I am so confused about P-Value

[Panda_Food]

In my point of view, when P become larger than alpha, means more data fall outside of the difference (between mean and observation mean),

then it means H_0 (mean didn’t change) is wrong.

Why the conclusion in the screen capture is opposite? (Do not reject H_0)???

Anyone can help?

[Panda_Food]

Does the H_0 should actually mean “Mu” has changed? (Instead of no change)

[_kurt]

Hello @Panda_Food

For what the p-value means, I recommend rewatching the video as it explains its definition and intuition. If you are still confused about it, feel free to ask again here!

H_0 means no change. The conclusion “Do not reject H_0” is correct since the p-value (0.0663) is greater than alpha (0.05), as discussed in the decision rule from the video.

[Panda_Food]

Yes I re-watched it

[Deepti_Prasad]

hi @Panda_Food

See if this helps you understand better!

C3_W4(p-value) : Why are we rejecting null hypothesis when type-1 error is under significance level? (https://www.coursera.org/learn/machine-learning-probability-and-statistics/lecture/znGVX/p-value)

Hello, @GORRELA_SRI_SATYA_VE, The larger the sample mean \bar{X}, the more right (extreme) it is to the population mean \mu, the more likely the sample does not belong to the population (H_0) and thus H_0 rejected. In other words, very “right” (“extreme”) sample is unlikely generated by the population (or generated under H_0)! But how right is right enough? We use \alpha for that! [image] \alpha is the area (at the right tail) in which any sample fallen is considered "unlikely by the popula…

Regards
DP

[SNaveenMathew]

The true interpretation of a (frequentist) p-value and confidence interval is tricky. Deepti’s explanation is a good simplified version. I’ll try to add an example to explain.

Assume we’re looking at the population of males a country A with an average height of 180cm. We want to compare the average height of another country B with the average height of country A - first let’s try to infer if they are “different”, not whether the average of A is higher or vice versa. Unlike the “true average” reported for A, we have access to only a random sample of 2 males from B and the average is 175cm. Is the “true average” height of males in country B “different” from the average of “true average” country A?

Since we don’t know the true average for country B, to answer this question using the random sample of 2 from country B we need to do some guess work (we can only make inferences, but we can never state “country B males have a different average height than country A males”) - this comes with a measure of uncertainty (p-value) because of 1) how close the sample average of country B is to the true average of country A, 2) the sample size of males in country B considered in the analysis. Let’s see why:

1. Suppose the average of the 2 randomly chosen males from country B was 180cm, the estimated difference suddenly becomes 0. We may be able to randomly sample 2 other males randomly from country B and observe a different average, but the fact that the selection was random gives us confidence that the overall average height of males in country B should be close to 180cm - therefore, there is “no difference”
2. a) Suppose the average height of 2 randomly sampled males from country B was 175cm. Now let’s say there’s another randomly sampled male from country B of height 190cm - now the average is 180cm.
   b) Suppose the average height of 199 randomly sampled males from country B was 175cm. Now let’s say there’s another randomly sampled male from country B of height 190cm - now the average is 175.15cm.

Conclusion:

1. From 1 we understand that the “distance” of the sample averages of the two countries is one factor in determining the confidence associated with answering “is country B’s average different from that of country A?”. If the difference is small, the two averages are likely to be close. If the difference is large, the two averages are likely to be far. “How far is far enough?” - can be answered using 2a and 2b.
2. From 2a and 2b we observe that the “uncertainty” associated with the average of country B reduces as the sample size increases - therefore, with a larger sample we can conclude more “confidently” about the difference in average heights of males of country A vs country B.

p-value is a single summary that combines the uncertainty with 1 and 2 into a single “probability”. We start with the assumption that the two averages are equal and assign a probability of “observing the samples given the averages are equal”. If the probability is low (say less than 0.05), we conclude that the assumption that the “averages are equal” is incorrect.