# Test of significant relationship and difference

### T-Test Statistical Significance Example and Definition

What makes the relationship statistically significant? These questions imply that a test for correlation between two variables was made stated in such a way that there is “no” difference between the two variables being tested. Statistical Significance (T-Test). Statwing represents t-test results as distribution curves. Assuming there is a large enough sample size, the difference between. State the assumptions for testing the difference between two means; Estimate will compute a significance test on the difference between the mean score of the .

### Statistical Significance

Significance is a statistical term that tells how sure you are that a difference or relationship exists. To say that a significant difference or relationship exists only tells half the story.

We might be very sure that a relationship exists, but is it a strong, moderate, or weak relationship? After finding a significant relationship, it is important to evaluate its strength.

### Testing Differences Between Means

Significant relationships can be strong or weak. Significant differences can be large or small. It just depends on your sample size. Many researchers use the word "significant" to describe a finding that may have decision-making utility to a client.

From a statistician's viewpoint, this is an incorrect use of the word. However, the word "significant" has virtually universal meaning to the public. Thus, many researchers use the word "significant" to describe a difference or relationship that may be strategically important to a client regardless of any statistical tests.

In these situations, the word "significant" is used to advise a client to take note of a particular difference or relationship because it may be relevant to the company's strategic plan. The word "significant" is not the exclusive domain of statisticians and either use is correct in the business world.

Thus, for the statistician, it may be wise to adopt a policy of always referring to "statistical significance" rather than simply "significance" when communicating with the public.

One-Tailed and Two-Tailed Significance Tests One important concept in significance testing is whether you use a one-tailed or two-tailed test of significance. The answer is that it depends on your hypothesis.

- Types of Statistical Tests

When your research hypothesis states the direction of the difference or relationship, then you use a one-tailed probability. For example, a one-tailed test would be used to test these null hypotheses: Females will not score significantly higher than males on an IQ test. Blue collar workers are will not buy significantly more product than white collar workers.

Superman is not significantly stronger than the average person. In each case, the null hypothesis indirectly predicts the direction of the difference. A two-tailed test would be used to test these null hypotheses: There will be no significant difference in IQ scores between males and females.

## Statistical Significance

There will be no significant difference in the amount of product purchased between blue collar and white collar workers. There is no significant difference in strength between Superman and the average person.

**What is Statistically Significant?**

The one-tailed probability is exactly half the value of the two-tailed probability. There is a raging controversy for about the last hundred years on whether or not it is ever appropriate to use a one-tailed test.

The rationale is that if you already know the direction of the difference, why bother doing any statistical tests. While it is generally safest to use a two-tailed tests, there are situations where a one-tailed test seems more appropriate.

This sample difference between the female mean of 5. However, the gender difference in this particular sample is not very important.

What is important is whether there is a difference in the population means. In order to test whether there is a difference between population means, we are going to make three assumptions: The two populations have the same variance. This assumption is called the assumption of homogeneity of variance. The populations are normally distributed. Each value is sampled independently from each other value.

## Statistical Significance (T-Test)

This assumption requires that each subject provide only one value. If a subject provides two scores, then the scores are not independent. The analysis of data with two scores per subject is shown in the section on the correlated t test later in this chapter.

The consequences of violating the first two assumptions are investigated in the simulation in the next section.