t-test Tutorial Aliza McConnahey & Josh Petkash

Transcription

1 t-test Tutorial Aliza McConnahey & Josh Petkash

2 t-testing? A t-test is used to test against the mean of a population when the population standard deviation is not known. In order to conduct a t-test, a sample size of 30 or more needs to be utilized. Or, the distribution needs to be approximately normal. The formula for a t-score can be used: x = sample mean μ= population mean s= sample standard deviation N= sample size

3 What to do? When performing a t-test, there are five steps which must be followed. 1. State the null and alternate hypothesis. -Null: The claim that is known Alternate: The claim to be tested- 2.) Compute the t-score or test value. 3.) Find the critical t-score from the t-distribution table. 4.) Make a decision to accept or not accept the alternate. -Compare the test value to the critical t-score- 5.) Summarize the results.

4 t-distribution table When using a t-distribution table, the degree of freedom, or df, should be the sample size minus one. The formula can be used: d.f.= n-1 Also, the probability values of.05 and.01 shall be used to determine the critical t-score.

5 Example: One of the best indicators of the health of a baby is his/her weight at birth. Birthweight is an outcome that is sensitive to the conditions in which mothers experienced pregnancy, particularly to issues of deprivation and poor diet, which are tied to lower birthweight. It is also an excellent predictor of some difficulties that infants may experience in their first weeks of life. The National Center for Health Statistics reports that although infants weighing 5 1/2 pounds (88 ounces) or less account for only 7% of births, they account for nearly 2/3 of infant deaths. In the United States, mothers who live in poverty generally have babies with lower birthweight than those who do not live in poverty. While the average birthweight for babies born in the U.S. is approximately 3300 grams, the average birthweight for women living in poverty is 2800 grams. Eliminating the linkage between poverty and low birthweight status has been a prominent dimension of health policy for the past decade. Recently, a local hospital introduced an innovative new prenatal care program to reduce the number of low birthweight babies born in the hospital. In the first year, 25 mothers, all of whom live in poverty, participated in this program. Data drawn from hospital records reveals that the babies born to these women had a birthweight of 3075 grams, with a standard deviation of 500 grams. The question posed to you, the researcher, is whether this program has been effective at improving the birthweights of babies born to poor women (ccnmtl.columbia.edu).

6 Step 1 x = 3075 grams μ= 2800 grams s= 500 grams N= 25 mothers Null hypothesis: The difference between the observed mean of birthweight for program babies and the expected mean of birthweight for poor women is zero. Alternative hypothesis: the difference between the observed mean of birthweight for program babies and the expected mean of birthweight for poor women is not zero.

7 Step 2 Using the equation previously stated, the t-score can be calculated:

8 Step 3 Using the degree of freedom of 24 (using the formula previously stated), and the probability values of.05 &.01, the critical t-scores can be determined. In review of the t distribution table, It can be determined that the critical t-scores are:.05 = = 2.492

9 Step 4 Calculated t-score: t = 2.75 Critical t-scores: t (.05) = t (.01) = The calculated t-score is greater than both critical t-scores.

10 Step 5 Because the calculated t-score is greater than both of the critical t-scores, there is significant evidence to accept that the difference between the observed mean of birthweight for program babies and the expected mean of birthweight for poor women is not zero.

11 What was learned? In using this tutorial, an accurate t-test can be performed. The t-score of a sample can be used to test the significance of the mean of a population when the standard deviation of that population is unknown. An accurate t-score calculation can be a very solid statistic to help determine the significance of the data portrayed.

12 Works Cited QMSS e-lessons. (n.d.). Retrieved May 20, 2015, from