Pt1420 Unit 5 Assignment

Introduction

For this SPSS final assignment, we will follow our step by step to create supporting statistical output that will include graphs and tables that will assimilate our text and the appropriate data set in their correct place within our research document. Then analyze and explain each section and the variables so that we can gain a much better understanding of the one-way ANOVA and GPA.

Description of Data File

For our data set, we will explore the association amongst quiz 3 and the section that was given to us to evaluate for unit 10 Assignment 1. We will create a sample size which is 105 for this data set. Our predictor variable will be referred to within the class section because there are 3 class sections which make up our

current data set. Within, each of these sections we have around 35 students, it also shows us within this section the measurement of the nominal scale of measurement. Warner (2013), states that nominal scale of measurement can be used to label variables without us having to give a quantitative value. Now, within quiz 3 we noted that the outcome of our variable, unveiled itself and was excepted as the number that represented as the correct answer for quiz 3, and our variable used the ratio scale of measurement. Thereby, the relative amount of the scale of “dimension is the same as our interval within the true value of zero (0 ) in our quizzes where the lowest score is zero., so, this will be a better fit for the variable” (Warner, 2013).
Testing Assumptions
For the testing of the assumptions of the one-way ANOVA, which is comparable to the assumptions of our autonomous t-test. Now, for the first assumption in regards to the one-way ANOVA which is the outcome variable which is considered as quantitative. Therefore, it can either be the interval scale of measurement or ratio. Next, the data score will be normally distributed through our sample and will have no significant outliers.Then there is the following, which has an assumption of homogeneity in the variance. Finally, Warner, (2013), states there should be an independence of observations which means that there will be no relationship amongst the observations within between each group or groups themselves. For our first data set in our histogram which explored the relationship amongst quiz 3 and the frequency, by us looking at the visual interpretations of our graph which can be followed so that our result can be concluded. Therefore, we will have a positive skewness, and it is considered unimodal, and there will be one low outlier which can be considered extreme within our data set and has a positive kurtosis.
Figure 1

Descriptives
Descriptive Statistics
N Minimum Maximum Mean Std. Deviation Skewness Kurtosis
Statistic
Statistic
Statistic Statistic Statistic
Statistic Std. Error Statistic Std. Error
Quiz3 105 0 10 8.05 2.322 1.177 .236 .805 .467
Valid N (listwise) 105

Figure 2
The next display is the descriptive statistics for the data set for Quiz 3. According to George and Mallery (2016), the range for the skewness and kurtosis is considered an output of ±1.0, and it also has an acceptable range, but the application will need to be ±2.0. Thereby, the data must be able to generate an output which needs to be greater than a +2 or less than a - 2 to be considered unacceptable. By gaining this information we can conclude that the quiz 3 scores are acceptable because it is within the range of acceptance for skewness statistic (-1.177) and is in an excellent range for kurtosis statistic (.805), and our standard (Std) deviation which is 2.322 and our mean is 8.05.
Figure 3
In regards to Figure 3, Warner (2013) states that the test of normality, that only the Shapiro-Wilk section of this table can be interpreted, and if the Sig. value of this test is greater than a 0.05, then the data will be considered as normal. But, if the 0.05 is below this number, then the data will be considered as not normal. Therefore, if our reading and understanding of the Shapiro-Wilk test give us the following conclusion then we can state that there is a violation within the normality of all sections in this test.
Example of the Test of Normality for section and Figure 3
Tests of Normality
section Kolmogorov-Smirnova Shapiro-Wilk
Statistic df Sig. Statistic df Sig.
qquiz3 1 .440 33 .000 .550 33 .000
2 .156 39 .018 .909 39 .004
3 .223 33 .000 .853 33 .000
a. Lilliefors Significance Correction

Example of the Test of Normality for section and Figure 4
As we can see with figure 4, the Levene’s test shows that a result of within the p-value of .212 (sig.) and the p-value is much greater than our standard p-value of .05 therefore, based on our test we can state that there is no defilement for this specific assumption., and based on our visual interpretation of descriptive statistics, histogram, and the Levene’s test does not in anyway violate any of this test assumptions, and the results of the Shapiro-Wilk test shows that there are some violations of our assumptions.
Figure 4

Test of Homogeneity of Variances
quiz3
Levene Statistic df1 df 2 Sig.

1.576 2 102 212

Research Question, Hypotheses, and Alpha Level

The question for our research will be very relevant to our statistical test, therefore, the question will be: Is there going to be any significant dissimilarity amongst quiz 3 in different sections of our data set? Then the null hypothesis question is: Are there (no) any difference in the Quiz 3 by the sections. Then our alternative hypothesis will be the quiz 3 by the section. Therefore, we will have an alpha level of 5%.

Interpretation

Figure 5

So, for figure 5 which is the means plot, we use the means plots to see if our mean will be different with the groups of data. Because when we are ale to see the visual interpretation of this section, we will come to the following conclusions, which we can the mean scores for the section that is higher than our mean scores for the section 2 and 3.

Means Plots

Figure 6

Descriptives

For this section, this is where things get a little harder to explain. The above chart represents what we call the descriptive for the one-way ANOVA. This form helps us to conduct the analyzation of the above chart so that we can determine the standard deviation and the mean scores for the quiz 3 and each section. Therefore, once we know what the section is we can show their

representation:
Section 1 M = 9.00, SD = 2.107
Section 2 M = 7.62, SD = 2.098
Section 3 M = 7.61, SD = 2.549
Total (M = 8.05 SD = 2.322
Descriptives
Quiz3
N Mean Std. Deviation Std. Error 95% Confidence Interval for Mean Minimum Maximum
Lower Bound Upper Bound
1 33 9.00 2.107 .367 8.25 9.75 2 10
2 39 7.62 2.098 .336 6.94 8.30 2 10
3 33 7.61 2.549 .444 6.70 8.51 0 10
Total 105 8.05 2.322 .227 7.60 8.50 0 10

Figure 7
ANOVA
Next, we have the one-way ANOVA test that this learner run from our IBM SPSS data set Grade2.sav. By using this data we were able to check the degree of freedom amongst the groups which tells us that it is equal to two and the degree of freedom is equals to 102, and the f value result is 4.305, our p-value is .016. The effect size is identified by using the eta squared (η2 = .077) and the Cohen’s d effect size for this data will index that shows us that it has a small effect size. Thereby, it will have a statistically important dissimilarity amongst groups that we have determined in our one-way ANOVA the: F is 2,102 = 4.305, p = .016.
quiz3
Sum of Squares df Mean Square F Sig.
Between Groups 43.652 2 21.826 4.305 .016
Within Groups 517.110 102 5.070
Total 560.762 104

Figure 8
Now we have to take a look at the F value, which is statistically significant to the post hoc test which can be run as the data output of our data set test. Therefore, the post hoc test is where it shows us how it is our data will be concluded, which is show us any form of significant difference within section 1, 2 and 3 nonetheless we can state that there is no significant difference amongst section 2 and 3.

Multiple Comparisons
Dependent Variable: Quiz3
Tukey HSD
(I) Section (J) Section Mean Difference (I-J) Std. Error Sig. 95% Confidence Interval
Lower Bound Upper Bound
1 2 1.385* .533 .029 .12 2.65
3 1.394* .554 .036 .08 2.71
2 1 -1.385* .533 .029 -2.65 -.12
3 .009 .533 1.000 -1.26 1.28
3 1 -1.394* .554 .036 -2.71 -.08
2 -.009 .533 1.000 -1.28 1.26
*. The mean difference is significant at the 0.05 level.

Conclusion
The one-way ANOVA for this research was performed utilizing the IBM SPSS software so that we can determine if we can identify if there was a statistical significance amongst the sections and the quiz 3 grades. The rejection of the data set null hypothesis shows us a significant dissimilarity within the sections and quiz 3 grade. The statistical test which researchers ran, it shows us the limitation as well as the data strengths. As we can see the strengths of our one-way ANOVA explains the ease of the data, as well as offer an offers an understanding, and a diminution within type 1 errors. This was compared by to the multiple independent t-tests, and it allows the researchers to compare more than two types of conditions that are unlike the current independent t-test. Therefore, as researchers we would be able to see the one main limitation of our one-way ANOVA test, which allows us to see the overall results of our one- way ANOVA and tells us if there will be any difference, however, the data will not stipulate which groups only because of the post hoc test and the Tukey HSD that determines which of these groups are dissimilar which is responsible for adding time to our research process.

References
George, D., & Mallery, P. (2016). IBM SPSS statistics 23 step by step: A simple guide and reference (14th ed.). New York, NY: Routledge. ISBN: 9780134320250.Note: This textbook varies little across editions, should you already possess a prior edition. It is also common for this SPSS reference book to lag behind the software by one version.
Warner, R. M. (2013). Applied statistics: From bivariate through multivariate techniques (2nd ed.). Thousand Oaks, CA: Sage. ISBN: 9781412991346.