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Answer Sheet
1-2 are one point each; 3-9 are two points each; 10-12 are three points each; 13 is extra credit
1) Categorical Categorical
or continuous?
2) “1” on Night Owl
Sleep Schedule =
3) % Lower Class = 6.8%
4) Strongest = Neuroticism
5) R2 = .056
6) t-value = -2.47
p-value = .01
7) t-value = -1.77
p-value = .08
8) t-value = -1.03
p-value = .31
Meaning? SES was unrelated to cell phone use.
9) t-value = 3.22
p-value = .001
Meaning? People who are lower-middle class reported smoking more often than
people who are upper-middle class.
10) t-value = 4.80
p-value = < .001
Cohen’s d = 0.58
11) APA-style result: Age (r = -.13, p = .03), pro-environmental attitudes (r = .16, p = .01),
and anger (r = .14, p = .02) all predicted frequency of stealing.
However, vocabulary did not predict stealing frequency (r = -.07, p =
.24). Thus, people who were younger, pro-environment, or angry
tended to steal slightly more often than people who were not, but
vocabulary was unrelated to stealing. To examine the overall ability of
age, pro-environmental attitudes, and anger to predict stealing, a
multiple regression was performed. These three variables significantly
predicted stealing, R2 = .056, p = .001, which was a small overall effect.
Thus, age, pro-environmental attitudes, and anger accounted for about
6% of the differences in stealing frequency.
12) APA-style result: It was hypothesized that people who wear glasses are smarter than
people who do not wear glasses. However, a t-test revealed that people
who do not wear glasses (M = 3.47, SD = 0.46) actually had higher high
school GPAs than people who wear glasses (M = 3.14, SD = 0.66), d =
0.59, t(277) = 4.80, p < .001. Contrary to the hypothesis, people who
did not wear glasses had modestly better grades.
13) Bonus (optional) Results vary.
Output
3)
21. Socioe conom ic Status (SES)
Cumulativ e
Frequenc y Percent Valid Percent Percent
Valid Low er Class 19 6.8 6.8 6.8
Low er-Middle Clas s 121 43.4 43.4 50.2
Upper-Middle Class 135 48.4 48.4 98.6
Upper Class 4 1.4 1.4 100.0
Total 279 100.0 100.0
4)
Cor relations
83. 90. Political 97. 104.
Self -Esteem 59. Worrying Idealism Attractiv eness Neuroticism
83. Self -Esteem Pearson Correlation 1 -.316** -.042 .413** -.472**
Sig. (2-tailed) .000 .486 .000 .000
N 279 279 279 279 279
59. Worrying Pearson Correlation -.316** 1 .109 -.212** .653**
Sig. (2-tailed) .000 .069 .000 .000
N 279 279 279 279 279
90. Political Idealism Pearson Correlation -.042 .109 1 -.075 .128*
Sig. (2-tailed) .486 .069 .212 .033
N 279 279 279 279 279
97. Attractiv eness Pearson Correlation .413** -.212** -.075 1 -.221**
Sig. (2-tailed) .000 .000 .212 .000
N 279 279 279 279 279
104. Neurotic is m Pearson Correlation -.472** .653** .128* -.221** 1
Sig. (2-tailed) .000 .000 .033 .000
N 279 279 279 279 279
**. Correlation is s ignif icant at the 0.01 level (2-tailed).
*. Correlation is s ignif icant at the 0.05 level (2-tailed).
5)
Cor relations
79.
Pro- 110.
62. Stealing 44. A ge Environment 96. A nger V oc abulary
62. Stealing Pearson Correlation 1 -.129* .161** .139* -.071
Sig. (2-tailed) .031 .007 .020 .239
N 279 279 279 279 279
44. A ge Pearson Correlation -.129* 1 -.044 -.054 .201**
Sig. (2-tailed) .031 .465 .369 .001
N 279 279 279 279 279
79. Pro-Environment Pearson Correlation .161** -.044 1 .057 -.009
Sig. (2-tailed) .007 .465 .344 .877
N 279 279 279 279 279
96. A nger Pearson Correlation .139* -.054 .057 1 .010
Sig. (2-tailed) .020 .369 .344 .865
N 279 279 279 279 279
110. Vocabulary Pearson Correlation -.071 .201** -.009 .010 1
Sig. (2-tailed) .239 .001 .877 .865
N 279 279 279 279 279
*. Correlation is s ignif icant at the 0.05 level (2-tailed).
**. Correlation is s ignif icant at the 0.01 level (2-tailed).
Model Sum m ary
Adjusted Std. Error of
Model R R Square R Square the Estimate
1 .237 a .056 .046 1.097
a. Predictors: (Constant), 96. Anger, 44. Age, 79.
Pro-Env ironment
ANOVAb
Sum of
Model Squares df Mean Square F Sig.
1 Regression 19.764 3 6.588 5.479 .001 a
Residual 330.673 275 1.202
Total 350.437 278
a. Predictors: (Constant), 96. Anger, 44. Age, 79. Pro-Environment
b. Dependent Variable: 62. Stealing
6/7)
Group Statis tics
Std. Error
16. Relationship Status N Mean Std. Deviation Mean
37. Days per Week Single 113 3.27 2.281 .215
Eating Breakf ast In a Relations hip 166 3.99 2.466 .191
107. Consc ientiousness Single 113 6.04 1.861 .175
In a Relations hip 166 6.42 1.749 .136
Inde pe nde nt Sam ples Te st
Levene's Test f or
Equality of V ariances t-test f or Equality of Means
95% Conf idence
Interval of the
Mean Std. Error Dif f erence
F Sig. t df Sig. (2-tailed) Dif f erence Dif f erence Low er Upper
37. Day s per Week Equal variances
1.919 .167 -2.466 277 .014 -.720 .292 -1.294 -.145
Eating Breakf as t as sumed
Equal variances
-2.503 252.586 .013 -.720 .287 -1.286 -.153
not assumed
107. Consc ientiousness Equal variances
.325 .569 -1.765 277 .079 -.386 .219 -.817 .045
as sumed
Equal variances
-1.744 230.552 .083 -.386 .222 -.823 .050
not assumed
8/9)
Group Statis tics
21. Socioeconomic Std. Error
Status (SES) N Mean Std. Deviation Mean
57. Cell Phone Use Low er-Middle Clas s 121 6.84 2.025 .184
Upper-Middle Class 135 7.08 1.697 .146
49. Smoking Low er-Middle Clas s 121 3.00 2.890 .263
Upper-Middle Class 135 1.99 2.086 .180
Inde pe nde nt Sam ples Te st
Levene's Test f or
Equality of V ariances t-test f or Equality of Means
95% Conf idence
Interval of the
Mean Std. Error Dif f erence
F Sig. t df Sig. (2-tailed) Dif f erence Dif f erence Low er Upper
57. Cell Phone Use Equal variances
1.591 .208 -1.025 254 .306 -.239 .233 -.697 .220
as sumed
Equal variances
-1.015 235.210 .311 -.239 .235 -.701 .224
not assumed
49. Smoking Equal variances
25.326 .000 3.221 254 .001 1.007 .313 .392 1.623
as sumed
Equal variances
3.166 216.055 .002 1.007 .318 .380 1.635
not assumed
10)
Group Statis tics
Std. Error
Wears Glass es N Mean Std. Deviation Mean
41. GPA (High School) .00 186 3.468 .4634 .0340
1.00 93 3.141 .6604 .0685
Inde pe nde nt Sam ples Te s t
Levene's Test f or
Equality of V ariances t-test f or Equality of Means
95% Conf idence
Interval of the
Mean Std. Error Dif f erence
F Sig. t df Sig. (2-tailed) Dif f erence Dif f erence Low er Upper
41. GPA (High School) Equal variances
16.382 .000 4.802 277 .000 .3274 .0682 .1932 .4616
as sumed
Equal variances
4.283 138.689 .000 .3274 .0764 .1763 .4786
not assumed
Homework #6
Due Thursday, March 27th
Begin Early: For this assignment, you will use SPSS, so plan to begin the assignment a couple
days before the deadline in case you run into computer problems or get stuck. Print it out the
night before.
A) Include a cover sheet.
B) Type your answers on the answer sheet that has been provided.
C) Attach all SPSS Output after the answer sheet.
D) Work independently and answer questions using your own words.
E) Print an extra copy for yourself so you can check your answers later.
Section 1: Review from Homework #3
Instructions: These review questions are used to increase the probability that you will remember
how to use SPSS after the course has ended. Most students will need to refer back to the
instructions in the previous computer assignment at some point:
http://www.psychmike.com/psy211/homework3.doc
1. Is Favorite Music (#32) a categorical or continuous variable?
2. What does a score of “1” on Sleep Schedule (#17) mean?
3. What percentage of people said they were “Lower Class” on the Socioeconomic Status
variable (#21)?
4. Indicate which of the following variables is most strongly correlated with self-esteem (#83):
Worrying (#59), Political Idealism (#90), Attractiveness (#97), or Neuroticism (#104).
5. Determine which of the following variables have a statistically significant correlation with
Stealing (#62): Age (#44), being Pro-Environment (#79), having Anger (#96), and Vocabulary
(#110). Take any of these variables that significantly correlate with stealing and include them in
a multiple regression. Report the R2 value.
Section 2: An Easy Example of Between-groups t-Tests
A. Overview
The between-group t-test is used when we want to see how two groups of people differ on some
continuous variable.
The t-test is similar to a z-test, except the exact value needed for statistical significance varies,
depending on sample size.
Look at the p-value to determine if a result is statistically significant. If p < .05, the difference
between groups is reliable. If not, there is no reliable difference, and we tend to ignore the result.
B. Running a t-Test
Go to the Analyze menu, point to Compare Means, and choose “Independent-Samples T Test”
In the window that pops up, we always put the independent variable (grouping or categorical
variable) in the “Grouping Variable” section of the box. In the “Test Variable(s)” box, put any
continuous dependent variables you want to examine (you can choose more than one if you like).
The analysis will tell us if the groups differ in terms of their scores on the “Test Variables”.
Try putting Smoker (#3) in the “Grouping Variable” area, and put College GPA (#42) and
Activism (#81) in the “Test Variables” section, so we can see if smokers differ on these
variables. At this point you will notice that the OK button is still gray, so we need to do one
more step.
Single-click where it says “smoker(? ?)” in the Grouping Variables area, and click on the Define
Groups button. SPSS needs you to tell it which numbers were used to describe the groups. In
the data file, we arbitrarily coded nonsmokers = 0 and smoker = 1, so type a 0 where is says
“Group 1” and a 1 where it says “Group 2”.
If you ever forget how a variable was coded, just look at the Data Guide file for help:
http://www.psychmike.com/psy211/data_guide.doc
Click the Continue button, and then the OK button to run the analysis. Your Output should look
something like this:
Group Statis tics
Std. Error
3. Smoker N Mean Std. Deviation Mean
42. GPA (college) No 114 3.343 .6120 .0573
Yes 133 3.120 .5302 .0460
81. Activis m No 125 5.91 1.540 .138
Yes 154 6.11 1.462 .118
Inde pe nde nt Sam ples Te st
Levene's Test f or
Equality of V ariances t-test f or Equality of Means
95% Conf idence
Interval of the
Mean Std. Error Dif f erence
F Sig. t df Sig. (2-tailed) Dif f erence Dif f erence Low er Upper
42. GPA (college) Equal variances
.389 .533 3.074 245 .002 .2234 .0727 .0803 .3666
as sumed
Equal variances
3.041 225.336 .003 .2234 .0735 .0786 .3682
not assumed
81. A ctivis m Equal variances
.610 .436 -1.100 277 .272 -.198 .180 -.553 .157
as sumed
Equal variances
-1.095 259.341 .275 -.198 .181 -.555 .159
not assumed
Using the top box, we see that smokers had a lower GPA (M = 3.12, SD = 0.53) than non-
smokers (M = 3.32, SD = 0.61). The second box tells us the t-value (3.074), the degrees of
freedom (a reference number, 245) and the p-value (.002). The t-value and degrees of freedom
are basically just used by the computer in order to calculate the p-value. We are mainly
interested in the p-value. The p-value basically tells the probability of getting this mean
difference by “chance” or sampling error. In other words, there is only about a .002 or .2%
probability we’d see a result this extreme by chance. If p < .05 (less than 5%), the result is
significant (trustworthy, reliable, not likely due to chance). Otherwise, the result is unreliable.
The groups do not differ significantly on activism.
C. Run a t-Test on Your Own
Run a t-test to see if Relationship Status (#16) is related to Days per Week Eating Breakfast
(#37) or Conscientiousness (#107). [Conscientiousness = work ethic, if you didn’t know]
6. Indicate the t-value and p-value for the relationship between relationship status and days
eating breakfast.
7. Indicate the t-value and p-value for the relationship between relationship status and
conscientiousness.
Section 3: A Modestly Difficult Example of Between-groups t-Tests
A. Overview
One weakness of the t-test is that it only allows us to see how two groups differ on some variable
(How do psych majors differ from PT majors on exercise habits?). A lot of times, we have
categorical variables with more than two categories (Psych majors vs. PT vs. history vs. English,
etc.). Later, we will learn how to handle such cases with an analysis called ANOVA. However,
there are some ways to handle these cases using the between-group t-test.
In our data file, some variables are dichotomous (two categories): #2-18, #111-124
Some have multiple categories: #19-33
The rest are continuous variables (numeric rating scales): #34-110
B. Running a t-Test for a multiple category variable
The easiest way to deal with these multiple category variables is to only run an analysis looking
at two of the categories.
Favorite Entertainment (#26) is coded as 1 = TV, 2 = Internet, 3 = Books, and 4 = Exercise.
Suppose we want to see if these categories predict differences in ACT score (#43). The t-test
only allows us to compare two groups at once, so let’s compare the TV watchers to the Book
readers.
Run a t-test using Favorite Entertainment (#26) as the categorical or grouping variable and ACT
score (#43) as the continuous or test variable. You run it just like normal, but when you hit the
Define Groups button, type in 1 and 3 for the groups to examine (telling SPSS to compare TV
watcher to the Book readers).
The Output should look something like this:
Group Statis tics
26. Favorite Std. Error
Entertainment N Mean Std. Deviation Mean
43. ACT Sc ore TV 67 23.93 4.590 .561
Books 57 25.74 3.838 .508
Inde pe nde nt Sam ples Te s t
Levene's Test f or
Equality of V ariances t-test f or Equality of Means
95% Conf idence
Interval of the
Mean Std. Error Dif f erence
F Sig. t df Sig. (2-tailed) Dif f erence Dif f erence Low er Upper
43. A CT Sc ore Equal variances
3.994 .048 -2.359 122 .020 -1.811 .768 -3.332 -.291
as sumed
Equal variances
-2.393 121.969 .018 -1.811 .757 -3.310 -.313
not assumed
People who enjoy reading books (M = 25.74, SD = 3.84) scored higher than people who enjoy
watching television (M = 23.93, SD = 4.59) on the ACT, and this result was statistically
significant, t(122) = -2.36, p = .02.
C. Run a t-Test on Your Own
To determine whether Socioeconomic Status (#21) is related to Cell Phone Use (#57) or
frequency of Smoking (#49), compare the “Lower-Middle Class” to the “Upper-Middle Class”
on cell phone use and smoking.
8. Indicate the t-value and p-value for the relationship between SES and cell phone use. What
does this mean?
9. Indicate the t-value and p-value for the relationship between SES and smoking. What does
this mean?
Section 4. The Most Complex Example of Between-groups t-Tests
A. Overview
One way to handle these multiple category variables is to ignore some of the categories, as we
did in Section 3. An alternative way is to re-group the variables from a high number of
categories down to just two categories.
For example, earlier we compared TV watchers to Book readers (ignoring the people who prefer
Internet or Exercise). We could re-categorize our entertainment variable so that instead of four
groups, we lump the responses into just two groups. For example, we could compare TV
watchers to all non-TV watchers (Book readers, Internet users, and Exercisers). Alternatively,
we could compare people who like Exercise to people who are physically lazy (TV watchers,
Book readers, and Internet users).
There are many combinations:
Category 1: TV watchers Category 2: Book readers
ignoring Internet users and Exercisers
or
Category 1: TV watchers Category 2: Non-TV watchers (Book readers,
Internet users, Exercisers)
or
Category 1: Exercisers Category 2: Physically Lazy (Book readers,
Internet users, TV watchers)
or
Category 1: TV watchers, Internet users Category 2: Book readers
ignoring Exercisers
How we decide to group the variables likely depends on the research question we’re interested
in. If we wanted to compare the groups on health, we might use the third option above. If we
wanted to compare them on visual acuity or vocabulary, we might use the fourth grouping.
Regardless, it can be very useful to learn how to re-classify variables
B. Re-coding Variables
Go to the Transform menu, point to Recode and choose “Into Different Variables…”
The window that pops up has a number of commands. You can use this feature to take a
continuous variable and make it categorical, to re-number variables, or to re-code them in any
number of ways. We will keep it simple, but it is a powerful tool.
Let us recode the Entertainment variable (#26) we’ve been discussing such that Exercisers will
be in one group and everybody else will get classified in a second group (lazy folks). Move the
entertainment variable to the box that says “Numeric variable Output variable” in the middle
area of the screen. Off to the right, in the “Output Variable” section type in a name for the new
variable (something simple) in the Name area and a more detailed label in the Label area. I
chose “lazy” for the name and “Enjoy Laziness” for the label. Once you’ve typed in a name and
label for the new variable you’re making, hit the Change button right below it.
After that, click on the button called, Old and New Values. Here we will tell SPSS how to
recode the Entertainment variable into our new laziness variable. Re-coding is simple. You type
in the old value in the Old Value section on the left, the New Value on the right, and click the
Add button. Our goal is to re-code Exercise from a 4 0, re-code TV from 1 1, re-code
Internet from 2 1, and re-code Book from 3 1.
Type a 4 in the Old Value section, a 0 in the New Value section, and click the Add button.
Type a 1 in the Old Value section, a 1 in the New Value section, and click the Add button.
Type a 2 in the Old Value section, a 1 in the New Value section, and click the Add button.
Type a 3 in the Old Value section, a 1 in the New Value section, and click the Add button.
Then, click the Continue button. Then, in the original pop-up window click the OK button. This
tells SPSS to make Exercise a 0 and all of the physically lazy activities a 1. To check that you
did this correctly, you can go to Data View (the spreadsheet area with all the data) and scroll all
the way to the last variable, way off to the right. The last variable should say “lazy” and all
scores should be 0’s or 1’s.
C. Running a t-Test
Now, you can run an analysis using the new dichotomous “lazy” variable, using the procedures
already learned. Compare laziness to Physical Health (#86). You should get the following
Output, which indicate that the lazy people (coded as 1) are significantly less healthy than the
non-lazy or exercise group (coded as 0).
Group Statis tics
Std. Error
Enjoy Laz iness N Mean Std. Deviation Mean
86. Phys ic al Health .00 24 8.08 1.018 .208
1.00 255 6.09 2.029 .127
Inde pe nde nt Sam ples Te st
Levene's Test f or
Equality of V ariances t-test f or Equality of Means
95% Conf idence
Interval of the
Mean Std. Error Dif f erence
F Sig. t df Sig. (2-tailed) Dif f erence Dif f erence Low er Upper
86. Phys ic al Health Equal variances
14.055 .000 4.759 277 .000 1.997 .420 1.171 2.823
as sumed
Equal variances
8.199 42.882 .000 1.997 .244 1.506 2.488
not assumed
D. Re-coding and Running Your Own t-Test
Mike has to go to court and has a hypothesis that people who wear glasses seem smarter than
people who do not wear glasses, so he wears his glasses to court that day. Is there any scientific
basis to this perception? Re-code the Lenses variable (#29). Make a new variable, where one
group consists only of people who wear glasses, and the other group consists of people who wear
contact lenses or neither types of corrective lenses. Then compare the glasses-wearers to those
who don’t wear glasses in terms of High School GPA (#41).
10. Report the t-value, p-value, and Cohen’s d for this result. Cohen’s d requires a hand
calculation.
Section 5: APA-Format
A. Overview
Most researchers in the social sciences stick to a general format when writing up their results.
Below are some instructions and examples about reporting results in APA-style. Read this over,
and then answer questions 11 and 12.
Here are some examples of how to write results in APA-style. This is just a guide. If you are a
good writer, it is okay to deviate from this somewhat. Remember, p-values can be recorded
exactly (e.g. p = .013, p = .46, etc.) or by merely stating significance (p < .05), or by merely
stating non-significance (ns). It is okay to separate statistical results from the rest of the sentence
by enclosing statistics in parentheses or by using commas. For correlations, provide the r value
and p value. For regression, provide the initial correlational results, then conduct the regression,
and provide the R2 and p-value. For t-tests, provide the Cohen’s d (calculated by hand, do not
need to show hand-calculations this time), t-value, and p-value.
Correlation (Statistically Significant):
The correlation between IQ and hours of television watched was significant, r = -.35, p = .02.
That is, people who were smarter watched moderately less television.
The correlation between IQ and hours of television watched was significant, r = -.35, p < .05.
That is, people who were smarter watched moderately less television.
For correlations of magnitude < .10, we say something to the effect of “no sizeable relationship.”
For correlations of magnitude .10 to .29, say the relationship is “small” or use a related synonym.
For correlations of magnitude .30 to .49, say the relationship is “medium” or “modest” or some
other synonym. For correlations of .50 or greater, say “large” or some other synonym.
Correlation (Non-Significant):
IQ and number of hours of television watched were not significantly related, r = .08, p = .67.
Thus, one’s level of intelligence was not related to time spent watching television.
IQ and number of hours of television watched were not sizably related, r = .08, ns. Thus, one’s
level of intelligence was not related to time spent watching TV.
Multiple Regression (after discussion of correlational results):
Family stress (r = .48, p < .05), work stress (r = .56, p < .05), and school stress (r = .21, p < .05)
all significantly predicted overall life stress. However, social support did not predict level of life
stress, r = .03, ns. Thus, although social support was not related to life stress, one’s level of
school stress was slightly related, family stress was modestly related, and work stress was
strongly related to level of life stress. To examine the overall contribution of the three
significant predictors (school stress, family stress, and life stress) in accounting for life stress,
multiple regression was used. The results of the multiple regression analysis indicate that these
three predictors accounted for a large proportion of the variance in life stress, R2 = .40, p < .05.
Thus, school stress, family stress, and work stress together account for 40% of the differences in
overall life stress.
t-tests (Statistically Significant)
Males (M = 2.0, SD = 0.6) differed from females (M = 5.0, SD = 0.4) in terms of number of pairs
of shoes owned. This difference was large and statistically significant, d = 6.0, t(128) = 3.89, p <
.05. In conclusion, males tend to own fewer pairs of shoes than females.
Cohen’s d is a measure of how big the relationship is (effect size), see 10/31 PPT notes for
details. d = (M1 – M2) / s where M1 is the mean of the first group (2.0), and M2 is the mean of
the second group (5.0), and s is the average standard deviation across groups [(.6+.4)/2 = .5].
d = (2-5)/.5 = -3/.5 = -6. You can make d positive if you like , just make sure you interpret it
correctly (males are lower than females). When d has a magnitude less than .2, we say
something like “there was no relationship;” .2-.49 means “a small relationship;” .5-.79 means “a
modest relationship;” .8 or higher means “a large relationship.” There is no maximum value for
d.
The values in the parentheses after the t is the degrees of freedom for the whole sample, which is
provided by SPSS, but also equals the total sample size minus 2, that is N-2.
dftotal = df1 + df2 = (n1 – 1) + (n2 – 1) = N -2
t-tests (non-Significant)
Males (M = 2.9, SD = 0.6) did not differ from females (M = 3.1, SD = 0.4) in terms of number of
pairs of shoes owned. This difference was small and not statistically significant, d = 0.4, t(128)
= 1.12, ns. In conclusion, males tend to own about as many pairs of shoes as females.
B. Reporting Your Results
You will need to be able to report results in APA-format for the term paper, so check with me if
you are unsure how to do it.
11. Report the results of problem 5 in APA format, as best you can.
12. Report the results of problem 10 in APA format, as best you can.
C. Bonus
13. (Optional, extra points). Out of your own curiosity, conduct an interesting analysis using the
re-coding function, and report the result in APA-format.
Answer Sheet
1-2 are one point each; 3-9 are two points each; 10-12 are three points each; 13 is extra credit
1) Categorical
or continuous?
2) “1” on
Sleep Schedule =
3) % Lower Class =
4) Strongest =
5) R2 =
6) t-value =
p-value =
7) t-value =
p-value =
8) t-value =
p-value =
Meaning?
9) t-value =
p-value =
Meaning?
10) t-value =
p-value =
Cohen’s d =
11) APA-style result:
12) APA-style result:
13) Bonus (optional)
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