Statistical Analysis ANOVA │Easy Guide On How To Prepare ANOVA Table

Statistical Analysis ANOVA has been the major problem of most students. However, free online tutorials in the absence of your teachers will go a long way to help them out of this problem.

statistical analysis anova

Now, everybody must not learn one thing at the same time. So people understands easily while others will take time to do. Analysis of Variance (ANOVA) table is a guide table that will help you make decisions on the samples being studied.

Read Also: List Of Ongoing Scholarships For Nigerian Students & How To Apply

Trending: Science Technology Project Topics – How To Write A Good Assay

However, there are some calculations which should be made in order to arrive at the table. Here, we are going to use a clear example to illustrate this. Please do well to follow the steps carefully and you problem will all be over.

Let’s use this example to learn Statistical Analysis ANOVA step by step guidelines. First of all the analysis carried out looks like this.

Statistical Analysis ANOVA │Easy Guide On How To Prepare ANOVA Table

An Analyst analyzed Three biscuit samples which he produced with composite flour of wheat and cocoyam at different concentrations. He also analyzed each parameter in three places (triplicate).

Now, we have an example to look at. Below are the values obtained from the analysis. However, we are going to pick out only the Tannin Content Determination among other parameters.

Table 1: Statistical Analysis for Proofing Ability

Sample                        A                      B                      C                      Total

1                                 0.18                 5.58                 3.58                 6.34

2                                 0.18                 5.50                 3.58                 9.26

3                                 0.20                 5.52                 3.50                 9.22

Total                          0.56                 16.60               10.66               27.82

Mean (X)                   0.17                 5.53                 3.55

Now see the following calculations on how to use the Table 1 above and arrive at your ANOVA Table.

1. CF = Square of the Sum Total of samples ÷ no. of sample x no. of treatments

= 27.822 ÷ 3 x 3 = 85.99

2. SS Treatment = Sum of squares of the total of each sample – CF  ÷ no. of replicate

= (0.56)2 + (16.60)2 + (10.66)2 – 85.99 ÷ 3

= 0.3136 + 275.56 + 113.64 – 85.99 ÷ 3

= 129.84 – 85.99

= 43.85

3. SS Total = Sum of squares of the each replicate – CF

= (0.18)2 x 2 + (0.20)2 + (5.58)2 + (5.50)2 + (5.52)2 + (3.58)2 x 2 + (3.50)2 – 85.99

= 0.06 + 0.04 + 31.14 + 30.25 + 30.47 + 25.64 + 12.25 – 85.99

= 129.85 – 85.99

= 43.86

4. SS Error = SS Total – SS Treatment

= 43.86 – 43.85

= 0.01

5.                   Analysis of Variance (ANOVA) Table

Source of variation     df                     ss                     ms                   fcal

Treatment                   2                      43.85               21.93               10965

Error                            6                      0.01                 0.002

Keynote: ss = sum of squares; ms = mean square

* At 5% level of significance, ftab= 5.14; fcal = 10965  (To find ftab, you use the statistical ftab table. In this example, you find 2 under 6 in the table. This will give you 5.14)

Conclusion: fcal > ftab, therefore there is significant difference between the samples

Sample                        A                      B                      C

Mean                          0.17                 5.53                 3.55

Re-arrangement of sample means in their decreasing order of magnitude

Sample                        B                      C                      A

Mean                          5.53                 3.55                 0.17

6. Standard error of mean (S∑ or Sx)

=  √ms error ÷ No. of replicate             =  √0.002 ÷ 3

= 0.03

7. LSD = SSR x S∑

But SSR = 4.34

Therefore, LSD = 4.34 x 0.03

= 0.13

Rule: Anyway two means that differ with more than 0.13 are significantly different

8. 5.53 – 3.55 = 1.98sd

5.53 – 0.17 = 5.36sd

3.55 – 0.17 = 3.38sd

Sample                        B                      C                      A

Mean                           5.53a                3.55b                0.17c

See Also: Flash Share Free Download │Flash share Apk Latest v2.2.0115

∗ That will be all. Lastly, I hope this was helpful? For more tutorial, comment on this post – Statistical Analysis ANOVA │Easy Guide On How To Prepare ANOVA Table. Also subscribe to virginjist.com at the top right hand corner of this page. Subscription is free of charge.

Leave a Reply

Your email address will not be published. Required fields are marked *