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PSYC 212 Eighth Week Objectives True Experimental Research: Chapter 9 and 10 of the textbook Objectives Chapter 9. The t-test is a modified form of z and can be used when you do not have the population standard deviation available. When sample sizes are large (n = 100 or more) the estimate of standard error is a very close approximation of the population standard deviation and the results from a t-test or a z-test are practically identical. In summary, use t when o You have a sample size of less than 100 and o You do not know the population standard deviation One-Sample t-test: Just as its name implies, the one sample t-test is used when you want to compare a sample mean to a population mean or any “test mean” that you can imagine. The one tailed t-test is used to answer the question: Given a particular sample and corresponding sample mean (M), what are the odds that this sample has been drawn from a population with a particular mean value (μ)? The critical values you select will be based on the sample size (actually df), whether or not you are conducting a one-tailed or two-tailed test, and your chosen alpha level. USING SPSS Setting up a one-tailed t-test in SPSS is very simple. Simply open the program and enter your set of data under the first VAR column. You can name the variable by opening the variable view tab, but for now, leave it. Try the following with SPSS A sample of freshmen takes a reading comprehension test and their scores are summarized below. If the mean for the general population on this test is = 12, can you conclude that this sample is significantly different from the population? Test with = .05. Sample Scores: 16, 8, 8, 6, 9, 11, 13, 9, 10 Depending on your version of SPSS, things will look something like this: Click on the Analyze tab, then click on, Compare Means (that’s what every t-test does), then select OneSample t-test. A window will open up and ask you to select a test variable. You have only one so select it and click the arrow to move it over into the window. Then, enter the value for your population or test mean. In this case, = 12. Click OK and SPSS will open a new window with your results that looks like this: One-Sample Statistics N VAR00001 9 Mean 10.0000 Std. Deviation 3.00000 Std. Error Mean 1.00000 One-Sample Test Test Value = 12 95% Confidence Interval of the Difference VAR00001 t -2.000 df 8 Sig. (2-tailed) .081 Mean Difference -2.00000 Lower -4.3060 Upper .3060 All of the values should be familiar to you except for the confidence interval. The confidence interval tells you that if you took samples over an over again, 95% of the time, the difference between your sample mean and the test mean (M-μ) will be between -4.306 and 0.3060. Notice that zero is included in this range. This means that it would not be surprising to occasionally find that M and μ are exactly the same which would be the ultimate support of the null hypothesis. This is a helpful way to clarify what the t-test is telling you. If you are conducting a two-tailed t-test and you have exceeded the critical value for t, then zero will not be in the 95% confidence interval. Beating the critical value with α = 0.05 means that you are 95% sure that the difference is not zero. Get it? You do not need to look up anything on a t-table when you are using SPSS. SPSS doesn’t care what your value for α is, it will simply give you your probability (p) of making a Type I error if you reject the null hypothesis. This is given as Sig. (2-tailed). Here that value is 0.081 for a two-tailed test. If you set α at 0.05, your value for p is greater than α and you fail to reject the null hypothesis. HOWEVER, if you wish to run a one-tailed test, you know that the critical value for t would change. SPSS doesn’t care about critical values so the thing to remember is that the p value for a One-tailed test is simply half of that for a two-tailed test. In this case, if you were running a one-tailed test and if you had predicted that this sample mean would be lower than the population mean, your value for p would now become p = 0.04 and you would reject the null hypothesis. Lab Assignment (20 Points) - Print this sheet, write your answers on it, and turn it in along with your research plan sheet from last week. Recall the reaction time experiment you conducted at the beginning of the semester. Assume that a researcher has discovered that it takes 160 milliseconds for a visual message to get to the brain and 125 milliseconds for a motor message to get a finger to press a key. Use the set of data below to determine if there is a significant amount of processing going on during the Simple, Go/No-Go, and Choice reaction time tasks. That is, take each of the three sample sets and see of the sample means are significantly greater than 285 ms. Test the hypothesis that the mean reaction times for the Simple data set is significantly longer than 285 ms by hand below and show your work. If you decide to reject the null hypothesis, calculate Cohen’s d and state whether the effect size is small, medium or large. Simple 209 220 237 253 254 260 269 285 291 295 306 315 345 346 206 213 255 258 289 310 GNG Choice 275 367 401 450 387 510 373 492 603 754 377 420 295 495 394 463 294 361 433 388 405 503 465 591 564 411 386 501 330 457 326 349 396 515 360 369 344 395 396 465 n= df = Decision : d= sm = tcrit = t( )= USE SPSS to calculate t and p to test the hypothesis that the mean reaction times for the other two sets of sample data are greater than 285 ms. t( )= p= Decision : d= t ( )= p= Decision : d=