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# Analysis of Variance (anova) (Coursework Sample)

Instructions:

A statistical analysis, interpretation and presentation of data

source..Content:

ANALYSIS OF VARIANCE (ANOVA)

Anova (analysis of variance) is a statistical tool used to establish if there is substantial difference between two means. There is a relationship between the Anova and the t-test for independent variables. The two statistical approaches give the same result only if the groups under comparison are two dissimilar observation or cases. The result will also be a replica of each method if the two variables are from one set of observation or cases like in this scenario. The working principle behind Anova is the fact that it is possible to partition variance. Since variance is calculated as the sum of squared derivation out of the total mean, variance is thus a function of the sum of squares or deviations (Murray & Stephens 2011).

The data used to perform the Anova manipulation in this case came from observation. The method employed to collect the data is correlation as opposed to experimental since the data collected could not be manipulated as the variables could not be influenced. Data came from observing the speed of vehicles as they approached a bend on the road. Since the distance was predetermined, time was measured and used to compute the vehicle’s speed. The sample space consists of 21 vehicles as indicated in the tabled below.

Vehicle123456789101112131415161718192021Speed (km/hr)504060205045652530302040707066374352604020 Table1: Showing observational data

The first eight observation and the last seven observations were used as the samples for Anova computation. This is shown in the tables below.

Vehicle12345678Speed (km/hr)5040602050456525 Table 2: First 8 observational data

Vehicle15161718192021Speed (km/hr)66374352604020 Table3: Last 7 observational data

The data from tables 2 and 3 were used to perform Anova with the help of an online calculation and the results are as follows.

Table 4: Data entry

Table 5: Mean, variance, standard deviation and standard error

Table 6: Sum of squares (SS),

Analysis of results

Table 5 shows the mean and variance of the data which is used to calculate the standard deviation and error. The means are used to calculate the SS from each group of data. The total SS between each g...

Anova (analysis of variance) is a statistical tool used to establish if there is substantial difference between two means. There is a relationship between the Anova and the t-test for independent variables. The two statistical approaches give the same result only if the groups under comparison are two dissimilar observation or cases. The result will also be a replica of each method if the two variables are from one set of observation or cases like in this scenario. The working principle behind Anova is the fact that it is possible to partition variance. Since variance is calculated as the sum of squared derivation out of the total mean, variance is thus a function of the sum of squares or deviations (Murray & Stephens 2011).

The data used to perform the Anova manipulation in this case came from observation. The method employed to collect the data is correlation as opposed to experimental since the data collected could not be manipulated as the variables could not be influenced. Data came from observing the speed of vehicles as they approached a bend on the road. Since the distance was predetermined, time was measured and used to compute the vehicle’s speed. The sample space consists of 21 vehicles as indicated in the tabled below.

Vehicle123456789101112131415161718192021Speed (km/hr)504060205045652530302040707066374352604020 Table1: Showing observational data

The first eight observation and the last seven observations were used as the samples for Anova computation. This is shown in the tables below.

Vehicle12345678Speed (km/hr)5040602050456525 Table 2: First 8 observational data

Vehicle15161718192021Speed (km/hr)66374352604020 Table3: Last 7 observational data

The data from tables 2 and 3 were used to perform Anova with the help of an online calculation and the results are as follows.

Table 4: Data entry

Table 5: Mean, variance, standard deviation and standard error

Table 6: Sum of squares (SS),

Analysis of results

Table 5 shows the mean and variance of the data which is used to calculate the standard deviation and error. The means are used to calculate the SS from each group of data. The total SS between each g...

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