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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=