four basic components:. Although you could include those sections in your report without separate headings, the underlying logic of your paper will be readily apparent with headings that identify its basic components: The Statistics research paper is intended to demonstrate your competence in applying statistics to political and social analysis.

The paper should be no more than 5 typewritten pages double-spaced, not counting tables or graphs. It should be similar to articles in the "Research Notes" section of the Journal of Politics , source of the Lacy reading on Analysis of Variance.. Virtually all these articles are structured some explicitly, other implicitly according to the outline below. To help us evaluate your papers for the 25 points that they can earn, please follow the outline explicitly in writing your papers.

They will be scored as indicated under the four section headings: Begin by stating briefly the intellectual concern with the topic, indicating why it is worthy of study. For example, does the topic reflect an established interest e. To emphasize the ongoing nature of research, each paper should cite at least one previous study or publication relevant to your research. The subject index to Sociological Abstracts , which contains articles in political science, is a good source for publications.

United States Political Science Documents is another good source, and it also contains abstracts of the articles cited. Both sources are in the Reference Room.

You can either cite your references in footnotes giving author, title, and publication particulars , or you can cite the author and date in parentheses within the text.

For example, Tufte, This section should translate the intellectual concerns expressed above into your research. Indicate here the nature and source of your data i. For example, do you expect the hypothesized relationship to hold across sex and race for individual-level data or across types of political systems for national-level data?

You must also formalize your hypotheses in this section. By formalize, I mean physically distinguish your hypotheses from the rest of the text in two ways: For example, you might say, "This leads to our first hypothesis: Hypotheses should be bold assertions of expectations that lend themselves to falsification.

They gain in credibility as they survive attempts to test them -- i. Admittedly, it is intellectually more satisfying to propose hypotheses that are supported rather than falsified through data analysis. Whenever possible, formulate directional hypotheses, which invite falsification more readily than non-directional hypotheses. We will discuss the difference between the two soon.

Also pay attention to the linkage between the concepts in your theory and in the way you operationalize those concepts in formulating your hypotheses. Be careful not to throw away data by collapsing variables to do crosstabulations when they might more properly be analyzed instead through correlational and regression analysis.

For example, the "thermometer" variables in the VOTE88 data are expressed from 0 to , while those in VOTE96 are collapsed into a few ordinal categories. Report here the results of your statistical tests. Refer explicitly to the hypotheses being tested by number: H1, H2, and so on.

In most cases, your data should report tabulations of statistics. If you use ordinal or continuous data, your statistics will involve correlation coefficients, regression coefficients, or results of t-tests or F-tests. Do not simply accept and report the format of SPSS computer printout. Instead, reformat the data into tables like those in the Journal of Politics or someother professional journal. Take some care in reporting your tables. Be sure to include the Ns on which any percentages are based.

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