ONE-WAY ANOVA TEST 2
One-Way ANOVA Test
In the field of statistics there are many tests performed in order to analyze different data
sets. Each test is
... [Show More] designed to interpret information given differently for in order to analyze
different aspects of the data set. An ANOVA is one test that is commonly used in the field of
statistics. The ANOVA tests according to Warner (2013) an ANOVA is used to identify part of the
individual score that is within the group membership, as well as the part of the score that is not
associated with the group membership. For a further look in how the ANOVA works the section
and quiz3 will be used from the grades.sav set.
Section 1: Data File Description
The following data is received from sample SPSS data set with the variables being represented
by a teacher’s recording of the performances and demographics of a group of students. The
variables in which are being analyzed are the section and quiz3 variables given by the SPSS data
set. The sample size of the data set is 105 (N=105), which is then broken down into three
separate sections. These sections are labeled as 1,2, and 3 with sections 1 and 3 having 33
students and section 2 involving 39 students. When it comes to the variables the section variable
is going to act as the predictor variable because it does not represent a quantitative value and
being a nominal scale of measurement. With that the quiz3 variable will be acting as the outcome
variable and with a true value of zero, will be a ratio scale of measurement. The true value of
zero with the outcome variable is being based on it being the lowest score a student could receive
on quiz3. These two variables will be used together in order to create analytical data for
ANOVA.
Section 2: Testing Assumptions
Before the ANOVA test is performed it is important to identify an assumption that may
come along with the test. According to Warner (2013) there are three assumptions with the
ONE-WAY ANOVA TEST 3
ANOVA test that need to be addressed. Within the first assumption the independence needs to be
determined. This per Warner (2013) means that there is no existing relationship with the
observation in or between each group. The next assumption that needs to be looked at is that
there are no significant outliers. This means that all single points should fall within the trend with
no points too far from the rest of the group. Lastly the assumption that needs to be addressed
stated from Warner (2013) is that the dependent variable is normally distributed. This allows for
a normal curve to be seen.
Figure 1.1: SPSS histogram of quiz3.
In figure 1.1 the histogram is showing the results for quiz3. Within the histogram the data
shows that there is a standard deviation of 1.6, a mean of 7.13, and N=105. The histogram is also
showing that the tail is not skewed in either direction and scaled almost evenly. Meaning that the
ONE-WAY ANOVA TEST 4
distribution appears to be normal. However, when it comes to the kurtosis per figure 1.1 it is
showing to be more peaked than normal. According to George and Mallery (2016) “A positive
value for the kurtosis indicates a distribution more peaked than normal.” (p.114). By looking at
the histogram the curve peaks towards the top instead of having a more normal bell curve to it.
Descriptive Statistics
N Skewness Kurtosis
Statistic Statistic Std. Error Statistic Std. Error
quiz3 105 -.078 .236 .149 .467
Valid N (listwise) 105
Figure 1.2: SPSS output of quiz3 descriptive statistics with skewness and kurtosis
Within figure 1.2 also referred to as the descriptive statistics the skewness as well as the
kurtosis of quiz3 is being shown. Figure 1.2 is showing that the skewness of quiz3 is at about a
-.078 and a kurtosis of .149. According to George and Mallery (2016) in order for the kurtosis
and skewness values to be excellent they must be at a ±1 or a ±2 to be considered acceptable.
With the values listed above the skewness is at an acceptable level with the kurtosis being
excellent. This helps represent a normal distribution.
Tests of Normality
Kolmogorov-Smirnova Shapiro-Wilk
Statistic df Sig. Statistic df Sig.
quiz3 .143 105 .000 .948 105 .000
a. Lilliefors Significance Correction
Figure 1.3: SPSS output of the Shapiro-Wilk test results for quiz3
Figure 1.3 is showing that the p value is set at .000. With a p value at .000 it is then
considered significant as p < .05. Per Warner (2013) the p value is the value that represents the
risk of a type I error meaning, researchers are normally looking for this to be low. With a p value
of .000 the risk then proved to be significant it also indicates that the null hypothesis is then
rejected.
ONE-WAY ANOVA TEST 5
Test of Homogeneity of Variances
quiz3
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