Question

othods in Psychological Research PSYCH248 Dr Dunn Spring 2019 andra Computer Assignment #2 Comparing means using ttests This assignment will give research designs that all use SPSS to test the hypothesis, and you practice choosing the appropriate test statistic to use for different involve comparing means using t-tests. You will need to enter the data, means the samples differed significantly. To run all 3 -Hests use ANALYZE, COMPARE MEANS, then select the type of test and the variables. Problem 1: On a standardized spatial skills task, normative data reveal that people typically get u- 17 correct solutions. A rehabilitation psychologist tests 18 individuals who have brain injuries in the right cerebral hemisphere. Use the data presented below to determine whether right-hemisphere damage has significantly reduced performance on the spatial skills task. Lower scores indicate poorer spatial performance. Is the performance of this sample significantly lower than the normal Spatial skills scores for sample: 15, 16, 16, 19, 19, 15, 15, 14, 16, 15, 19, 16, 15, 14, 15, 18, 19.15 ldentify the State Hypotheses: Hol State Hypotheses in words. One-tailed or two-tailed? Proper t-test: Stat Perform the proper t-test using SPSS and print the output. Summarize the results of the statistical test and what it means in this study using APA-style (Hint: do you remember how to convert the output to make it a one-tailed test?)

Answer 1

Based on the given data, we have to test whether right hemisphere damage significantly reduces the performance on the spatial skill task.

Let $\mu$ denote the mean score of spatial skill task for subjects with right hemisphere damage.We have to test:

$H_{0}:\mu=17$ Vs   $H_{a}: \mu<17$

Using SPSS,

View Data Transform Analyze Direct Marketing Graphs Utilities Add-ons Window Help Reports Descriptive Statistics Tables Compare Means General Linear Model Generalized Linear Models Mixed Models Correlate Regression Loglinear Neural Networks Scores var Means. 15.00 16.00 16.00 19.00 19.00 15.00 15.00 One-Sample T Test.. Independent-Samples T Test.. Paired-Samples T Test. One-Way ANOVA.

Scores var One-Sample T Test 15.00 16.00 16.00 19.00 19.00 15.00 15.00 14.00 16.00 15.00 19.00 16.00 Test Variable(s): Options Scores Bootstrap... Test Value: 17 OK Paste Reset Cancel Help

We get the Output:

* T-Test [DataSeto] One-Sample Statistics Std. Error Mean MeanStd. Deviation 1.79050 Scores 18 16.1667 42202 One-Sample Test Test Value 17 95% Confidence Interval ofthe Difference Mean df ig. (2-tailed) Difference Lower Upper Scores 1.975 17 065 .83333 1.7237 0571

But SPSS gives the result for a two tailed t test, by default; Here, the value of the test statistic is compared with critical t for 17 df with 2 tailed significance (Rejection region |t| > t_critical). For two tailed test, |t| = 1.975 < 2.110; hence, the test is not significant.

Since, ours is a one tailed (left tailed) test, the rejection region would be t < - tcritical.

Here, t = - 1.975 < - 1.740. Hence, the test statistic does lie in the rejection region. Also, its p - value would be half of the two tailed p value i.e. p-value = 0.065 / 2 = 0.0325 (approx.) < 0.05 which is significant at 5% level. We may reject H₀ and conclude that right hemisphere damage significantly reduces the performance on the spatial skill task.

t Table cum one-tail0.50 0.25 0.20 0.15 0.10 0.05 0.025 0.01 0.005 0.001 0.0005 two-tails 1.00 0.50 0.40 0.30 0.200.10 0.05 0.02 0.01 0.002 0.001 6 8 4 1 0.000 1.000 .376 1.963 3.078 6.31412.7131.82 63.66 318.31 636.62 2 0.000 0.816 .0611.386 1.886 2.920 4.303 6.965 9.925 22.327 31.599 3 0.000 0.765 0.978 1.250 .638 2.3533.182 4.541 5.841 10.215 12.924 0.000 0.741 0.941 1.190 1.533 2.132 2.776 3.747 4.604 7.173 8.610 5 0.000 0.727 0.920 1.156 1.476 2.0152.5713.365 4.032 5.893 6.869 6 0.000 0.718 0.906 1.134 1.440 1.943 2.447 3.143 3.707 5.208 5.959 7 0.000 0.7110.896 1.119 1.415 1.895 2.365 2.998 3.499 4.785 5.408 0.000 0.706 0.889 1.108 1.397 1.860 2.306 2.896 3.355 4.501 5.041 0.000 0.703 0.883 1.100 1.383 1.833 2.262 2.821 3.250 4.297 4.781 00.000 0.700 0.879 1.093 1.372 1.8122.228 2.764 3.169 4.1444.587 11 0.000 0.697 0.876 1.088 1.363 1.796 2.201 2.718 3.106 4.025 4.437 12 0.000 0.695 0.873 1.083 .356 1.782 2.179 2.681 3.055 3.930 4.318 13 0.000 0.694 0.870 1.079 .3501.771 2.160 2.650 3.012 3.852 4.221 14 0.000 0.692 0.868 1.076 1.3451.761 2.145 2.624 2.9773.787 4.140 16 0.000 0.690 0.865 1.071 1.337 1.746 2.120 2,583 2,9213.686 4.015 1.740 2.110 190.000 0.688 0.861 1.066 1.328 1.729 2.093 2.539 2.861 3.5793.883 20 0.000 0.687 0.860 1.064 1.325 1.725 2.086 2.528 2.845 3.552 3.850 21 0.000 0.686 0.859 1.063 1.3231.72 2.080 2.518 2.8313.527 3.819 22 0.000 0.686 0.858 1.061 1.3211.717 2.074 2.508 2.819 3.505 3.792

In APA format:

A one sample t test was conducted to determine whether a significant difference existed between the scores obtained on spatial skill task for subjects with a right hemisphere damage and the normal subjects.

Subjects with right hemisphere damage had a significantly lower score ($\mu=16.167,sd=1.7905$) as compared to the normal population (t=-1.975,p = 0.0325).