Question

Question 3. T-test Technique

a. Describe the purpose of the T-test technique

b. State at least two research problems or question that requires the use of the T-Test technique

c. Identify, describe and test the assumptions related to the T-Test technique.

d. State examples of the T-Test technique outcomes

e. State examples of the T-Test Technique report results

Answer 1

a. Describe the purpose of the T-test technique

A t-test is commonly used for testing the difference between the samples when the variances of two normal distributions are not known.

There are three main types of a t-test:

• An Independent Samples t-test compares the means for two groups.

• A Paired sample t-test compares means from the same group at different times (say, one year apart).

• A One sample t-test tests the mean of a single group against a known mean.

b. State at least two research problems or question that requires the use of the T-Test technique

Example 1: Let’s say you have a cold and you try a naturopathic remedy. Your cold lasts a couple of days. The next time you have a cold, you buy an over-the-counter pharmaceutical and the cold lasts a week. You survey your friends and they all tell you that their colds were of a shorter duration (an average of 3 days) when they took the homeopathic remedy. What you really want to know is, are these results repeatable? A t-test can tell you by comparing the means of the two groups and letting you know the probability of those results happening by chance.

Example 2: A drug company may want to test a new cancer drug to find out if it improves life expectancy. In an experiment, there’s always a control group (a group who are placebo or given a“sugar pill”). The control group may show an average life expectancy of +5 years, while the group taking the new drug might have a life expectancy of +6 years. It would seem that the drug might work. But it could be due to a fluke. To test this, researchers would use a t-test to find out if the results are repeatable for an entire population.

c. Identify, describe and test the assumptions related to the T-Test technique.

1. The scale of measurement: The assumption for a t-test is that the scale of measurement applied to the data collected follows a continuous or ordinal scale, such as the scores for an IQ test.

2. Simple Random Sample: The data is collected from a representative, randomly selected portion of the total population.

3. Normality: The data, when plotted, results in a normal distribution, bell-shaped distribution curve.

4. Homogeneity of variance: Homogeneous, or equal, variance exists when the standard deviations of samples are approximately equal.

d. State examples of the T-Test technique outcomes

The formula used to calculate the test is a ratio: The top portion of the ratio is the easiest portion to calculate and understand, as it is simply the difference between the means or averages of the two samples. The lower half of the ratio is a measurement of the dispersion, or variability, of the scores. The bottom part of this ratio is known as the standard error of the difference. To compute this part of the ratio, the variance for each sample is determined and is then divided by the number of individuals the compose the sample or group. These two values are then added together, and a square root is taken of the result.

where

= Proposed constant for the population mean

= Sample mean

n = Sample size (i.e., number of observations)

s = Sample standard deviation

= Estimated standard error of the mean (s/sqrt(n))

e. State examples of the T-Test Technique report results

The larger the t score, the more difference there is between groups. The smaller the t score, the more similarity there is between groups. How big is “big enough”? Every t-value has a p-value to go with it. A p-value is a probability that the results from your sample data occurred by chance. P-values are from 0% to 100%. They are usually written as a decimal. For example, a p-value of 5% is 0.05. Low p-values are good; They indicate your data did not occur by chance. For example, a p-value of .01 means there is only a 1% probability that the results of an experiment happened by chance. In most cases, a p-value of 0.05 (5%) is accepted to mean the data is valid.