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# Anova

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### Anova

1. 1. ANOVA Test the means of several samples have significance difference or not
2. 2. ANOVA Test the given samples can be considered as having been drawn from population with same mean or all from the same population significance difference or not
3. 3. <ul><li>Agricultural research </li></ul>
4. 4. One way classification <ul><li>Observations are classified into groups on the basis of single criterion.In such classification there are k samples ,one from each k normal populations with common variance </li></ul>
5. 5. MSE N-k SSE Within samples N-1 SST Total MSC K-1 SSC Between samples Mean square Degree of freedom Sum of Squares Source of variation
6. 6. ANOVA table for two way analysis of variance N-1 SST Total F R MSE (C-1)(r-1) SSE Residual F C MSR r-1 SSR Between rows MSC C-1 SSC Between columns F ratio Mean square Degree of freedom Sum of squares Sources of variation
7. 7. ANOVA <ul><li>The analysis of variance frequently referred to us ANOVA. </li></ul><ul><li>It is a statistical technique, specially designed to test whether the means of more than 2 quantitative populations are equal. </li></ul><ul><li>The analysis of variance technique developed by prof. R.A Fischer in 1920’s is capable of fruitful application to a diversity of practical problems. </li></ul>
8. 8. <ul><li>Basically it consist of classifying and cross classifying statistical results and testing whether the means of a specified classification differ significantly </li></ul><ul><li>Eg. The output of a given process might be cross classified by machines & operators. Each operator having worked on each machine. </li></ul>
9. 9. One way Classification <ul><li>In this the data are classified according to only one criteria.The null hypothesis is </li></ul>
10. 10. Correlation in Bivariate frequency Table <ul><li>In a bivariate distribution the data are fairly large ,they must be summarized in the form of a two way table. Here for each variable the values are grouped into various classes( not necessarily the same for both the variable) keeping in view the same consideration as in the case of univariate distribution. </li></ul><ul><li>Eg. If there are m classes for the x variable series and n classes for the y variable series then there will be m*n cells in the two way table. By going through the different pairs of the values(x,y) and using tally marks we can find the frequency for each cell and thus obtained the so called bivariate frequency table . </li></ul>