|
Superball one (data x) |
Superball two (data y) |
b1 |
63 |
47 |
b2 |
65 |
77 |
b3 |
66 |
76 |
b4 |
68 |
74 |
b5 |
69 |
75 |
b6 |
69 |
71 |
b7 |
70 |
68 |
b8 |
70 |
72 |
b9 |
71 |
83 |
b10 |
71 |
80 |
|
|
|
n |
10 |
10 |
mean |
68.2 |
72.3 |
st dev |
2.7 |
9.89 |
mean diff |
4.1 |
|
c |
0.95 |
|
α |
0.05 |
|
tc |
2.26 |
|
se |
3.24 |
|
E |
7.33 |
|
|
|
|
1 |
-3.23 < µ <11.43 |
ci includes zero, includes no difference as possibility. Not significant |
2 |
Yes |
|
3 |
No |
|
4 |
0.23 |
p-value > 0.05: not significant. |
5 |
No |
|
6 |
Fail to reject |
|
7 |
No |
|
|
Maximum confidence of difference |
|
|
0.77 |
|
|
|
|
|
Difference in the means not significant |
Difference in the means significant |
|
[Either pairwise or for independent samples] |
Confidence interval approach |
Zero is in the confidence interval for the difference of the means |
Zero is not in the confidence interval for the mean difference |
alpha α |
Our willingness to risk rejecting a true null hypothesis |
P-value approach |
p-value is greater than alpha |
p-value is less than alpha |
Max c |
max c is less than 1-α |
max c is greater than 1-α |
result |
fail to reject the null hypothesis |
reject the null hypothesis |
Difference is real? |
No |
yes |
Change is real? |
No |
yes |
statistically significant? |
No |
yes |
If type I risk is 0.05 |
p-value > 0.05 |
p-value < 0.05 |