"This means that there's only a 5% chance that this data was due to pure chance rather than a real difference between a fair coin and the coin you flipped."
Uh, I think you mean the other way around; there's a 5% chance that there's a real difference, and 95% that it was just a matter of luck. You're 95% sure that there is no difference.
Jesse
· 1 year ago
Tordek,
The sentence is awkward, but I think it's correct.
P(O | H<sub>0</sub>) ≤ 0.05 means that if the null hypothesis is correct then there's only a 5% chance of observing what you did.
Jaynes
· 1 year ago
I'm confused about one thing. If the null hypothesis is that the coin is fair and there is insufficient evidence to reject this, but we cannot assert the null hypothesis, doesn't that mean we cannot conclude that the coin is fair?
Jesse Farmer
· 1 year ago
You can never know if a coin is fair, at least not by taking a statistical approach. There will always be some level of variance in the process.
Hypothesis testing lets us quantify that variance and see whether or not the observed results fall outside that bounds. If they do we can say with some level of confidence that the coin is biased.
Let's say a coin lands on heads 51% of the time. If we flip a coin 100 times and get 51 heads it's impossible to tell whether that was the natural variance of a fair coin or the bias of a 51% coin.
In reality a "fair coin" means a "fair enough coin." We'd have to flip a coin 10,000 times before we'd be able to detect a 51% bias for heads.
C
· 1 year ago
I have a question; Why do we need to test the null hypothesis and not the experimental hypothesis?
Jesse Farmer
· 1 year ago
C,
What do you mean by "experimental hypothesis?" The only hypotheses involved are the null hypothesis and its negation, the alternative hypothesis.
If the data is unlikely to have occurred under the null hypothesis, we accept the alternative hypothesis with some level of confidence — usually 95%.
C
· 1 year ago
More specifically; why does a researcher try to disprove the null hypotheses rather then prove the research hypothesis? Why not just test the research hypothesis?
Jesse Farmer
· 1 year ago
How would you prove the alternative hypothesis?
Jesse Farmer
· 1 year ago
Let me put my question another way.
You have a coin and don't know if it's fair. You flip it 100 times and it lands on heads 51 times.
What can you say about the coin? Can you say it's fair? Can you say it's biased?
More generally, it's difficult, if not impossible, to prove a hypothesis is correct. You can prove a hypothesis is false, however. So if you want to know whether a coin is biased you should see whether the data falsifies the converse, viz., that the coin is biased.
Charles
· 8 months ago
I think that the "p" in the denominator for the "z score" should be the hypothesized value, in this case 0.50. You table uses calculated values to find z.
This text is from the referenced web site. (McClave and Sincich also define the formula that way.) "Analyze Sample Data Using sample data, find the test statistic and its associated P-Value. • Standard deviation. Compute the standard deviation (σ) of the sampling distribution. σ = sqrt[ P * ( 1 - P ) / n ] where P is the hypothesized value of population proportion in the null hypothesis, and n is the sample size."
Jesse Farmer
· 8 months ago
You're right, I equivocated in my use of "p". At first I use it to mean the value of p under the null hypothesis, H_0: p = 0.50, but then use it to mean the measured value elsewhere.
I'll fix it.
kayla
· 6 months ago
i would like for this page to tell me the answer not give me examples. i need an answer not stupid examples.please thank you
Jesse Farmer
· 6 months ago
The answer to what?
Bill Smith
· 2 weeks ago
Jesse, thank you for writing this series of articles on statistics.
I understand that small z-scores are better than big ones, but where is the dividing line?
All Comments
Uh, I think you mean the other way around; there's a 5% chance that there's a real difference, and 95% that it was just a matter of luck. You're 95% sure that there is no difference.
The sentence is awkward, but I think it's correct.
P(O | H<sub>0</sub>) ≤ 0.05 means that if the null hypothesis is correct then there's only a 5% chance of observing what you did.
Hypothesis testing lets us quantify that variance and see whether or not the observed results fall outside that bounds. If they do we can say with some level of confidence that the coin is biased.
Let's say a coin lands on heads 51% of the time. If we flip a coin 100 times and get 51 heads it's impossible to tell whether that was the natural variance of a fair coin or the bias of a 51% coin.
In reality a "fair coin" means a "fair enough coin." We'd have to flip a coin 10,000 times before we'd be able to detect a 51% bias for heads.
Why do we need to test the null hypothesis and not the experimental hypothesis?
What do you mean by "experimental hypothesis?" The only hypotheses involved are the null hypothesis and its negation, the alternative hypothesis.
If the data is unlikely to have occurred under the null hypothesis, we accept the alternative hypothesis with some level of confidence — usually 95%.
You have a coin and don't know if it's fair. You flip it 100 times and it lands on heads 51 times.
What can you say about the coin? Can you say it's fair? Can you say it's biased?
More generally, it's difficult, if not impossible, to prove a hypothesis is correct. You can prove a hypothesis is false, however. So if you want to know whether a coin is biased you should see whether the data falsifies the converse, viz., that the coin is biased.
This text is from the referenced web site. (McClave and Sincich also define the formula that way.)
"Analyze Sample Data
Using sample data, find the test statistic and its associated P-Value.
• Standard deviation. Compute the standard deviation (σ) of the sampling distribution.
σ = sqrt[ P * ( 1 - P ) / n ]
where P is the hypothesized value of population proportion in the null hypothesis, and n is the sample size."
I'll fix it.
I understand that small z-scores are better than big ones, but where is the dividing line?