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The t Test - What The Heck Is It?

The t test is a statistics test generally used to test whether means of populations are different. In the t test, a t value is calculated based upon the difference in the means and variances of the two populations. This t value is compared to a critical t value, which is based upon the required level of certainty (perhaps you need to be at least 95% certain of the outcome) and the degrees of freedom present in the test. If the t value is greater than the critical t value, it could be stated that, within the required degree of certainty, the 2 means are different.

The t value is generally calculated as follows:

t value = (Difference between the group means) / (Variability of the groups)

To sum up the above calculation, if the groups have a high degree of variance (noise), it is harder to tell whether there really is a difference in the means. The higher amount of variance that exists in the groups, the higher will be the denominator of the above fraction. The higher the denominator, the lower will be the t value. The lower the t value, the less likely that the two means are different. The means are considered different if the t value is greater than the critical t value. It is the t value that is compared with a critical t value to determine within a required degree of certainty whether there really is a difference in the means.

The t value's numerator (Difference between group means) and the denominator (variability of the groups) are calculated in difference ways depending on what type of t test is being run.

The t test has a number of variations but the t test is most commonly used to test whether the means of two populations that are normally distributed are equal. This type of t test is referred to as a Student's t test, or sometimes just the student t test. Drawing samples from different populations in this fashion is referred to as an unpaired t test.

A one-sample t test uses one sample drawn from a single population to test whether the population's mean is equal to a specified value. In other words, the one-sample t test is used to test the Null Hypothesis that the population's mean is equal to that specified value. All other types of t tests are variations of the two sample t test.

A paired t test or paired difference t test is use to test whether "before" and "after" measurements taken of a single object are the same. The Null Hypothesis being tested states that there is no difference between "before" and "after." Specifically, the Null Hypothesis states that "after" values - "before" value = 0.

The Student's t test works well if sample sizes are equal even when the populations being compared have unequal variances. A similar t test called Welch's t test works fine for unequal sample sizes taken from populations with unequal variances.

The two populations from which sample are drawn should be normally distributed.

The t test (specifically, the Student's t test) is equivalent to a one-way ANOVA test when it is being applied to test the equality of means of two normally distributed populations.

A one-sample t test uses one sample drawn from a single population to test whether the population's mean is equal to a specified value. In other words, the one-sample t test is used to test the Null Hypothesis that the population's mean is equal to that specified value.

A two-sample t test is used to test whether two separate normally-distributed populations have the same mean. The Student's t test works well if sample sizes are equal but the populations have different variances. Welch's t test works well for unequal sample sizes drawn from populations of unequal variance.

My blog provides a number of articles which show explicit examples of t Tests being performed in Excel.

Mark Harmon has helped numerous marketers and business students understand how to use business statistics to solve real-world problems. His web site, [http://excelmasterseries.com/]The Excel Statistical Master, is becoming increasingly popular among people wishing for simplified instruction on how to perform graduate-level business statistics. It uses an easy-to-follow, step-by-step learning method and has lots of worked-out problems. His blog, [http://blog.excelmasterseries.com/]Advanced Marketing Statistics in Excel, which explains how to do advanced marketing statistics in Excel to make better marketing decisions, is also rapidly growing in popularity. Finally, Business Statistics Made Simple!

Article Source: [http://EzineArticles.com/?The-t-Test---What-The-Heck-Is-It?&id=5257906] The t Test - What The Heck Is It?

The 5 Most Common Situations That Require Nonparametric Testing

Statistical procedures are either parametric or nonparametric. Parametric statistical tests require assumptions about the population from which the samples are drawn. For example, many data analysis tools such as the t Test, Chi-Square tests, z Tests, and F tests, and many types of hypothesis tests require the underlying population to be normally distributed. Some of these also require equal variances of both populations.

Sometimes these requirements cannot be assumed. Examples of this would be if the population is highly skewed or if the underlying distribution or variances were entirely unknown.

Nonparametric tools have no assumptions regarding distribution of underlying populations or variance. Most of this are very easy to perform but they are not usually as precise as parametric methods and the Null Hypothesis usually difficult to reject when using a nonparametric method.

When To Use Nonparametric Methods

1) The most important use of nonparametric tools occurs when samples are drawn from populations that are not known to be normally distributed. Parametric methods require that all underlying populations are normally distributed. Parametric testing will produce wrong answers when samples are taken from non-normally distributed populations. Non-parametric testing is one answer for this situation.

2) Nonparametric approaches are often used as shortcut replacements for more complicated parametric analysis. You can quite often get a quick answer that requires little calculation by running a nonparametric test.

3) Nonparametric tools are often used when the data is ranked but cannot be quantified. For example, how would you quantify consumer rankings such as very satisfied, moderately satisfied, just satisfied, less than satisfied, dissatisfied?

4) Nonparametric statistics can be applied when there are a lot of outliers that might skew the results. Nonparametric statistics often evaluate medians rather than means and therefore if the data have one or two outliers, the outcome of the analysis is not affected.

5) They come in especially handy when dealing with non-numeric data, such as having customers rank products or attributes according to preference.

The most widely-used nonparametric tests are:

- The Sign Test

- Wilcoxon Signed Rank

- Wilcoxon Ranked Sum

- Mann-Whitney

- Kruskal-Wallis

- Spearman Correlation Coefficient

My blog contains articles with specific instructions on how and when to do each one of these nonparametric tests in Excel. Nonparametric methods are perhaps more useful than the classic parametric tools which require that samples are drawn from normally distributed populations. Nonparametric testing is rarely taught in statistics courses. That is too bad because nonparametric testing can often be a real lifesaver for anyone who has to analyze data on a regular basis.

Mark Harmon has helped numerous marketers and business students understand how to use business statistics to solve real-world problems. His web site, [http://excelmasterseries.com/]The Excel Statistical Master, is becoming increasingly popular among people wishing for simplified instruction on how to perform graduate-level business statistics. It uses an easy-to-follow, step-by-step learning method and has lots of worked-out problems. His blog, [http://blog.excelmasterseries.com/]Advanced Marketing Statistics in Excel, which explains how to do advanced marketing statistics in Excel to make better marketing decisions, is also rapidly growing in popularity. Finally, Business Statistics Made Simple!

Article Source: [http://EzineArticles.com/?The-5-Most-Common-Situations-That-Require-Nonparame...] The 5 Most Common Situations That Require Nonparametric Testing