Question

I did the SPSS work, but I struggle to write the results in APA format

An investigator wishes to compare the effects of two different training methods on the performance of a particular task. He recruits 16 participants and randomly assigns them to Training Method 1 or Training Method 2. Assume that the following results are obtained, where higher scores indicate better performance. Training Method Performance Method 1: 7, 8, 10, 14, 12, 13, 15, 16 Method 2: 5, 3, 12, 10, 11, 10, 12, 12 Conduct an appropriate statistical test using SPSS and a = .05. There is no data file; you must enter the data yourself. Write the results in paragraph form and attach your SPSS output.

Answer 1

To carry out this independent t test we will see all the assumptions are satisfied.

• Two populations are independent to each other.
• Samples are randomly selected.
• Populations variances are equal and unknown.  

To see if the Equal variances assumption satisfied. See Levene's Test P value= 0.973 > 0.05 therefore Populations variances are equal.

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho: μ1​ = μ2​

Ha: μ1​ ≠ μ2​

This corresponds to a two-tailed test, for which a t-test for two population means, with two independent samples, with unknown population standard deviations will be used.

(2) Rejection Region: Based on the information provided, the significance level is α=0.05, and the degrees of freedom are df=14. In fact, the degrees of freedom are computed as follows, assuming that the population variances are equal:

Hence, it is found that the critical value for this two-tailed test is tc​=2.145, for α=0.05 and df=14.

The rejection region for this two-tailed test is R={t:∣t∣>2.145}.

(3) Test Statistics

Since it is assumed that the population variances are equal, the t-statistic is computed as follows:

test statistic t=1.485

(4) Decision about the null hypothesis

Since it is observed that ∣t∣=1.485≤tc​=2.145, it is then concluded that the null hypothesis is not rejected.

Using the P-value approach: The p-value is p = 0.1596 p=0.1596≥0.05, it is concluded that the null hypothesis is not rejected.

(5) Conclusion: It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that the population mean μ1​ is different than μ2​, at the 0.05 significance level.