T-Test and Anova

We conduct an independent sample t-test using Excel, and obtain the following output (see t-test-height)

15 In testing the hypotheses: H0 β1 ’ 0: vs. H1: β 1 ≠ 0 , the following statistics are available: n = 10, b0 = 1.8, b1 = 2.45, and Sb1= 1.20. The value of the test statistic is:

When you perform a test of hypothesis, you must always use the 4-step approach: i. S1:the “Null” and “Alternate” hypotheses, ii. S2: calculate value of the test statistic, iii. S3: the level of significance and the critical value of the statistic, iv. S4: your decision rule and the conclusion reached in not rejecting or rejecting the null hypothesis. When asked to calculate p–value, S5, relate the p-value to the level of significance in reaching your conclusion.

If 9 t tests were conducted and the set alpha for this study is 0.05, then the alpha level that should be used to determine the differences between the two groups is 0.05/9=0.0056 and the resulting alpha will be used to determine significant differences.

This test is a bit more complicated, in particular because the degrees of freedom are calculated from a much more complicated formula. Statistical software packages will handle this part for you under normal circumstances, but if you need to have the formula, here it

V. What changes to your original idea/USP/aims do you have to consider in light of this new data?

The t-test is a parametric analysis technique used to determine significant differences between the scores obtained from two groups. The t-test uses the standard deviation to estimate the standard error of the sampling distribution and examines the differences between the means of the two groups. Since the t-test is considered fairly easy to calculate, researchers often use it in determining differences between two groups. When interpreting the results of t-tests, the larger the calculated t ratio, in absolute value, the greater the difference between the two groups. The significance of a t ratio can be determined by comparison with the critical values in a

In a quantitative analysis the interest is more likely to compare means or variances; whereas, a qualitative experiment with two outcomes is more likely to focus on success or failure. When comparing the means of two or more groups these populations can both or all be independent and the expectation is to determine the reason for a difference in the means—this would deliver a result where the means are other than zero. The typical assumption is that there will be a normal distribution and that a random sample is collected for each of the populations. Another characteristic of comparing means of two or more groups is that when standard deviation is known or unknown and the population sample is large, then a z distribution (z-test) is used and in the case where it is unknown and the sample size is small, then a t distribution (t-test) is used. However, in the case where the experiment calls for a test of two or more dependent samples for one group or population, then a paired t-test is used to draw results (Lind, Marchal, & Wathen, 2011).

Analysis of variance is a statistical method used to test differences between two or more means. ANOVA is used to test general rather than specific differences among means. An ANOVA conducted on a design in which there is only one factor is called a one-way ANOVA. The One-Way ANOVA is considered an omnibus test because it indicates whether or not there are any significant differences in the means between any of the groups. However, it does not indicate which mean are different. The One-way ANOVA compares the means of the samples or groups to make inferences about the population means. The one-way ANOVA, two kinds of variables: independent and dependent. Also, the one-way ANOVA is used to determine whether there are any statistically

Two boats, the Prada (Italy) and the Oracle (USA), are competing for a spot in the upcoming America’s Cup race. They race over a part of the course several times. The sample times in minutes for the Prada were: 12.9, 12.5, 11.0, 13.3, 11.2, 11.4, 11.6, 12.3, 14.2, and 11.3. The sample times in minutes for the Oracle were: 14.1, 14.1, 14.2, 17.4, 15.8, 16.7, 16.1, 13.3, 13.4, 13.6, 10.8, and 19.0. For data analysis, the appropriate test is the t-Test: Two-Sample Assuming Unequal Variances.

We conduct an independent sample t-test using Excel, and obtain the following output (see sheet T-TEST)

Conclusion : Reject the null hypothesis. The sample provide enough evidence to support the claim that mean is significantly different from 12 .

The paired t-test is a parameter test that compares the means between two correlated pair

Sue: if we have these vendors in house (testing/trials) and runs through August we would be running 2 programs simultaneously.

s squared subscript p=(n1-1)s squared2 subscript1+(n2-1)s squared2 subscript2]/n1+n2-2. The numerator of the function, n1+n2-2, is the degrees of freedom.