Analysis of Variance commonly known as ANOVA is both a method and model used in statistics for the purposes of analyzing differences in mean of a variable across a number of observations. Analysis of Variance utilizes the ratios of variance for purposes of determining whether there exists a difference in the means of the observations. Simply put, Analysis of Variance seeks to test differences between three or more variables normally measured on an interval scale (Lecture 2 Notes).
Analysis of Variance is relied on as a statistical tool since it is a pertinent building block for numerous statistical analyses, and for its ability to give a measure of the average squared deviation of a set of values around the mean. It is also a basic descriptive statistics and is the square of the standard deviation. Analysis of Variance will therefore be an extension of the difference of means test in a case where three or more variables differ in their ability to give similar outcomes (Lecture 2 Notes).
Analysis of Variance utilizes various testing structures including One-way Analysis of Variance, Two-way Analysis of Variance, and Multi-factor Analysis of variance. The One-way Analysis of Variance aims at testing the differences in a single dependent variable among three or more groups. In this experiment, One-way Analysis of Variance will seek to test the difference in the three different ways of learning a choropleth map. One-way Analysis of Variance will test whether the results obtained in the score sheet formed by the categories of choropleth map learning seem similar. In the event that the results on the score sheet seem to differ, it can then be concluded that the way of learning the choropleth map has an effect on the groups ability to answer correctly and fast. This means that different treatment groups have different outcomes (Lecture 2 Notes).
Analysis of Variance is based on certain requirements and assumptions. These include the assumption that three or more independent and randomly selected observations are independent, there are approximately equal number of participants in each observation, there is roughly equal variance between the conditions, and that the data are at an interval or the ration scale. All these requirements and assumptions should be true for all versions of the test (Lecture 2 Notes).
Method
Analysis of Variance will attempt to examine the manner in which the groups internally against the differences that are observable between them. In this experiment, Analysis of Variance will attempt to determine whether the mean response time from the three groups is significantly different as well as to examine the effect that a logarithmic transform have on a positively skewed data.
The following steps are to be followed for the One-way Analysis of Variance
The mean response time for each of the observations is to be calculated. This is known as the Group Means.
The mean for the entire group combined is calculated. This is known as the Overall Mean or Grand Mean.
The total deviation of each individual score from the Group Mean is calculated within each group. This is known as Within Group Variation.
The deviation of each Group Mean from the Overall Mean is calculated. This is known as Between Group Variation.
Analysis of Variance will then produce the F statistic which is the ratio between Group Variation to the Within
Group Variation.
In the event that the Between Group Variation is significantly greater than the Within Group Variation, then it is most probable that there exists a statistically significant difference the groups. The statistical package should be able to confirm if the F ratio is significant or not. If the Group Variance is close to the Within Group Variance, then the null hypothesis is accepted. However, if the Group Variance is significantly greater than Within Group Variance, then it is enough reason to have less confidence in the null hypothesis.
Results
The response time for individual tests within each group were recorded on a score sheet as indicated in table 1 (see appendix). The following Group Means and Overall Mean were calculated from the results
Group Means
Group 1 789102410871220126313411359146215131518157916702010233225852601261531249734 4082619 2148.73
Group 2
48783012061286148115631569158016161623162618382019219525465427 2891916 1807.44
Group 3
317579617741796104011821198123412721510160116911757216023544503 2455217 1444.24
Overall Mean Grand Mean
Group 1 total Group 2 total Group 3 total total responses
408262891924552 52 1813.40
Between Group Variation
Grand Mean Group 1 Mean
1831.40 2148.73 -317.33
Grand Mean Group 2 Mean
1831.40 1807.44 23.96
Grand Mean Group 3 Mean 369.16
In working out if the three groups differ in their ability to correctly answer to the choropleth map questions and the response time taken by each group, and then it will be important to conduct a standard t-test between the group means. Analysis of Variance would be the ideal extension of the difference of means test to the three groups. In this experiment, all the Group Means are different
Since the Group Means seem different, it can therefore be concluded that the method of learning the choropleth map has an effect on the correctness of the response obtained as well as the response time duration by the subjects in each group.
Discussion
The results of this experiment indicate that the subjects in group 1 took the longest mean response time in answering the choropleth map questions. The subjects in group 2 took less response time compared to group 1 subjects while the group 3 subjects took the shortest mean response time. The null hypothesis that was being tested was the correctness of the answers and the response time duration by a subject in remembering a choropleth map is dependent on the method used on learning the map. The alternative hypothesis was that there is no correlation between the correctness of the answers and the response time taken by subjects in remembering a choropleth map, and the method of learning the map. In this experiment, all the Group Means are different
Since the Group Means seem different, it can therefore be concluded that the method of learning the choropleth map has an effect on the correctness of the response obtained as well as the response time duration by the subjects in each group.
In conducting a One-way Analysis of Variance in testing the difference in a single dependent variable, in this case the time response duration among the three groups, it is clear that the three groups formed by the categories of the independent variable are different. The groups have different pattern of dispersion as measured by comparing estimates of group variances. It is on this basis of the difference of variances that it is concluded that the method of learning the choropleth map has an effect on the response time duration taken by the subjects. This means that showing the three groups the choropleth map in different ways produced different outcomes.
In this experiment, there is no significant difference between the Between Group Variation and the Within Group Variation. This means that there is no statistically significant difference between the three groups. Because our Between Group Variance is close to Within Group Variance, then the null hypothesis can be confidently accepted. It is therefore right to say that the correctness of the answers and the response time duration by a subject in remembering a choropleth map is dependent on the method used on learning the map.
Analysis of Variance is relied on as a statistical tool since it is a pertinent building block for numerous statistical analyses, and for its ability to give a measure of the average squared deviation of a set of values around the mean. It is also a basic descriptive statistics and is the square of the standard deviation. Analysis of Variance will therefore be an extension of the difference of means test in a case where three or more variables differ in their ability to give similar outcomes (Lecture 2 Notes).
Analysis of Variance utilizes various testing structures including One-way Analysis of Variance, Two-way Analysis of Variance, and Multi-factor Analysis of variance. The One-way Analysis of Variance aims at testing the differences in a single dependent variable among three or more groups. In this experiment, One-way Analysis of Variance will seek to test the difference in the three different ways of learning a choropleth map. One-way Analysis of Variance will test whether the results obtained in the score sheet formed by the categories of choropleth map learning seem similar. In the event that the results on the score sheet seem to differ, it can then be concluded that the way of learning the choropleth map has an effect on the groups ability to answer correctly and fast. This means that different treatment groups have different outcomes (Lecture 2 Notes).
Analysis of Variance is based on certain requirements and assumptions. These include the assumption that three or more independent and randomly selected observations are independent, there are approximately equal number of participants in each observation, there is roughly equal variance between the conditions, and that the data are at an interval or the ration scale. All these requirements and assumptions should be true for all versions of the test (Lecture 2 Notes).
Method
Analysis of Variance will attempt to examine the manner in which the groups internally against the differences that are observable between them. In this experiment, Analysis of Variance will attempt to determine whether the mean response time from the three groups is significantly different as well as to examine the effect that a logarithmic transform have on a positively skewed data.
The following steps are to be followed for the One-way Analysis of Variance
The mean response time for each of the observations is to be calculated. This is known as the Group Means.
The mean for the entire group combined is calculated. This is known as the Overall Mean or Grand Mean.
The total deviation of each individual score from the Group Mean is calculated within each group. This is known as Within Group Variation.
The deviation of each Group Mean from the Overall Mean is calculated. This is known as Between Group Variation.
Analysis of Variance will then produce the F statistic which is the ratio between Group Variation to the Within
Group Variation.
In the event that the Between Group Variation is significantly greater than the Within Group Variation, then it is most probable that there exists a statistically significant difference the groups. The statistical package should be able to confirm if the F ratio is significant or not. If the Group Variance is close to the Within Group Variance, then the null hypothesis is accepted. However, if the Group Variance is significantly greater than Within Group Variance, then it is enough reason to have less confidence in the null hypothesis.
Results
The response time for individual tests within each group were recorded on a score sheet as indicated in table 1 (see appendix). The following Group Means and Overall Mean were calculated from the results
Group Means
Group 1 789102410871220126313411359146215131518157916702010233225852601261531249734 4082619 2148.73
Group 2
48783012061286148115631569158016161623162618382019219525465427 2891916 1807.44
Group 3
317579617741796104011821198123412721510160116911757216023544503 2455217 1444.24
Overall Mean Grand Mean
Group 1 total Group 2 total Group 3 total total responses
408262891924552 52 1813.40
Between Group Variation
Grand Mean Group 1 Mean
1831.40 2148.73 -317.33
Grand Mean Group 2 Mean
1831.40 1807.44 23.96
Grand Mean Group 3 Mean 369.16
In working out if the three groups differ in their ability to correctly answer to the choropleth map questions and the response time taken by each group, and then it will be important to conduct a standard t-test between the group means. Analysis of Variance would be the ideal extension of the difference of means test to the three groups. In this experiment, all the Group Means are different
Since the Group Means seem different, it can therefore be concluded that the method of learning the choropleth map has an effect on the correctness of the response obtained as well as the response time duration by the subjects in each group.
Discussion
The results of this experiment indicate that the subjects in group 1 took the longest mean response time in answering the choropleth map questions. The subjects in group 2 took less response time compared to group 1 subjects while the group 3 subjects took the shortest mean response time. The null hypothesis that was being tested was the correctness of the answers and the response time duration by a subject in remembering a choropleth map is dependent on the method used on learning the map. The alternative hypothesis was that there is no correlation between the correctness of the answers and the response time taken by subjects in remembering a choropleth map, and the method of learning the map. In this experiment, all the Group Means are different
Since the Group Means seem different, it can therefore be concluded that the method of learning the choropleth map has an effect on the correctness of the response obtained as well as the response time duration by the subjects in each group.
In conducting a One-way Analysis of Variance in testing the difference in a single dependent variable, in this case the time response duration among the three groups, it is clear that the three groups formed by the categories of the independent variable are different. The groups have different pattern of dispersion as measured by comparing estimates of group variances. It is on this basis of the difference of variances that it is concluded that the method of learning the choropleth map has an effect on the response time duration taken by the subjects. This means that showing the three groups the choropleth map in different ways produced different outcomes.
In this experiment, there is no significant difference between the Between Group Variation and the Within Group Variation. This means that there is no statistically significant difference between the three groups. Because our Between Group Variance is close to Within Group Variance, then the null hypothesis can be confidently accepted. It is therefore right to say that the correctness of the answers and the response time duration by a subject in remembering a choropleth map is dependent on the method used on learning the map.
No comments:
Post a Comment