Hypothesis testing in ANOVA
Introduction:
The case study deals with hypothesis testing in ANOVA. Where we have more than two samples. The samples are denoted by treatment also. We compare that whether the average effect of all the treatments is same or they differ significantly. Or we compare the independent mean and we conclude that whether the mean is same for all the populations or it differs significantly.
Case Study: We have picked 3 balls foam, whiffle and rubber. We threw all the balls 11 different times and noted the distance travelled by the ball. Now we have to test that whether any specific ball has the significant effect on the distance. Or all the balls are same. That means average effect of all the balls are same or whether …show more content…
And we have one response variable called distance travelled.
Stating Hypothesis
Null Hypothesis, H0: µ1 = µ2 = µ3
That means we assume that average distance traveled by all the balls are same
Alternative Hypothesis, H1: µ1 ≠ µ2 ≠ µ3
That means average distance traveled by all the balls are not same, balls are significantly different.
For testing the hypothesis we need to make ANOVA table, the format of ANOVA table is as follows
Source of variation Degrees of Freedom Sum of Squares Mean Squares
Between Treatments k – 1 SSB SSB /(k – 1)
Residuals n – k SSR SSR/(n – k)
Total n – 1 SST
The relevant calculations are as follows k = Total number of samples or treatment = 3 n – sum total of all the data points of all the sample = (11 + 11 + 11) = 33
SST = SSB + SSR
i – stands for number of treatment j – stands for number of response the first treatment is foam, second is whiffle and third is rubber yij2 = (1232 + 1202 + 1182 + 1202 +1192 + 1202 + 1202 + 1222 + 1212 + 1172 + 1202) +
(1092 +1112 + 1092 + 1082 + 1072 + 1102 + 1132 + 1092 + 1082 +1082 + 1082) …show more content…
The average distance travelled by foam ball is more than whiffle ball.
The foam ball and rubber balls have no statistically different effect on distance travelled.
The whiffle ball and rubber ball have no statistically different effect on distance
Introduction:
The case study deals with hypothesis testing in ANOVA. Where we have more than two samples. The samples are denoted by treatment also. We compare that whether the average effect of all the treatments is same or they differ significantly. Or we compare the independent mean and we conclude that whether the mean is same for all the populations or it differs significantly.
Case Study: We have picked 3 balls foam, whiffle and rubber. We threw all the balls 11 different times and noted the distance travelled by the ball. Now we have to test that whether any specific ball has the significant effect on the distance. Or all the balls are same. That means average effect of all the balls are same or whether …show more content…
And we have one response variable called distance travelled.
Stating Hypothesis
Null Hypothesis, H0: µ1 = µ2 = µ3
That means we assume that average distance traveled by all the balls are same
Alternative Hypothesis, H1: µ1 ≠ µ2 ≠ µ3
That means average distance traveled by all the balls are not same, balls are significantly different.
For testing the hypothesis we need to make ANOVA table, the format of ANOVA table is as follows
Source of variation Degrees of Freedom Sum of Squares Mean Squares
Between Treatments k – 1 SSB SSB /(k – 1)
Residuals n – k SSR SSR/(n – k)
Total n – 1 SST
The relevant calculations are as follows k = Total number of samples or treatment = 3 n – sum total of all the data points of all the sample = (11 + 11 + 11) = 33
SST = SSB + SSR
i – stands for number of treatment j – stands for number of response the first treatment is foam, second is whiffle and third is rubber yij2 = (1232 + 1202 + 1182 + 1202 +1192 + 1202 + 1202 + 1222 + 1212 + 1172 + 1202) +
(1092 +1112 + 1092 + 1082 + 1072 + 1102 + 1132 + 1092 + 1082 +1082 + 1082) …show more content…
The average distance travelled by foam ball is more than whiffle ball.
The foam ball and rubber balls have no statistically different effect on distance travelled.
The whiffle ball and rubber ball have no statistically different effect on distance