PSYC 510 WORKSHEET:
Using hypothesis testing (with crv and obt values) to make conclusions
Background review (because there are a lot of new terms!):
Remember, we are always testing the null hypothesis using an alpha level (aka p value) of 0.05. This is the
probability value (hence why it is also called a p value) of making a Type I error. (Type I error is when a researcher
states there is an effect when in actuality there is no effect).
The “Obtained value” is the value produced by YOUR data. You can do this by hand, or SPSS output provides it.
oWhen using hand calculations, you use your given p value (also known as alpha value – and we always use
0.05 in this class) and other factors (e.g., degrees of freedom, one or two-tailed hypothesis) to look up a
“critical value” in the tables provided in the appendix of your textbook. Your obtained value must be larger
than your critical value to be significant. Your conclusions are either p>.05 (the null hypothesis fails to be
rejected - findings are NOT significant) or p < .05 (null hypothesis is rejected because your value was less
than .05 for making a Type I error, thus findings ARE significant).
oWhen using SPSS output, you don’t see a “critical value”. Rather, SPSS can give you the exact p-value of your
data. Since we use a p value (alpha value) of 0.05, if the SPSS column that says “Sig” is below 0.05, you get to
reject the null hypothesis and state there is a significant effect. You should write out the EXACT p value since
SPSS provides it. Here are two examples:
p=.032 – since this is BELOW .05, you reject the null hypothesis and conclude there WAS an effect
p=.475 – since this is larger than .05, you fail to reject the null hypothesis and conclude there is no
effect.
Now, let’s practice! Write out your answers and check yourself against the answer key at the
end of this document.
1. Given: robt = 0.40 and the df = 17 and the test was one-tailed
a. Determine the rcv.
b. What is the sample size?
c. Should you fail to reject (i.e. accept) or reject the null hypothesis?
d. How do you write this in APA format?
2. Given: robt = 0.40 and the df = 17 and the test was two-tailed
a. Determine the rcv.
b. Should you fail to reject (i.e. accept) or reject the null hypothesis?
c. How do you write this in APA format?
3. Given: robt = 0.40 and N = 17 and the test was two-tailed
Review of Material: finding and interpreting critical (crv) and obtained (obt) values as they relate to hypothesis testing
Information from: the portions assigned from chapters 7 and 8 in Jackson and all three Week 5 presentations
Additional practice: starting on slide #13 Week 5 correlations and regression to practice using a provided correlation
with no SPSS output (akin to hand calculations), and starting on slide #6 in Week 5 correlations and regression in SPSS
for practice reading SPSS output to interpret and present conclusions in APA format.
Note: this is an OPTIONAL worksheet to practice applying some of this week’s key concepts. Please make sure you
complete all assigned readings and watch this week’s presentations before attempting the worksheet! Try to complete
it on your own, then check your answers with the answer key details (at the end of the document).
a. Determine the rcv.
b. Should you fail to reject (i.e. accept) or reject the null hypothesis?
c. How do you write this in APA format?
4. Given the following output from SPSS examining the correlation between self-esteem and perceived control of
internal states (PCOISS), answer the following questions: (Note: both were likert-based scales and higher
numbers indicate greater degrees of self-esteem or perceived control, respectively).
a. What is the robt.
b. Calculate the degrees of freedom.
c. What is the p-value?
d. Should you fail to reject (i.e. accept) or reject the null hypothesis?
e. How do you write this in APA format?
5. Given the following output from SPSS examining the correlation between negative affect and perceived stress,
answer the following questions: (Note both were likert-based scales and higher numbers indicate greater
degrees of negative affect or perceived stress, respectively)
f. What is the robt.
g. Calculate the degrees of freedom.
h. What is the p-value?
i. Should you fail to reject (i.e. accept) or reject the null hypothesis?
j. How do you write this in APA format?
ANSWER KEY
Using hypothesis testing (with crv and obt values) to make conclusions (Week 5)
From Appendix A.4 in the e-book:
1. Given: robt = 0.40 and the df = 17 and the test was one-tailed
a. Determine the rcv. Read the df = 17 row first column that is .05 (note the table got scrunched when I
pasted it here, so the number before the decimal is the degrees of freedom; correlations never exceed
1.0, so hopefully you already caught this ;)) so our critical value is 0.3887
b. What is the sample size? Remember for correlations, df = N-2, so it’d be 17 = N-2, sample size thus is 19.
c. Should you fail to reject (i.e. accept) or reject the null hypothesis? Since our obtained value is larger than
our critical value, we get to reject the null hypothesis!!
d. How do you write this in APA format? A Pearson’s r correlation revealed a statistically significant
relationship between X and Y (variable names weren’t provided so these are placeholders), r (17) = 0.40,
p <.05 (one-tailed). 16% of the variation in X is accounted for by Y. (Note 16% was calculated by squaring
the r, i.e. by entering 0.40 and squaring it in my calculator).
2. Given: robt = 0.40 and the df = 17 and the test was two-tailed
a. Determine the rcv. Read the df = 17 row SECOND column for two tailed .05- so our critical value is 0.4555
b. Should you fail to reject (i.e. accept) or reject the null hypothesis? Since our obtained value does not
reach our critical value, we fail to reject the null hypothesis.
c. How do you write this in APA format? As evidenced by a pearson’s r correlation, there is no relationship
between X and Y (variable names weren’t provided so these are placeholders), r (17) = 0.40, p >.05 (two-
tailed). (NOTE you don’t report the coefficient of determination if it is nonsignificant!)
3. Given: robt = 0.40 and N = 17 and the test was two-tailed
a. Determine the rcv. Since we are not given the degrees of freedom, we first have to calculate this. Df = N-
2, so df = 17-2, meaning our df = 15. Read the df = 15 row SECOND column for two tailed .05- so our
critical value is 0.4821
b. Should you fail to reject (i.e. accept) or reject the null hypothesis? Since our obtained value does not
reach our critical value, we fail to reject the null hypothesis.
c. How do you write this in APA format? As evidenced by a pearson’s r correlation, there is no relationship
between X and Y (variable names weren’t provided so these are placeholders), r (15) = 0.40, p >.05 (two-
tailed). (NOTE you don’t report the coefficient of determination if it is nonsignificant!)
4. Given the following output from SPSS examining the correlation between self-esteem and perceived control of
internal states (PCOISS), answer the following questions: (Note: both were likert-based scales and higher
numbers indicate greater degrees of self-esteem or perceived control, respectively).
a. What is the robt. Read the line that says “Pearson correlation” so r = 0.549
b. Calculate the degrees of freedom. Since there are two separate sample sizes, note that SPSS uses the
smallest – make sure you use the N associated with the correlation, which in this example is N = 430.
Since Df = N-2, so df = 430-2 = 428
c. What is the p-value? 0.000 and since probability can never truly be 0 or 1.0, we will write it as p<.001
d. Should you fail to reject (i.e. accept) or reject the null hypothesis? Since the “sig” value is less than .05
we reject the null hypothesis. (Conceptually it is because the probability of making a Type 1 error is less
than .001 if we state there is a relationship, thus we are rejecting the null hypothesis.)
e. How do you write this in APA format? A Pearson’s r correlation revealed a statistically significant
relationship between self esteem and perceived control of internal states, r (428) = 0.549, p <.001 (two-
tailed). 30.14% of the variation in self esteem is accounted for by perceived control of internal states.
(Note 30.14% was calculated by squaring the r, i.e. by entering 0.549 and squaring it in my calculator).
5. Given the following output from SPSS examining a potential positive correlation between negative affect and
perceived stress, answer the following questions: (Note both were likert-based scales and higher numbers
indicate greater degrees of negative affect or perceived stress, respectively)
a. What is the robt. Read the line that says “Pearson correlation” so r = 0.647
b. Calculate the degrees of freedom. Df = N-2, so df = 432-2 = 430 (see comment in #4b)
c. What is the p-value? 0.000 and since probability can never truly be 0 or 1.0, we will write it as p<.001
However – please note that if the sig line reads any other number, you must write out the EXACT value –
do not just write p< .05 or p>.05 when basing it off of SPSS output, because precision is always preferred
in research, and an exact number is way more telling than simply < or > .05.
d. Should you fail to reject (i.e. accept) or reject the null hypothesis? Since the “sig” value is less than .05
we reject the null hypothesis. (Conceptually it is because the probability of making a Type 1 error is less
than .001 if we state there is a relationship, thus we are rejecting the null hypothesis.)
e. How do you write this in APA format? A Pearson’s r correlation revealed a statistically significant
relationship between negative affect and perceived stress, r (430) = 0.674, p <.001 (one-tailed). 45.23%
of the variation in negative affect is accounted for by perceived stress. (Note 45.23% was calculated by
squaring the r, i.e. by entering 0.674 and squaring it in my calculator).
NOTE: There are still opportunities for extra practice! Try following along with examples:
starting on slide #13 Week 5 correlations and regression to practice using a provided
correlation with no SPSS output (akin to hand calculations), and starting on slide #6 in Week
5 correlations and regression in SPSS for practice reading SPSS output to interpret and
present conclusions in APA format.
