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# Statistics Tutorial

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Depending on the research, the scientist may also want to use statistics descriptively or for exploratory research. What is great about raw data is that you can go back and check things if you suspect something different is going on than you originally thought. This happens after you have analyzed the meaning of the results. The raw data can give you ideas for new hypotheses, since you get a better view of what is going on. You can also control the variables which might influence the conclusion e.

In statistics, a parameter is any numerical quantity that characterizes a given population or some aspect of it. This part of the statistics tutorial will help you understand distribution, central tendency and how it relates to data sets.

Much data from the real world is normal distributed , that is, a frequency curve, or a frequency distribution , which has the most frequent number near the middle. Many experiments rely on assumptions of a normal distribution. This is a reason why researchers very often measure the central tendency in statistical research, such as the mean arithmetic mean or geometric mean , median or mode.

The central tendency may give a fairly good idea about the nature of the data mean, median and mode shows the "middle value" , especially when combined with measurements on how the data is distributed.

Scientists normally calculate the standard deviation to measure how the data is distributed. But there are various methods to measure how data is distributed: However, the sampling distribution will not be normally distributed if the distribution is skewed naturally or has outliers often rare outcomes or measurement errors messing up the data.

One example of a distribution which is not normally distributed is the F-distribution , which is skewed to the right. So, often researchers double check that their results are normally distributed using range, median and mode. How do we know whether a hypothesis is correct or not? Why use statistics to determine this? Using statistics in research involves a lot more than make use of statistical formulas or getting to know statistical software. Making use of statistics in research basically involves.

Statistics in research is not just about formulas and calculation. Many wrong conclusions have been conducted from not understanding basic statistical concepts.

Statistics inference helps us to draw conclusions from samples of a population. 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.

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.

We will deduct points if Ns are not included. Statistical tables should contain all the information that the reader needs to analyze the test. Your job as writer is to point out the key features of the analysis, not to repeat all the numbers in the tables. The data are in the table; the text should be used to summarize its particulars.

Please report correlations and slopes if you employ regression analysis only to the second decimal point. Do not slavishly reproduce them to the ultimate decimal point from the SPSS output. If your analysis involves plots, you may use the PLOT printout if you label it properly and mount it on a page in your paper with aesthetic feeling. Where possible, avoid reference to variables by their SPSS labels e.

Instead, refer to them in more descriptive terms: This section should return you to the problem raised at the beginning of the paper. It provides the link between your narrow data analysis and the broader intellectual concerns with which you began.

You might start by summarizing the results of your statistical tests and determining whether your research supported or contradicted prevailing theory. If your hypotheses are supported, how powerful is the theory?

That is, how much variance are you explaining in the dependent variable? If your research fails to support the theory tested, what are the possible sources of failure? The presence of confounding variables? The inadequacy of the data or the way the variables were measured?

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