Description
answer the following questions
Unformatted Attachment Preview
This assignment is related to your Chapter 11 (Salkind) material. Please save your responses to
this assignment, as you will need them for your discussion assignment this week!
Instructions: In 2023, the Denver Nuggets unfortunately beat the Miami Heat in the NBA
Championships. Beth is a Nuggets fan. Alex is Heat fan. Even though the Nuggets won the
championship, they need to know once and for all: which team had the better players during the
regular season in 2023? You decide to test this using an independent samples t-test to compare
the average points per game for the players on each team during the regular season.
Flag question: Spacer
data table
NUGGETS PLAYER NAMES
Aaron Gordon
Bones Hyland
Bruce Brown
Christian Braun
Davon Reed
DeAndre Jordan
Ish Smith
Jack White
Jamal Murray
Jeff Green
Kentavious Caldwell-Pope
Michael Porter Jr.
Nikola Jokic
Peyton Watson
Reggie Jackson
Thomas Bryant
Vlatko Cancar
Zeke Nnaji
POINTS PER GAME
16.3
12.1
11.5
4.7
2.3
5.1
2.5
1.2
20
7.8
10.8
17.4
24.5
3.3
7.9
4.6
5
5.2
Flag question: Question 1
Question 10 pts
Data
HEAT PLAYER NAME
Points Per Game
Bam Adebayo
20.4
Caleb Martin
9.6
Cody Zeller
6.5
Dewayne Dedmon
5.7
Dru Smith
2.2
Duncan Robinson
6.4
Gabe Vincent
9.4
Haywood Highsmith
4.4
Jamal Cain
5.4
Jamaree Bouyea
3.8
Jimmy Butler
22.9
Kevin Love
7.7
Kyle Lowry
11.2
Max Strus
11.5
Nikola Jovic
5.5
Omer Yurtseven
4.4
Orlando Robinson
3.7
Tyler Herro
20.1
Udonis Haslem
3.9
Victor Oladipo
10.7
Question 2
What is the null hypothesis?
Question 3
What is the alternative hypothesis?
Question 4
What is the risk level?
.01
.5
.25
.05
Question 5
What is the best statistical test to use?
t-Test for independent samples
t-Test for dependent samples
z-test
ANOVA
correlation test
Question 6
Compute the test statistic. The formula is below for you. Also, remember to use the
variance rather than the standard deviation in your calculation. You have already calculated
the variance for your previous assignment, so that part is already done! Put your
calculated t value below, round your answer to two decimal places:
Question 7
Now it’s time to compare our obtained value (the one you just calculated) to the critical
value. First, we’ll need the degrees of freedom. What are the degrees of freedom?
28
36
39
40
Question 8
Should we use a “one tailed” or a “two tailed” test for this?
Hint: To figure this out, think about whether it is directional or non-directional. Take a
look at your alternative hypothesis (above!), and think about the prompt for the
assignment—did we expect a specific team to be better than the other (directional), or
are we simply looking at whether the teams are different (non-directional)?
two tailed
one tailed
Question 9
What is the critical value for this statistical test? (hint: you’ll need your answers to the
previous two questions, as well as your “level of risk”; remember, if the exact degrees of freedom
aren’t in the t-test table of critical values, you can choose the closest value that is there).
1.69
2.438
2.021
2.03
Question 10
Write up your results as you would see it in a results section of an empirical research
paper (in APA style). Make sure to include the means and SDs.
Question 11
Based on your answer to the previous question, what is your decision?
Reject the null hypothesis
Not enough information to decide
Fail to reject the null hypothesis
Question 12
Imagine that you also wanted to compare if there was a difference between the average
amount of time people get stuck in traffic in Denver versus Miami (unlike all the other
data we have used this semester, these results are entirely made up!).
An independent samples t-Test comparing the average amount of time spent in traffic
per week was statistically significant t(500) = 4.56, p < .05. The average time spent in
traffic was significantly more for those living in Miami (M = 1.84, SD = .75) than in
Boston (M = 1.22, SD = 0.25)
Calculate the effect size for this new t-test, using the Pooled Variance Formula (Below).
Round your answer to two decimal places.
Question 13
What "size" is this effect size?
Small
Medium
Large
There isn't enough information to answer this question.
Chapter Eleven (Salkind)
t(ea) For Two:
Tests Between The Means Of Different Groups
One IV With Two Levels
One caveat before we move deeper into this chapter …
When we discuss studies that have two groups, students often
get a little confused and think we are looking at two different
independent variables. This is a mistake!
When looking at two group designs in this chapter, we are still
focusing on one independent variable—it just happens to have
two levels. For example, “Condition” might be our single IV, but
the two levels in “Condition” include 1). the experimental group
and 2). the control group. To put it another way …
Any IV Has At Least Two Levels
An independent variable, almost by definition, involves the
comparison of at least two different levels. Take the control
group and the experimental group design …
– If the “experimental” group is its own IV, then what are you
comparing it to?
You may be tempted to say “the control group”. But if
you mistakenly think the control group is a second IV,
then what are you comparing that group to?
Circular argument, right! No, we have one IV with two
levels (experimental versus control)
More Complex Research Designs
Of course, this doesn’t mean that we can’t have a second IV in
a research study. In fact, lots of studies look at more than one
IV at a time, something you will see more next semester when
you begin Research Methods and Design II. In that class, you
will actually run a 2 X 2 factorial study (two IV’s with two levels
each, or four conditions)!
What About More Than Two Levels?
We could also have a single independent variable that has
three levels (maybe two different control conditions and one
experimental condition), four levels, or a hundred levels!
Just keep in mind that the number of IVs and number of levels
for the IV are two different concepts
For our present Chapter 11, though, we are only going to focus
on one IV, and our one IV has two levels (or two groups total)
Good & Bad News
Here’s the bad news …
– We have another formula, a looooong one, but one we will
figure out together
Here’s the good news!
– We see the SPSS t-Test version, too! Yes, that’s good news
– We will once again use our 8 steps for significance (from
Chapter 9) to see how two groups differ from one another
Chapter Outline
In this chapter we cover the following items …
Part One: Introduction To The t-Test For Independent Samples
Part Two: Computing The Test Statistic
Part Three: Special Effects: Are Those Differences For Real?
Part Four: Using The Computer To Perform A t-Test
Part Five: An Eye Toward The Future
Part One
Introduction To The t-Test For Independent Samples
Trick or Treat!
Imagine you are twelve years old, trick-or-treating for what may
be the last time before you are “too mature for that nonsense”
You’re a little greedy with the candy. You’re twelve, so the
more candy the better, right?
What Would You DO?
You approach a house where no one is obviously at home, but
the front porch light is on and you happen to see a pot of gold!
Literally – a pot of golden (chocolate) coins.
No one is around. It’s you and that candy. There’s a sign that
says “Please take no more than three pieces.” Do you comply,
or do you dig in like the greedy pirate you might be dressed as?
Let’s Test This Question!
Let us set up a couple of different study groups, much like a
researcher name Gibbons once did
– Group #1: There is a large mirror right behind the candy
bowl (plus the note!). This way, the trick-or-treater will see
themselves in the mirror (which might make them pause in
deciding to break the “take only three pieces of candy” rule)
– Group #2: There is no mirror. It’s just a bowl of candy with
the note pleading to take no more than three pieces
Who do you think will break the “three piece” rule more often?
What Kind of Study Design?
Let’s take a step back and figure out what kind of study design
we need in order to look at our two trick-or-treater conditions
– 1. Are you examining relationships between variables or are
you examining the difference between groups?
In Chapter 11, we are looking
at two different groups, not
variables, so we choose our
between groups option
Are Participants The Same?
– 2. Next, we must ask ourselves, “Are the same participants
being tested more than once?”
If yes, it will lead us to a test that deals with dependent
samples (which we will get to in Chapter 12, Salkind)
If no (which is our answer here), we have one more
question to ask: How many groups are we dealing with?
How Many Groups?
– 3. How many groups are we dealing with?
If we are looking at only two groups (which we are), we
will use a t-Test for independent samples
If we are looking at more than two groups (at least three
minimum), we will use an analysis of variance (ANOVA)
Don’t worry – we’ll get to this one in Chapter 13!
These decisions might be easier with a handy flow chart …
This is where
we are in
Chapter 11
Pop-Quiz 1: Quiz Yourself
The t-Test for independent means is used when there are
____________________.
A). only two groups in total
B). only one group
C). two groups or more
D). one group or more
Answer 1: A
The t-Test for independent means is used when there are
____________________.
A). only two groups in total
B). only one group
C). two groups or more
D). one group or more
Pop-Quiz 2: Quiz Yourself
If you want to examine the difference between the average
scores of three unrelated groups, which of the following
statistical techniques should you select?
A). Regression
B). Dependent samples t test
C). Analysis of variance
D). Independent samples t test
Answer 2: C
If you want to examine the difference between the average
scores of three unrelated groups, which of the following
statistical techniques should you select?
A). Regression
B). Dependent samples t test
C). Analysis of variance – We’ll get to this one in our later!
D). Independent samples t test
Assumption # 1
All statistical tests have assumptions, and the t-Test is no
different. Here are the three assumptions to keep in mind …
– First, t-Tests assume a homogeneity of variance between
the two groups in the study
This is just a fancy way of saying that the amount of
variability in one group is similar to the amount of
variability in the other group
The larger the sample size, the more likely variance will
be homogenous (this is something we will discuss more
next semester in Research Methods and Design II)
Assumption # 2
All statistical tests have assumptions, and the t-Test is no
different. Here are the three assumptions to keep in mind …
– Second, t-Tests assume that we are using data based on
the mean (rather than the median or the mode). As long as
we have scaled, continuous data (plus a normal curve for
each condition), we can determine a mean (average), and
thus we can use the t-Test
Assumption # 3
All statistical tests have assumptions, and the t-Test is no
different. Here are the three assumptions to keep in mind …
– Third, in Research Methods at FIU, we will only look at tTests that have two groups, but there are other t-Tests—like
a single samples t-Test—that compare one sample mean to
something like the population mean (much like we did with
the Z-test).
Part Two
Computing The Test Statistic
Computing The Test Statistic: t -Test
Computing The Test Statistic – The Independent Samples t-Test
Ready for that loooooong formula? Here it is.
=
1 − 2
1 − 1 12 + 2 − 1 22 1 + 2
1 + 2 − 2
1 2
This Formula Is Not As Hard As It Looks!
Let’s unpack this a bit now …
Computing The Test Statistic: t -Test
Computing The Test Statistic – The Independent Samples t-Test
t-Test Formula
=
1 − 2
1 − 1 12 + 2 − 1 22 1 + 2
1 + 2 − 2
1 2
1 is the mean for group 1
2 is the mean for group 2
n1 is the number of participants in Group 1
n2 is the number of participants in Group 2
12 is the variance for Group 1
22 is the variance for Group 2
Really, Don’t Worry!
Like I said, don’t panic. We’ve already done a lot of these
calculations before (like variance), this just puts them into a
slightly longer formula
Study Design Summary
Before we start plugging in numbers, recall our study design
– We have two conditions (one independent variable, though it
has two levels)
In condition #1, we have a mirror behind the candy bowl
In condition #2, we do not have a mirror
In BOTH conditions, we have a sign that says “Take no
more than three pieces of candy”
– Our dependent variable is how many pieces of candy the
trick-or-treaters actually take
Step 1 (of 8)
Step One: State The Null And Alternative Hypotheses
– These are easy, right:
Null hypothesis: The groups do not differ, Ho: µ1 = µ2
Alternative hypothesis: The groups differ, H1: 1 ≠ 2
This hypothesis looks non-directional, right? we’re not
predicting that they differ in a specific way, just that they’re
different! Keep this in mind for later.
– Why am I predicting the groups will differ? An important part
of hypothesis building (which we will discuss a lot when you
get to Research Methods and Design II) is relying on theory
to help justify your hypotheses
Theory to Support The Hypothesis
– Social psychologist Gibbons used the theory of self-focusing
situations to predict that people who are more aware of
themselves “self-focus” more. When thinking about yourself,
it’s easier to ask, “Would I be a good person if I did this?”
– Research shows that de-individuated people (those who are
not self-aware, like rioters caught up in the excitement of a
mob!) are more likely to act against their own morals.
– Halloween costumes can easily de-individuate people. That
is, you lose your sense of “self” when in costume. But if you
see yourself in a mirror, it might remind you of … you!
Of course, this threat
might be a good way
to get obedience from
trick-or-treaters, too!
Steps 3 & 4 (of 8)
Step Two: Set The Level Of Risk
– Again, pretty easy. In psychology we’ll stick with p < .05
Step Three: Select The Appropriate Test Statistic
– We know from our nifty flowchart (and the fact that we are
comparing only two groups on a dependent variable that
relies on the mean) that we are using an independent
samples t-Test
Step 4 (of 8)
Step Four: Compute The Test Statistic Value
– Okay, ready for the hard part?
– First, we need our data set, so let’s see how many pieces of
candy trick-or-treaters take (Warning: I am making this data
up!). Let’s say we have 20 trick-or-treaters in each condition,
so total n = 40 …
Data for Groups 1 and 2
DV = Pieces of Candy Taken
Group #1 – Mirror Present
5
7
5
4
3
3
5
2
3
4
2
4
3
3
3
Group #2 – Mirror Absent
7
6
7
8
8
6
12
9
3
11
9
8
8
10
4
3
4
7
5
8
5
4
-
Mean = 80/20 = 4 pieces each
13
14
5
-
Mean = 160/20 = 8 pieces each
Computing The Mean
– We must first compute the mean and the variance
The mean is easy.
For condition #1 (mirror present), we have 20 scores
(20 participants) and a total of 80 pieces of candy
taken. 80/20 = a mean of 4 pieces taken
For condition #2 (mirror absent), we have 20 scores
and a total of 160 pieces of candy taken. 160/20 = a
mean of 8 pieces taken
Computing The Variance
– We must first compute the mean and the variance
The variance you’re also familiar with calculating!
Do you recall our variance formula? If not, here it is!
2
Σ
−
ҧ
2 =
−1
– Since you’re already very familiar with how to calculate the
variance (and SD), I’m not going to go through the steps
here. However, if you’d like a little reminder of how to do it,
scroll allllll the way to the end of this lecture, and you can
see the calculations worked out step by step.
Computing The Test Statistic: t -Test
Computing The Test Statistic – The Independent Samples t-Test
Recall our t-Test Formula
=
1 − 2
1 − 1 12 + 2 − 1 22 1 + 2
1 + 2 − 2
1 2
1 is the mean for group 1 = 4
2 is the mean for group 2 = 8
n1 is the number of participants in Group 1 = 20
n2 is the number of participants in Group 2 = 20
12 is the variance for Group 1 = 2.32 (s1 or SD would be 1.52)
22 is the variance for Group 2 = 8.53 (s2 or SD would be 2.92)
Plugging In Values
=
4−8
20 − 1 2.32 + 20 − 1 8.53 20 + 20
20 + 20 − 2
20 ∗ 20
Note: This is the variance! If you have the SD, make sure to square it
to get the variance for 2.32 and 8.53. Also, be sure not to accidentally
square the variance again! The variance is already squared.
Working Through The Formula
−4
=
19(2.32) + 19 8.53 40
38
400
−4
=
44.08 + 162.07
.10
38
=
=
−4
5.425 .10
−4
−4
=
= −5.43
.5425 .73654
= −5.43
What Now?
t = – 5.43
Phew, all done! Or are we? What does a t value of – 5.43 really
tell us? Well, first let’s discuss that minus sign.
– We can actually ignore the negative or positive sign in
dealing with our t-Test statistic. Why?
– The negative or positive sign for our t-value all depends on
what we arbitrarily designate as “group 1” or “group 2”
– In other words, just ignore the negative sign!
Now, on to step 5!
Pop-Quiz 3: Quiz Yourself
In the formula that computes a t value, what does s12
represent?
A). Scores for group one
B). Mean for group one
C). Number of participants for group one
D). Variance for group one
Answer 3: D
In the formula that computes a t value, what does s12
represent?
A). Scores for group one
B). Mean for group one
C). Number of participants for group one
D). Variance for group one
Step 5 (of 8)
Step Five: Determine The Value Needed To Reject The Null
– Our “obtained” t-Test statistic value is of course t = 5.43
– We need to determine our “critical” value next
That is, what value does 5.43 need to be larger than in
order to say that 5.43 is so rare that it would occur by
chance in only 5% of the time?
Using The T-Test Table
– We actually have a t-Test table (much like our z Score table)
where we can look up our critical value.
You can find this table in Appendix B.2. (Salkind),
However, you can find the exact same table in
Appendix A of your Smith and Davis textbook
Yep, it is a table of standard t-values, so the table is
identical no matter where you find it!
Three Things We Need
– You’ll need three pieces of information to find the critical
value in the t-test table:
1. Your desired p values
2. Whether you’re doing a One-Tailed test or a TwoTailed
3. You’ll also see df (degrees of freedom)
Let’s look at each of these …
Choosing The P Value
1. There are tabled values for different p values
Salkind (and Smith & Davis) have t values for the p < .10
level, p < .05 level, and p < .01 level
We picked .05 in step 2, so we will use that!
One or Two Tailed Test?
– 2. One-tailed tests versus two-tailed tests
The difference between the one-tailed versus two-tailed
tests depends on whether you predict a specific outcome
or a more general outcome
For a specific outcome (Group A will be higher than
Group B, or Group A will be lower than Group B), the
one-tailed is best. This is a directional test
Consider our Halloween candy study …
One Tailed Tests Are Directional
– 2. One-tailed tests versus two-tailed tests
If you predict that trick-or-treaters in the mirror absent
condition will take more candy than those in the mirror
present condition, then use a one-tailed test
If you predict that trick-or-treaters in the mirror absent
condition will take less candy than those in the mirror
present condition, then use … a one-tailed test
Either way, you have a directional hypothesis, thus you
use a one-tailed t-Test.
Two Tailed Tests are Non-Directional
– 2. One-tailed tests versus two-tailed tests
For a general outcome (Group A will simply differ from
Group B), the two-tailed test is best.
If you predict trick-or-treaters in the mirror absent
condition will take a different amount of candy than
those in the mirror present condition, then use a twotailed test. Thus it could be higher OR lower
If you have a non-directional hypothesis, use a two
tailed t-Test.
One Tailed vs. Two Tailed
– 2. One-tailed tests versus two-tailed tests
It is easier to find significance using a one-tailed t-Test
Check yourself in Appendix B.2. If df = 1 (the first
row), for a one-tailed test to be significant at the .05
level, you only need to have a t value above 6.314.
For a two-tailed test to be significant at the same .05
level, your t-value needs to be above 12.706!
That’s quite a high critical t value to overcome
Pop-Quiz 3: Quiz Yourself
What t value for a one-tailed t-Test do you need to overcome
if your df is 55 and your risk is p < .05?
A). 1.297
B). 1.673
C). 2.396
D). 1.673
E). 2.004
Answer 3: B
What t value for a one-tailed t-Test do you need to overcome
if your df is 55 and your risk is p < .05?
A). 1.297
B). 1.673
C). 2.396
D). 1.673
E). 2.004
Pop-Quiz 4: Quiz Yourself
What t value for a two-tailed t-Test do you need to overcome
if your df is 55 and your risk is p < .05?
A). 1.297
B). 1.673
C). 2.396
D). 1.673
E). 2.004
Answer 4: E
What t value for a two-tailed t-Test do you need to overcome
if your df is 55 and your risk is p < .05?
A). 1.297
B). 1.673
C). 2.396
D). 1.673
E). 2.004
Why Would You Do A Two Tailed Test?
So why would you ever use a two-tailed t-Test if it is
harder to find significance?
The next few slides go on a bit of a tangent about why
you would use a one tailed vs a two tailed test.
Pay close attention, these concepts are important!
More About Two Tailed Tests
A two-tailed test splits up the 5% error. Half is at the bottom of
the normal curve (.025) while the other half is at the top (.025)
– Just like we did with the one sample z-tests!
– This is because your hypothesis is looking for a significant
effect in both directions (that either group 1 has a higher
mean OR that group 1 as a lower mean).
The Normal Curve (Again)
This curve represents all the possible t-values (outcomes of our study).
t-values at the far right represent outcomes in which the mean for group 1
was higher than group 2
t-values at the far left represent outcomes in which the mean for group 1
was lower than group 2
With a two-tailed test, our hypothesis is that it could go either way!
Accepting The Null (two-tailed)
Null hypothesis: The groups do not differ, Ho: µ1 = µ2
Alternative hypothesis: The groups differ, H1: 1 ≠ 2
t-values of this size happen too frequently (95% of the time), it is
not significant. The groups are equal (not different)
Accepting The Alternative (two-tailed)
Null hypothesis: The groups do not differ, Ho: µ1 = µ2
Alternative hypothesis: The groups differ, H1: 1 ≠ 2
if your t value is here or here, you accept the
alternative hypothesis.
t-values of this size happen infrequently, it is probably
not due to chance. The groups are different.
More About One-Tailed Tests
The one-tailed critical value is easier to overcome. All of
that 5% error is on one side of the curve. Thus you need
to be sure that the outcome would occur only 5 times out
of a 100 by chance. No splitting percentages here!
Accepting The Null (One-Tailed)
Null hypothesis: The groups do not differ or they differ in the opposite of the
expected direction , Ho: µ1 ≤µ2
Alternative hypothesis: The groups differ only in the expected direction, H1:
1 > 2
t-values of this size happen too frequently (95% of the time), it is
not significant. The groups are equal (not different), or they differ
in the wrong direction.
Accepting The Null (One-Tailed)
Null hypothesis: The groups do not differ or differ in the opposite of the
expected direction , Ho: µ1 ≤µ2
Alternative hypothesis: The groups differ only in the expected direction, H1:
1 > 2
NOTE: Even if your t value is down here, in the opposite of the
expected direction, this is still part of the null hypothesis (it is not
the expected effect) Ho: µ1 ≤µ2
Accepting The Alternative (one-tailed)
Null hypothesis: The groups do not differ or differ in the opposite of the
expected direction , Ho: µ1 ≤µ2
Alternative hypothesis: The groups differ only in the expected direction, H1:
1 > 2
if your t value is here, you accept the alternative
hypothesis.
t-values of this size happen infrequently, it is probably not
due to chance. Group 1 has a higher mean than Group 2
Summary: One Vs Two Tailed Tests
If you’re not sure which direction your results could go, you should do a
two-tailed test.
If you do a one-tailed test, and you get the opposite of your expected
findings, then you’d be unable to accept the alternative hypothesis! You’d
have to accept the null.
Even if it’s harder to find a significant effect with a two-tailed test, it is
worth doing if you think there is a chance your results might go either
way.
Most researchers stick with a two-tailed test.
Degrees of Freedom
Wow, that was a lot…where were we again? Oh right, finding the
critical value. We have the first two pieces of info we need to find
the critical value, now we just need:
– 3. df (degrees of freedom)?
The third element in our Appendix table is the degrees of
freedom, or the df. These are based on sample size for
each group, and use the formula …
df = (n1 – 1) + (n2 – 1)
For our Halloween candy example, this is easy
df = (20 – 1) + (20 – 1) = 19 + 19 = 38
Warning About The T-Table
Warning:
Sometimes you will see the actual df in the table, but not all values are
listed there to save space.
Our Halloween study df of 38 is not listed in the t-test table, so we can
look at either the df = 35 row or we can look at the df = 40 row.
Just go with the df that is closest (in our case, 38 is closer to 40 than 35),
– As you see, the .05 critical values for df 35 (2.03) and df 40 (2.021)
are really, really close, so there’s not much of a difference!
Back to Step 5 (of 8)
Step Five: Determine The Value Needed To Reject The Null
– Remember, we needed 3 pieces of information to find the critical
value in the t-test table:
1. Your desired p values, that’s .05!
2. Whether you’re doing a One-Tailed test or a Two-Tailed
We’re doing a two-tailed test, based on our null and
alternative hypotheses
3. df = 38
Finding our Critical Value:
1. desired p value is .05!
2. Two-Tailed
3. df = 38 (remember, 38 isn’t
listed here so we’ll go with 40
because it’s closest)
Our critical value is 2.021
Step 6 (of 8)
Step Six: Compare The Obtained And Critical Values
– Here, our critical value is 2.021. Our obtained value is 5.43!
– Our obtained value exceeds our critical value.
Steps 7 & 8 (of 8)
Step Seven and Eight: Make A Decision
– As we saw in step six, our obtained value of 5.43 exceeds
the critical value of 2.03.
– Thus we REJECT the null hypothesis and conclude that the
mirror present and mirror absent groups differ significantly
Pop-Quiz 5: Quiz Yourself
If we ran a one-tailed t-Test with two groups of 21 participants
each and found a t obtained value of 1.75 (p < .05 level), what
does this tell us?
A). We should retain the null hypothesis
B). We should reject the null hypothesis
C). There isn’t enough information here to render a conclusion
Answer 5: B
If we ran a one-tailed t-Test with two groups of 21 participants
each and found a t obtained value of 1.75 (p < .05 level), what
does this tell us?
B). We should reject the null hypothesis
The groups did differ
– Your df is 40
(21 – 1) + (21 – 1) = 40
– The critical t value is 1.68 at the p < .05 level
– Your obtained value of 1.75 is high enough to overcome the
critical t value of 1.68, thus you reject the null hypothesis
Pop-Quiz 6: Quiz Yourself
Let’s say you have a sample of 60 participants divided into
two groups of 30. What df would you use when checking your
critical value in a t-Test table?
A). 30
B). 48
C). 58
D). 60
E). 68
Answer 6: C
Let’s say you have a sample of 60 participants divided into
two groups of 30. What df would you use when checking your
critical value in a t-Test table?
A). 30
B). 48
C). 58
D). 60
E). 68
(n – 1) + (n – 1) = (30 – 1) + (30 – 1) =
29 + 29 = 58
Pop-Quiz 7: Quiz Yourself
There is no df of 58 in your t-Test table. Which df(s) could you
use?
A). 50 or 60
B). 55 or 60
C). 60 or 65
D). 45 or 65
E). None of the above
Answer 7: B
There is no df of 58 in your t-Test table. Which df(s) could you
use?
A). 50 or 60
B). 55 or 60
C). 60 or 65
D). 45 or 65
E). None of the above
Pop-Quiz 8: Quiz Yourself
For a two-tailed t-Test at a p < .05 level, what is the difference
between a df of 55 and a df of 60?
A). 1.00
B). 0.10
C). 0.001
D). 0.002
E). 0.003
Answer 8: E
For a two-tailed t-Test at a p < .05 level, what is the difference
between a df of 55 and a df of 60?
A). 1.00
B). 0.10
C). 0.001
D). 0.002
E). 0.003 df 60 = 2.001 df 55 = 2.004
2.004 – 2.001 = 0.003
So, What Now?
– Sorry, still not done with our Halloween study! We know the
groups differ, but we need to go back and look at the means
to really understand HOW the groups differ.
– To see what the direction of the effect is, we can look at the
means…
– Group #1: Mirror Present M = 4.00
– Group #2: Mirror Absent M = 8.00
– So, those without the mirror present took significantly
MORE candy than those with the mirror.
Writing Up The T-Test
– Now we are nearly done. Our last step is to write this up as
we would see it in a journal results section.
– We’ll write up the t-test like this:
– t(38) = 5.43, p < .05
Note, that p < .05 means it was significant. If it were not
significant, it would say p > .05!
Full Write-Up
Here’s the full write up for the study. It needs to include
means, standard deviations, t-test, df, and p values, as well as
a brief explanation of the findings.
“We ran an independent samples t-Test with mirror condition as
our independent variable (mirror present versus mirror absent)
and the amount of candy trick-or-treaters took as the dependent
variable. The groups differed significantly, t(38) = 5.43, p < .001.
Trick-or-treaters took more candy in the mirror absent condition
(M = 8.00, SD = 1.52) than trick-or-treaters in the mirror present
condition (M = 4.00, SD = 2.92). Apparently, seeing themselves in
a mirror can lead participants to be less greedy!”
Part Four
Special Effects: Are Those Differences For Real?
Are Those Differences Real? Effect Size
Special Effects: Are Those Differences Real?
So we found significant differences in our Halloween candy
study, but are those differences meaningful?
– Effect size is a measure of just how different two groups are
from one another—that is, it is a measure of the magnitude
of the treatment
– The effect size does not rely on the sample size, so we can
compare effect sizes between different studies!
– So what is the magnitude of the our effect in our Halloween
candy example? …
Effect Size Formula
– Here is our formula for Effect Size (ES), also known as
Cohen’s d.
d= Effect Size (Cohn’s d)
1 = the mean of Group 1
1 = the mean of Group 2
12 = the variance of Group 1
22 = the variance of Group 2
=
1 − 2
12 + 22
2
Effect Size for The Halloween Data
Here is the calculation of the effect size for our example:
=
1 − 2
2
2
+
1 2
2
=
8−4
8.5263+2.3157
2
= 1.72
Interpreting The Effect Size
So our effect size is 1.72. Is that high? Consider the guidelines
that Jacob Cohen came up with to assess effect sizes:
– 1. A small effect size ranges from 0.00 to .20
– 2. A medium effect size ranges from .20 to .50
– 3. A large effect size is any value over .50
Full Write up With Effect SIze
We can include the effect size in our write up:
“We ran an independent samples t-Test with mirror condition as
our independent variable (mirror present versus mirror absent)
and the amount of candy trick-or-treaters took as the dependent
variable. The groups differed significantly, t(38) = 5.43, p < .05, d
= 1.72. Trick-or-treaters took more candy in the mirror absent
condition (M = 8.00, SD = 1.52) than trick-or-treaters in the mirror
present condition (M = 4.00, SD = 2.92). Apparently, seeing
themselves in a mirror can lead participants to be less greedy!”
The “d” is used to denote Cohen’s d!
Tip: Use An Effect Size Calculator
A Very Cool Effect Size Calculator
– As your book notes, we can get the effect size a lot easier
by plugging in the values in an effect size calculator.
– There are a lot of them available online. You can just google
“effect size calculator” or go to this address:
– http://www.uccs.edu/~lbecker/
– Insert your mean and SD for both conditions, and then click
“compute” and Cohen’s d will pop up!
Why Use Effect Size?
Why do we even look at effect size?
As mentioned earlier, the effect size let’s us assess the overall
magnitude of the difference. It’s not always enough to say two
groups differ – we want to know if that difference is big!
Cohen's d is a measure of effect size. Simply put, it i
