# Write a 2 paragraph analysis of your t test results for each research scenario

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 Cohens 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 Levenes 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 Cohens 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 ... Purchase answer to see full attachment

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