Hypothesis testing and interpretation
In ANOVA….
| H0 = m1=m2=m3 groups | = means are equal = No variance, m1, m2, m3 are mean value of the |
If F is larger than 1.96 and P<0.05 then distribution is significant
Null hypothesis H0 is rejected = Alternate hypothesis accepted = Means are not equal.
Significance indicates variance between groups exists.
Insignificant indicates the groups are equal.
In Correlation….
| H0 = ρ = 0 | ρ = rho = population correlation r = Sample correlation |
ρ = r
ρ = r = 0 means there is no correlation
Therefore H0 = ρ = r = 0
P = significant = reject null hypothesis that r = 0
Alternatively say r > 0 meaning that there is correlation.
Therefore P< 0.05 means significant correlation exists
In Regression…
H0 = β1 = 0 β = Beta = Regression Coefficient
β1 = 0 then there is no relationship between x and y
If p<0.05 = significant = reject null hypothesis that β1=0 and say β1 > 0
Β1 > 0 means there is relationship between x and Y or say X influences Y significantly
Significance means relationship or influence exists
In Chi-Square…
H0 = Row and column are independent = No relationship
P<0.05 = Significant = Reject Null hypothesis that No relationship exists and accept that
relationship exists. = Row is dependent on Column variable.
Significance means relationship or dependency of variables exists.
If you want to test if something is equal to sample mean, test the two tail significance so that
it test plus or minus from the mean value.
For two sided significance test P<0.025, F or t greater than 1.96 *2 = 3.92.
If you want to test if some value is greater than the sample mean, test the one tailed test.
For one sided significance test P < 0.05, F or t greater than 1.96
Z or t = 1.645 for 90% Confidence level
= 1.96 for 95% Confidence level
= 2,575 for 99% Confidence level
Comparing table value
If table value is less than calculated value – reject Null hypothesis
If calculated value is higher than Table value then hypothesis is significant and NULL
hypothesis is rejected.