The level of significance, α, specifies how rare the sample result must be in order to reject H0 as untenable. It is a probability (typically .05, .01, or .001) based on...
Level of Significance
The level of significance, α, specifies how rare the sample result must be in order to reject H0 as untenable. It is a probability (typically .05, .01, or .001) based on the assumption that H0 is true.
The probability, let’s say .05, is split evenly between the two tails—2.5% on each side—because of the non-directional, two-tailed nature of H1. The regions defined by the shaded tails are called regions of rejection (or critical regions), for if the sample mean falls in either, H0 is rejected as untenable. The critical values of z separate the regions of rejection from the middle region of retention.
There are two ways to evaluate the tenability of H0:
1. Compare p value to α (in this case, .0278 < .05)
2. Compare calculated z ratio to its critical value (+ 2.20 > + 1.96)
Because both p (i.e., area) and the calculated z reflect the location of the sample mean relative to the region of rejection, conclusion regarding H0 will be same.
α gives the probability of rejecting H0 when it is true - Type I error.
* * *
Sources:
Fundamentals of Statistical reasoning in Education, Theodore Coladarci, Casey D. Cobb, Edward W. Minium and Robert C. Clarke (Click for eBook)
The probability, let’s say .05, is split evenly between the two tails—2.5% on each side—because of the non-directional, two-tailed nature of H1. The regions defined by the shaded tails are called regions of rejection (or critical regions), for if the sample mean falls in either, H0 is rejected as untenable. The critical values of z separate the regions of rejection from the middle region of retention.
There are two ways to evaluate the tenability of H0:
1. Compare p value to α (in this case, .0278 < .05)
2. Compare calculated z ratio to its critical value (+ 2.20 > + 1.96)
Because both p (i.e., area) and the calculated z reflect the location of the sample mean relative to the region of rejection, conclusion regarding H0 will be same.
α gives the probability of rejecting H0 when it is true - Type I error.
* * *
Sources:
Fundamentals of Statistical reasoning in Education, Theodore Coladarci, Casey D. Cobb, Edward W. Minium and Robert C. Clarke (Click for eBook)
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