Describe about F TEST.
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
Describe about F TEST.
In ANOVA, “SS” stands for “sum of squares”, “df” stands for degrees of freedom, F is for the test statistic of the ANOVA test procedure. The sum of squares “between”, or the sum of squares of the factors measures the variability between the factors; the sum of squares “within” measures the sum of squares of the errors, that is, the variability that is not explained by any of the factors.
The “MS” or mean of squares is obtained by dividing the sum of squares by the corresponding df. Thus,
MSbetween = SSbetween / dfbetween.
MSwithin = SSwithin / dfwithin.
The F-statistic would follow the F-distribution with degrees of freedom (dfbetween , dfwithin), if the null hypothesis is true. The null hypothesis, H0 in an ANOVA is typically that, there is no significant difference between the mean effects of the factors under study and the alternative hypothesis is that, at least one pair of factor means are different.
The F-statistic is given by:
F = MSbetween / MSwithin
The F statistic is the ratio of variance between sample mean to the variance within sample mean. That is, F = variance between sample mean / variance within sample mean. Under the null hypothesis F ratio is approximately 1. If both variances are same then the F ratio takes the value 1.
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