Based on your results, provide an explanation of what the implications of social change might be.I have ran all the test for you all you need to do is write the explanation. It is called week 6 tables. I am also providing a example of a perfect paper so you know how it should like and what verbiage to use. It is called wk6assgn1 example Please use some of the citation from the example in my paper. I have labeled each table for you as well. I have done half the work this shouldn’t take up to much of your time thank you.

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RUNNING HEAD: WEEK 6 ASSIGNMENT 1

Quantitative Reasoning and Analysis: Week 6 Assignment 1

Walden University

WEEK 6 ASSIGNMENT 1

Statistical significance is important for determining whether an effect is real

(Frankfort-Nachmias & Leon-Guerrero, 2015). One of the ways statistical significance can be

determined is through a t-test. Three types of t-test are an independent-samples t-test, a pairedsample t-test, and a one-sample t-test. An independent-samples t-test is useful for determining

whether two distinct groups differ on some continuous measure. For a test of this kind, the

samples are assumed to be independent, and the tested variable is assumed to be continuous

(Frankfort-Nachmias & Leon-Guerrero, 2015). A paired-samples t-test is also useful for

determining whether two distinct groups differ on some continuous measure, but has a different

assumption: that the change for each entry to its matching in the other group is the relevant

quantity (Frankfort-Nachmias & Leon-Guerrero, 2015). A one-sample t-test is useful for

measuring difference in mean from a known quantity. The assumption of the one sample t-test is

that the dependent variable is continuous and normally distributed (Frankfort-Nachmias & LeonGuerrero, 2015). A normally distributed dependent variable is bell shaped. To understand these

three types of t-test and their assumptions it will be helpful to apply them to three different

scenarios.

In Scenario 1 of the three scenarios (Walden University), the question is whether the

average perception of democracy (n = 46,940; M = 5.52; SD = 2.883) is statistically different

from an expert-determined target of 6. This kind of question is best answered by a one-sample ttest because there is only one sample to be used in the comparison (Frankfort-Nachmias & LeonGuerrero, 2015). It is not clear at the outset whether the dependent variable (attitude about level

of democracy) is normally distributed, but this can be checked statistically. Using the

Kolmogorov-Smirnov test of normality in the SPSS software package, normality was checked.

The variable was found to not be normal (df = 46,940; F = .111; p < .001), which may pose a
WEEK 6 ASSIGNMENT 1
problem for validity because t-tests try to match the distribution of the dependent variable to a
normal distribution and then calculate where the mean is on the corresponding curve. The p
value from the t-test (t(49640) = 35.924, p < .001) is less than .001 and so less than .05,
indicating that the mean of the data is significantly different from 6. This indicates that statistical
significance was found. The mean difference is 0.478, which indicates that the average
perception is below 6. If the goal is to have a positive perception of democracy, then
improvement is needed. If a positive perception of democracy impacts political participation,
then it becomes clear that perception impacts the social good. Despite this, a calculation of effect
size by Cohens d gives 0.478 / 2.883 = 0.166. Because this is less than the threshold of 0.2 for
small effect size, the results are likely to have little practical significance (Frankfort-Nachmias &
Leon-Guerrero, 2015).
In Scenario 2, the question is whether there is a statistically significant difference
between perceptions of democracy in the northern and southern countries of Africa. This kind of
question is best answered by an independent-samples t-test because there are two samples to be
tested, but these samples may be of different sizes and no effort has been made to pair the
individual respondents between samples. It is not clear whether the dependent variable has the
same variance between groups. This can be checked, such as by using Levenes test for equal
variance, or the test can be run without the assumption of equal variance. The p value from the ttest (t(21395) = 19.453, p < .001) is less than .001 and so less than .05, indicating that the mean
for northern Africa (n = 15,979; M = 5.79; SD = 2.795) is significantly different from the mean
for southern Africa (n = 5,418; M = 4.90; SD = 3.092). This indicates that statistical significance
was found. The mean difference is 0.879, which indicates that the average perception is higher in
the north than in the south. This means that the north is doing better in creating a perception of
WEEK 6 ASSIGNMENT 1
democracy. If the regions had the same average perception before the mentioned reforms, the
results of the t-test could be construed to mean that those reforms were successful in changing
the north African perception of democracy. Testing the effect size, the standard deviation of the
northern and southern countries together on perception of democracy is 2.90. A difference of
0.879 gives a Cohens d value of 0.879 / 2.90 = 0.30. This is a small effect size because it is
between 0.2 and 0.5 (Frankfort-Nachmias & Leon-Guerrero, 2015). If it is assumed that
perception of democracy improves political participation, then it could be argued that the reforms
of the north should be carried out in the south.
In Scenario 3, the question asked is whether student perception of mathematical utility
changes over the high school career. For this type of question, a paired-samples t-test is useful
because it is the mean of the difference, not the difference of the mean, that is of interest. Here,
there is a natural pairing between the samples by matching the early (n = 16,021; M = .0096;
SD = .99040) and late (n = 16,021; M = 0.0059; SD = 1.00682) evaluations according to student.
This ensures that the reported change is not due to sampling. The p value of the t-test (t(16,020)
= 1.649, p = .099) was greater than .05, which indicates that the results are not significant
because a significance level of .05 was chosen. Because no significant difference was found,
effect size is irrelevant and not tested. If it is assumed that students with a higher perception of
math utility do better in math courses, then the social significance becomes clear, but this
difference not being statistically significant makes the point moot.
These three scenarios show the importance of testing for both statistical significance and
effect size. In Scenario 1, a statistically significant difference is found, but improving the mean
to 6 would have little practical effect, as judged by effect size. In Scenario 2, a statistically
significant effect with an effect size over the minimum threshold was found. In Scenario 3, no
WEEK 6 ASSIGNMENT 1
statistically significant effect was found. Each of these demonstrates a different aspect of
significance testing.
WEEK 6 ASSIGNMENT 1
Table 1 Test of normality for perception of democracy
Tests of Normality
Kolmogorov-Smirnova
Statistic
Q46a. Level of democracy:
.111
today
df
Sig.
46940
.000
a. Lilliefors Significance Correction
Table 2 Basic statistics for perception of democracy
One-Sample Statistics
N
Q46a. Level of democracy:
today
Mean
46940
Std. Deviation
5.52
Std. Error Mean
2.883
.013
Table 3 t-test for difference of perception of democracy from 6
One-Sample Test
Test Value = 6
95% Confidence Interval of the
Difference
t
Q46a. Level of democracy:
today
df
-35.924
Sig. (2-tailed)
46939
Mean Difference
.000
Lower
Upper
-.478
-.50
Std. Deviation
Std. Error Mean
Table 4 Basic statistics for perceived levels of democracy in north and southern Africa
Group Statistics
Country by region
N
Mean
Q46a. Level of democracy:
Southern Africa
15979
5.78
2.795
.022
today
North Africa
5418
4.90
3.092
.042
-.45
WEEK 6 ASSIGNMENT 1
Table 5 t-test of difference in means of perception of democracy between north and southern Africa
Independent Samples Test
Levene's Test
for Equality of
Variances
t-test for Equality of Means
95%
Confidence
Interval of the
Sig.
(2F
Q46a. Level
Equal
of
variances
democracy:
assumed
today
Equal
Sig.
130.649
t
df
.000 19.453
variances
Mean
Std. Error
tailed) Difference Difference Lower Upper
21395
.000
.879
.045
.790
.967
18.510 8610.815
.000
.879
.047
.786
.972
not assumed
Table 6 Basic statistics of student mathematical utility
Paired Samples Statistics
Mean
Pair 1
T1 Scale of student's
mathematics utility
T2 Scale of student's
mathematics utility
Difference
N
Std. Deviation
Std. Error Mean
-.0096
16021
.99040
.00782
.0059
16021
1.00682
.00795
WEEK 6 ASSIGNMENT 1
Table 7 Matched t-test of change in math utility during high school
Paired Samples Test
Paired Differences
95% Confidence
Interval of the
Mean
Pair
T1 Scale of
1
student's
mathematics utility
- T2 Scale of
student's
mathematics utility
-.01556
Std.
Std. Error
Deviation
Mean
1.19384
.00943
Difference
Lower
-.03404
Upper
.00293
Sig. (2t
df
-1.649
16020
tailed)
.099
WEEK 6 ASSIGNMENT 1
References
Frankfort-Nachmias, C., & Leon-Guerrero, A. (2015). Social statistics for a diverse society (7th ed.).
Thousand Oaks, CA: Sage Publications.
Walden University (n.d.). Week 5 Scenarios [Handout]. Retrieved from
https://class.waldenu.edu/bbcswebdav/institution/USW1/201730_27/XX_RSCH/RSCH_8210/art
ifacts/USW1_RSCH_8210_Week06_t_testScenarios.pdf
Scenario 1 table one-sample t-tests
One-Sample
Statistics
Q46a. Level of democracy:
today
N
46940
Mean
5.52
Std.
Error
Mean
.013
Std.
Deviation
2.883
One-Sample
Test
Test Value = 0
t
Q46a. Level of
democracy: today
415.007
df
46939
Sig.
(2tailed)
.000
Mean
Difference
5.522
95%
Confidence
Interval of
the
Difference
Lower
5.50
Upper
5.55
Scenario 2 independent-sample t-tests
Group Statistics
Q46a. Level of democracy:
today
Country
by region
Southern
Africa
North
Africa
N
15979
Mean
5.78
Std.
Deviation
2.795
5418
4.90
3.092
Std.
Error
Mean
.022
.042
Independent Samples Test
Q46a. Level of democracy: today
Levene's
Test for
Equality of
Variances
t-test for Equality of
Means
F
Sig.
Equal
variances
assumed
130.649
t
.000
df
19.453
Sig. (2tailed)
21395
Mean
Differenc
.00
Equal
variances not
assumed
18.510
8610.815
.00
Scenario 3 Paired-sample t-test
Paired
Samples
Statistics
Pair 1
Mean
T1 Scale of
student's
mathematics
utility
T2 Scale of
student's
mathematics
utility
N
.0096
Std.
Deviation
16021
Std.
Error
Mean
.99040
.00782
16021
1.00682
.00795
.0059
Paired
Samples
Correlations
Pair 1
N
T1 Scale of
student's
mathematics
utility & T2
Scale of
student's
mathematics
utility
Correlation
16021
Sig.
.285
.000
Paired Samples Test
Paired Differences
Pair 1
Mean
T1 Scale of
student's
mathematics utility T2 Scale of
student's
mathematics utility
t
df
Std.
Deviation
-.01556
Std.
Error
Mean
1.19384
Sig. (2-tailed)
95%
Confidence
Interval of the
Difference
Lower
.00943
-.03404
.00293
Upper
-1.649
16020
...
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