Summary worksheet: Determining which statistical test to use
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To use the decision tree, you start on the left side and answer the question based on the
description of the design of the research (i.e., the homework/lab/exam question). Based
on the answer to the first question, take the appropriate path to the next question. And so
on. After asking these questions about the design, you should arrive at the appropriate
statistical test.
Suggestion: One good way to study this is to make flash cards for review. On one side of
the card list a description of a research design (i.e., a homework problem, a question from
a quiz, etc.). On the reverse side of the card, list which statistical test is the appropriate
one (you can also list the formula of the test statistic, what the hypotheses are, whether it
is one-tailed or two tailed, etc.). Then shuffle this deck up and flip through it as a self
test. As we learn more tests, add more cards to your deck.
Summary Worksheet – One Sample t-test
When? The one sample t-test allows us to extend our hypothesis testing procedures to
cases where we DO NOT know the population standard deviation (σ)
Steps for one sample t-test
1) State Hypothesis and find critical area (use t-distribution in PIP packet)
2) Compute sample statistic (SS) and sample standard deviation (s)
3) Compute t-score
4) Make decision by comparing t-score to critical region
Example: The quiz average for a class is 7.5. The teacher predicts that if classical
music is playing in the background the quiz scores will increase. She tries this out with 5
students and they score 7, 8, 8, 9, and 9. Using alpha set at 0.05 see if the teacher’s
hypothesis is supported.
1) State Hypothesis and find the critical area
Ho:
-2
-1

1
2
Ha:
2) Compute sample statistic (SS) and sample standard deviation (s) and estimated sample error (s x)
X
SS  X  X  
2
s
SS
n 1
sX 
s

n
3) Compute t-score – Where
t
X = mean of the sample and μx = mean of the population
X

sX
4) Make decision by comparing t-score to critical region
What steps to you use to run a single-samples t-test on SPSS?
Summary Worksheet – Paired Samples t-test
The paired samples t-test is used when one group of subjects is tested more than once.
Steps for one sample t-test
1) State Hypothesis and find critical area
a. Finding the critical area:
I. Is your test one-tailed or two?
II. What is alpha? (if not stated, assume it is 0.05)
III. Compute df = (N – 1)
IV. Using this information look to find the t-critical (see PIP packet)
2) Compute sample statistics
3) Compute t-score
4) Make decision by comparing t-score to critical region
Example: Let’s look at data illustrating the comparison of college student's motivation
scores before and after Thanksgiving break to see the effect of a week off of school.
Student
A
B
C
D
E
Before
65
68
50
75
80
After
70
69
55
73
82
difference
(difference)2
∑D=
∑ D2 =
Pre-step – Find the sum of the differences (D) and the sum of the differences squared (D 2).
1) State Hypothesis. When using a paired samples t-test the mean you are comparing the mean
of the difference between the scores to zero (0), because if there isn’t a change between the
before and after scores then the difference will be equal to zero (Ho).
Ho:
Ha:
Finding the critical area:
Step 1. One-tailed
or
Two-tailed?
-2
-1

Step 2. α =
Step 3. df =
t-critical =
1
2
Step 4. t-critical =
2) Compute sample statistics.
D
D
n
 D 

2
SSD   D
2
-OR-
n
standard deviation of differences:
sD 
standard error of the differences:
sD 
SSD  D  D 
2
SSD
nD
sD
nD
3) Compute t-observed. Remember the mean (μD) that we are testing our hypothesis against is
zero (0) because if there isn’t a change between the before and after scores then the difference
will be equal to zero (Ho).
tD 
D  D
sD
4) Make decision by comparing t-observed to t-critical
t-observed =
t-critical =
Running a paired-samples t-test on SPSS
Remember. When using SPSS
you do NOT need to find the tcritical in order to reject or fail to
reject the null. Instead what you
are comparing is alpha (α) to the
p-value computed by SPSS.
Summary worksheet – Independent Samples t-test
This design allows for a comparison between two different groups of individuals.
Individual samples t-tests do not control for individual differences, and thus have more
error than a paired samples t-test.
Steps for one sample t-test – Same as a paired samples t-test
Hypothesis.
One – tailed
Two – tailed (IV ↑ DV)
Two – tailed (IV ↓ DV)
Independent Samples t-test Formula.
t obs 
X
1
 X2  1  2 
sX  X 
1
2
Example: Let’s look at data illustrating the motivation scores of PSY138 student's
compared to the scores of the general population of ISU students. I believe that PSY
138 students are more motivated than the general population. Assume alpha = 0.05
X1
5
3
4
5
3
∑X1 =
X12
∑X12 =
X2
2
4
1
3
2
∑X2 =
X22
∑X22 =
Pre-step – Find the sum of the scores (X)for each group and the sum of the squared scores (X2).
1) State Hypothesis. When using a paired samples t-test the mean you are comparing the mean
of the difference between the scores to zero (0), because if there isn’t a change between the
before and after scores then the difference will be equal to zero (Ho).
Ho:
Ha:
Finding the critical area:
Step 1. One-tailed
or
Two-tailed?
Step 2. α =
-2
-1

Step 3. df =
t-critical =
Step 4. t-critical =
(Hint remember to look at the table in the PIP packet)
1
2
2) Compute sample statistics.
X
X
n
 X 

2
SS   X 2
n
- OR -
SS  X  X 
2
df = n - 1
s 2p 
SS1  SS2
df1  df2
sX  X  
1
2
s 2p
n1
s 2p

n2
3) Compute t-observed. Remember the means (μ1 & μ2) that we are testing our hypothesis
against are zero (0).
t obs 
X
1
 X2  1  2 
sX  X 
1
2
4) Make decision by comparing t-observed to t-critical
Running an independent-samples t-test on SPSS
t-observed =
t-critical =
TEST
One-sample t
WHEN DO YOU USE
THIS TEST?
HYPOTHESES
H0 & HA
Two-tailed
HOW DO YOU RUN
THIS TEST IN SPSS?
USING SPSS, HOW DO
YOU KNOW WHEN TO
REJECT OR FAIL TO
REJECT THE H0?
One-tailed
IV ↑ DV
IV ↓ DV
FORMULA:
Paired-samples t
Two-tailed
One-tailed
IV ↑ DV
IV ↓ DV
FORMULA:
independent-sample t
FORMULA:
Two-tailed
One-tailed
IV ↑ DV
IV ↓ DV
The following are examples of how to correctly write up the results of a one-sample, paired, or independent samples t-test. (Note: The # in the parentheses is the
degrees of freedom)
2-TAILED EXAMPLE: The early morning classes grades were significantly different from the later morning classes grades, t (7) = 2.34, p = .034. Thus, we can
reject the null hypothesis and fail to reject the scientific hypothesis that time of day affected grades.
1-TAILED EXAMPLE: The post-test mood rating was not significantly lower than the pre-test mood rating, t (67) = 3.45, p = .064. Thus, we can fail to reject the null
hypothesis and reject the scientific hypothesis that the quiz would decrease mood.
1-TAILED EXAMPLE: The final exam score was significantly higher for the quiz group compared to the no quiz group, t (56) = 6.57, p < .0005. Thus, we can reject
the null hypothesis and fail to reject the scientific hypothesis that quizzes increase exam grades.