The data set used for this assignment was the grades.sav data file. The variables used were gender, GPA, total, and final. GPA and final were used in the histogram scales, along with skewness, kurtosis values, and scatter plot. This assignment included a sample size of (N) 105.
Testing Assumptions
There are two histograms, showing information on GPA, and showing information on final grade. Histograms are commonly used with interval or ratio level data (Corty, 2007). The data in the GPA is distributed and slightly skewed to the right, which means it has a positive skew and has a peaked distribution. The final histogram also has a leptokurtic frequency distribution, but is skewed to the left meaning this has a negative skew.
Descriptive Statistics
N Minimum Maximum Mean Std. Deviation Skewness Kurtosis
Statistic Statistic Statistic Statistic Statistic Statistic Std. Error Statistic Std. Error
GPA 105 1.14 4.00 2.7789 .76380 -.052 .236 -.811 .467
final 105 40 75 61.48 7.943 -.335 .236 -.332 .467
Valid N (listwise) 105
A kurtosis value near zero indicates a shape close to normal. A negative value indicates a distribution which is more peaked than normal, and a positive kurtosis indicates a shape flatter than normal. An extreme positive kurtosis indicates a distribution where more of the values are located in the tails of the distribution rather than around the mean (Grad pad, 2013). A kurtosis value of +/-1 is considered very good for most psychometric uses, but +/-2 is also usually acceptable (Grad pad, 2013). The above graph shows GPA with a kurtosis of -.811; awhile the final kurtosis is -33.2.
The extent to which a distribution of values deviates from symmetry around the mean is the skewness. A value of zero means the distribution is symmetric, while a positive skewness indicates a greater number of smaller values, and a negative value indicates a greater number of larger values (Grad pad, 2013). Values for acceptability for psychometric purposes (+/-1 to +/-2) are the same as with kurtosis.
Scatter plots are similar to line graphs in that they both use horizontal and vertical axes to plot data points. The closer the data aims to making a straight line, the higher the correlation between the two variables, or the stronger the relationship(MSTE,n.d) The scatter plot above does not have a straight line formation, so that showing that there is not a strong relationship between the two variables of GPA and final.
An example of a null hypothesis for the variables used in this data collection would be, “Does GPA predicts final exam scores? An alternative hypothesis would be that GPA scores do determine the exam scores.
1. Give some examples of how the results of a study might be significant statistically yet unimportant educationally. Could the reverse be true?
Then, a scatterplot was formed with the data (Figure 3). It was a crucial graph as it helped determine the outliers in the information (see Appendix D for the outlier chart). Some of these outliers were located in towns with really low population numbers (the average population for an American city or town is around 20000)
...will fall within the first standard deviation, 95% within the first two standard deviations, and 99.7% will fall within the first three standard deviations of the mean. The Empirical Rule is used in statistics for showing final outcomes. After a standard deviation is found, and before exact data can be collected, this rule can be used as an estimate to the outcome of the new data. This probability can be used for gathering data that may be time consuming, or even impossible to found. When the mean equals the median and the values cluster around the mean and median, producing a bell-shaped distribution, then we can use the empirical rule to examine the variability. In this bell-shaped data set, we can calculate the mean and the standard deviation. The mean means the average value of the set of data. The standard deviation means the average scatter around the mean.
Grades do motivate students to do better but, grades cause students to want to get a good grade instead of fully mastering the material. They look at school just trying to pass which promotes cheating on tests and homework. They also will choose the material that is the easiest and choose a class with a professor who doesn’t care to raise their GPA. School is supposed to be about learning and understanding new material to help gain knowledge and a new way of thinking.
The topic of outliers for scatter plots can be a confusing and a topic that is specific to a person’s interpretation. The point of (1300, 20), is not considered an outlier due to the point being part of the overall pattern. Outliers are considered “striking deviation from the overall pattern” (Gerstman, 2015, p. 334). The point (1300, 20), is an element of the positive association of the scatter plot. Different people may interpret a scatter plot in different ways. An excellent example is how you interpreted the point to be an outlier. However, the textbook stated that there was no outlier to the data set. This is a confusing component of interpreting a scatter plot; it is up to the reader’s interpretation. Excellent question, I hope this clarified
A trend line is a straight line drawn through the center of a group of points plotted on a scatter plot.
The traditional high school A-F grading system no longer reflects an accurate measurement of student success. Providing a new system where grades are measured by the rank of the student in the class will provide a system more honest than before, it will benefit students and prospective colleges. Changing the grading scale to a system where students are ranked from a curve based off the total percentage of points potentially earned in the course.
One of the most stressful experiences for a high school senior is the search for the college. So once these senior students finally develop a plan, why is it that they may not be able to achieve what they desire? Colleges and universities today are becoming more and more competitive, sometimes to the point of exclusive. With that it is fair to say that entrance to certain schools may be more difficult and extensive than the others based on popularity and demand. When this happens, colleges are looking for the best of the best in academics, the student who will represent and be the best for their institution. So what is the determining factor for college acceptance for students? The most accurate answer would be standardized test scores. While other factors are considered in acceptance, the ACT and SAT scores are what is most crucial to a student’s acceptance. Colleges put too much stock in standardized test scores when considering admission. Standardized test scores: limit diversity and creativity, represent skill more than progress, cause test taking anxiety, and result in inaccurate placement due to differently interpreted results. Due to these reasons, admission should be based on equal representation on all aspects of the applicant rather than a number that only defines how well a student can perform in their basic knowledge.
In “How Grading Reform Changed Our School,” author Jeffrey A. Erickson discusses about how it is common in high schools to pass each student by their accumulated average of the entire class period. He described many examples to display the way of grading in high schools such as in behaviors, lessons, and tasks. He talks about the changes that were made and were in effect to achieve a grading average that reflects the student 's’ abilities and knowledge .
Standard Deviation is a measure about how spreads the numbers are. It describes the dispersion of a data set from its mean. If the dispersion of the data set is higher from the mean value, then the deviation is also higher. It is expressed as the Greek letter Sigma (σ).
In evaluating statistical data one thing to consider is the measure that is used. By understanding the different statistical measurement tools and how they differ from one another, it is possible to judge whether a statistical graph can be accepted at face value. A good example is using the mean to depict averages. This was demonstrated by using the mean as a measure of determining the distribution of incomes. The mean income depicted was, $70,000 per year. At face value, it looks as though the sample population enjoys a rather high income. However, upon seeing individual salaries, it becomes obvious that only a few salaries are responsible for the high average income as depicted by the mean. The majority of the salaries were well under the $70,000 average. Therefore, the mean distributed income of $70,000 was at best misleading. By also looking at the median and mode measures of the income distributions, one has a clearer picture of the actual income distributions. Because this data contained extreme values, a standard deviation curve would have given better representation of salary distribution and would have highlighted the salaries at the high level and how they skewed the mean value.
Null hypothesis (pg. 49) – a type of hypothesis in which there is no relationship between the measured variables, and offers no support to the original hypothesis. An example of a null hypothesis would be that there was no relationship between time played and the number of concussions sustained by players who had high playing times.
__C__ 13. If the scores on X give us no information about the scores on Y, this indicates
From the graphs, it could be determined that the results are fairly precise due to the data points being fairly close rather than scattered. This can be seen as all the points are relatively close to the average value on graphs 1 and 2, not causing the trend line to be skewed.
Descriptive statistics are procedures used to describe and organize the basic characteristics of the data studied. Descriptive statistics provide simple summaries about the sample group and the measures. This application of statistics is used to present quantitative data in manageable forms such as charts, graphs, or averages. Descriptive statistics differ from inferential statistics in that they are simply describing what the data indicates.