If a relationship between two categorical variables is Statistical Significance. Basic steps for hypothesis testing: 1. Determine the null hypothesis and the. You use a test of statistical significance in conjunction with hypothesis testing to an observed relationship between variables in your probability sample to the. 1) what is the probability that the relationship exists;: 2) if it does, how strong is the For example, we may find that there is a statistically significant relationship A research hypothesis states the expected relationship between two variables.

Selection The second step you take when testing hypotheses is to choose the appropriate statistical test. One criterion is the level of data. There are different tests for different levels of data. Z scores, for example, are used with metric data. They are also used with a sample that is normally distributed and when you know the standard deviation of the population.

Z scores measure deviations from the means in terms of standard deviation units. They can be used with a single sample or with two samples.

- Lesson 6: Descriptive Statistics, Statistical Inference, and Bi-variate Relationships
- Your Answer

You use the Student's T or the t-test when the standard normal curve is inappropriate and when your data is measured at the metric level. Additionally, it may not be possible to know the standard deviation of the population. In such cases you would use the t-distribution. In addition, you use the standard deviation of the sample to estimate the standard deviation of the population. The t-test is also commonly used to test the significance of a regression coefficient when determining whether independent variables are significant for explaining variance in a dependent variable in regression models.

Other measures of statistical significance include the chi square measure and the F ratio. The chi square measure is used with nominal-level data.

## ANOVA, Regression, and Chi-Square

The F ratio is commonly used to test the statistical significance of simple, partial, and multiple correlation coefficients—tools that are normally used with metric-level data. We provide you with an in-depth discussion of these measures throughout the remainder of this section. Determining the Level of Significance Our next step in deciding whether you can generalize a relationship found in a sample to the overall population is to select a level of statistical significance.

Statistical significance is the exact probability or error that you are willing to accept in making an inference from the sample to the population. A significance level tells you the likelihood that a relationship found in a probability sample occurred as a result of sampling error. In other words, the relationship does not exist in the population. Put a bit differently, the level of significance gives you the probability that there is no real relationship between the independent and dependent variables in the study population you used to select your sample from.

You know that if you took repeated samples they would not always produce exactly the same results.

### ANOVA, Regression, and Chi-Square | Educational Research Basics by Del Siegle

You should expect the same from a single sample. You will experience some error. But you want to minimize that error. You want to increase the probability that your sample results reflect the population and did not occur just by chance. That is why you take random probability samples. You want to have a sample as representative of the population as possible.

How sure do you want to be that your sample results did not occur because of sampling error? Do you want to be right 90 percent of the time?

### M. Understand Statistical Significance and Hypothesis Testing

Or do you want to be right 95 or 99 percent of the time? Just what level of acceptance political scientists are willing to take is a matter of some debate.

Most of us, however, want to be sure that our sample results would occur by chance no more than 5 percent of the time. Therefore the most often used level of significance is.

This means that there is a probability of 5 percent that an incorrect inference will be made that a relationship exists in the population when in fact it does not.

Making the Decision To determine the statistical significance of an observed relationship, you need to compare the calculated value of the measure with values that relate to the different levels of significance. To do this, tables of statistic distributions developed by statisticians are often printed in the appendices of statistics books. You can use these tables to determine whether the value you calculate is statistically significant.

If it is, then you reject the null hypothesis and accept the research hypothesis that there is a real, or statistically significant, relationship between the independent and dependent variables. We discuss how to use these tables when we examine Table and Tablelater in the chapter. The need for these tables, however, has diminished over the years because most statistical analysis packages compute and display the statistics for you.

You can use Figure to help you to make a decision about retaining or rejecting the null hypothesis. The figure shows you that if the significance level is. In other words, there is a real relationship in the population from which you selected your sample. Errors When testing null hypotheses, two types of errors can occur.

**Hypothesis Testing by Hand: The Significance of a Correlation Coefficient - Part 1**

First it is possible that you erroneously reject the null hypothesis when it is, in fact, true. As a result, you will infer the existence of a real relationship when one does not exist. 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. Investigating Relationships Simple Correlation 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. Regression 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. R2 tells how much of the variation in the criterion e. The regression equation for such a study might look like the following: 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. 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.

## 6.2 Correlation & Significance

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. In Summary Each of the stats produces a test statistic e.