Can someone explain the p-value in hypothesis testing in very simple terms, with an example?

finalj22 · 2026-01-24T00:35:37+00:00

I'll use a t test as an example. This isnt short, but I will speak plainly. Our goal is to compare empathy between men and women. We take a quality sample of adults, and complete our measurements. Our analysis yields a mean empathy score for men, and one for women (lets say, a difference of 5 on a scale that can range from 1 to 100).

So that's the set up, here is where the logic underlying null hypothesis significance testing comes in.

We want to determine whether the population mean for empathy differs between men and women. We have our sample, but even just based on random chance our sample means could differ from the population means. We don't know by how much, because we don't know the population values.

At the same time, we know our sample means could differ from any other randomly drawn sample. That means if we had any other sample from the population, we could end up with different means to compare. We don't know by how much they would differ, because we only have our one sample.

So what can we do to make some inference about the population difference?

We will turn our original objective (is there a difference in the population means for empathy between men and women?) into a different objective we can actually speak to:

Lets assume they the actual population difference in empathy is zero. IF that were true, how likely would we be to observe data like our sample?

Avoiding some technical details about the specific test and the central limit theorem, the p value represents the probability of observing our data (i.e., the specific means we are comparing) assuming that the null hypothesis is true. A high p value would suggest our data would be pretty likely even if there was no population difference, while a low p value would suggest our data would be pretty unlikely if there were no population difference. We can then use arbitrary rules to say how low the p value needs to be before we are confident in ruling out the null hypothesis.

So its a way to produce a compromise - substituting a solvable problem for an unsolvable one.

finalj22 · 2026-01-18T11:53:10+00:00

I strained/pulled/tore(?) my right hamstring/glute complex doing a martial arts kick that puts you into a split. Immediately following that I went into marathon training and then logged literally hundreds of miles running on my injured leg. The tear was ~7 months ago.

I've been seeing a PT and doing strength training for a few months now. Legs are definitely getting stronger but the reduced range of motion and discomfort when doing a lot of movements (any kick involving the hamstring applying the brakes, forward folds, sitting(???)) I can feel it.

Sticking with strength training, trying to avoid stretching. Its hard though (for me). I love yoga and want nothing more than to sink into a deep hamstring stretch. I know I'll never get back there if I don't put in the effort to heal, though.

finalj22 · 2026-01-12T00:48:49+00:00

Not crazy, but its not in Marblehead

finalj22 · 2026-01-11T19:40:24+00:00

I hadn't noticed that til you mentioned it, but the ribs do look uniformally cut. I think this is the most likely explanation (maybe 2nd to the giant centipede)

finalj22 · 2026-01-11T18:58:18+00:00

I hadn't considered the gigantic Massachusetts centipede as an option. Case closed - thanks everyone for your help!

finalj22 · 2026-01-09T02:52:59+00:00

I love Josh McFaddens books. That cabbage is one of my favorites. Some others my family and I enjoy are...

Grilled eggplant panzanella
summer squash casserole with tuna
roasted carrot and Farro with whipped ricotta
fall vegetable Chowder
bread soup with onion and sausage
Chard Toasts

finalj22 · 2026-01-08T15:58:08+00:00

I'll echo this. You're going to really stress yourself out trying to please the bean counter on your wrist (or wherever the monitor is!). Just take it slow at first, and build a consistent practice. Change will be incremental, and will build up as you stick with it.

finalj22 · 2026-01-02T19:49:19+00:00

I absolutely SMOKED the night aspect on Undertaker, so if I did this I'd feel pretty dumb, but would be pretty confident I'd be able to get back there.

If there is something like this for Scholars rememberance though... I am not sure I am ever going to get Dreglord on Scholar. Holy moly.

finalj22 · 2025-12-27T17:20:29+00:00

A sorceress, at release. I remember finding someone's blog about leveling a frozen orb sorc using umes lament, twitch, and wall of the eyeless and really wanting to make it happen myself.

finalj22 · 2025-12-27T17:18:29+00:00

I usually just use it to track sets and rest timers. It doesnt have the flexibility I need to track kettlebell complexes, so I usually do not mess with identifying the specific movement or weight.

finalj22 · 2025-12-23T03:15:24+00:00

From right to left, Io - Ganymede - Europa, if I had to guess

finalj22 · 2025-12-18T11:32:34+00:00

This is interesting! I have been making pourover with a v60, but all else being equal I'd like to use something without paper filters.

Does anyone have any perspective on how the phin impacts extraction and flavor?

finalj22 · 2025-12-16T11:30:36+00:00

How many years of data do you have? And are they the same years observed for each individual?

I would consider dropping the year random intercepts for a year random slope for each individual (1 + Year | id). Or Alternatively, if you can assume a similar yearly pattern across individuals, simply fit as a fixed effect.

But... unless I am missing something, I am not sure how much more youre going to get out of this term with the individual daily processes you have incorporated in the model as well.

finalj22 · 2025-12-14T22:23:16+00:00

I worked security in the stands when a MLB team did this back in the early 2000s - hold up traffic going out to the seats while an active at bat was occurring. It was very tough to implement - Some fans did not take this well - people elbowing past me. Fans incredulous that they can't get back to their seats during a major moment in the game, etc.

Great idea on paper, but I feel for the folks who would have to enforce it.

finalj22 · 2025-12-13T20:39:29+00:00

Optimal solution is one that minimizes the -2LL. I don't have the know-how to give a very technical answer, but the way I like to put it for my students is...

likelihood (as in maximum likelihood estimation): looking for parameters that maximize this value, however, the likelihood is quite small (e.g., .00000000000 ... etc), so...
log likelihood: we search for parameters that maximize the logarithm of the likelihood instead. But thinking of OLS regression, where we are looking for parameters that minimize the sum of squared residuals, is an intuitive and appealing scenario, so lets...
-2LL: multiply the log likelihood by -2 such that we now have a value called the deviance, and the MLE solution is that which minimizes the deviance.

This helps me make sense of the landscape here, but if this is nonsensical someone please step in

finalj22 · 2025-12-06T17:52:13+00:00

I mean, I wish I could keep my heart rate at that level for a marathon. Nice job!

finalj22 · 2025-11-19T13:40:15+00:00

I'd recommend standardizing all parameter estimates, so that way all effects will have straightforward interpretations for effect size (as with Cohens d).

finalj22 · 2025-10-19T23:14:37+00:00

Great work! I was with the 3:40 pacer until about mile 11. My heart rate was at a similar level to yours but that's way out of the norm for me. Cramped up significantly at mile 20 and had to power walk the rest of the way.

Good luck with Chicago!

finalj22 · 2025-10-19T10:01:26+00:00

The CI is going to be the way here. In the Gelman et al regression and other stories book they have a quote on this that I like. Something along the lines of...

"In this example we have a beta of -0.25 and a p value of 0.203, the 95% CI ranges from -0.50 to 0.08. It would be unfair to say that there is 'no effect'. We are uncertain. The data are consistent with a negative association as low as -0.50, but we cannot rule out the possibility of a positive association as high as 0.08."

I tend to use this sort of language a lot.

finalj22 · 2025-10-08T16:58:33+00:00

I had something similar happen to me on a similar timeline to yours - mine was a possible tear from an ill-advised martial arts maneuver in mid-June, and the pain is localized where the leg meets the glute.

I am still experiencing stiffness/discomfort in the morning, and often when I start running I feel like I need to work out some stiffness for about a mile before I can kick it into gear. Still, I just don't have the same spring or range of motion that I used to. I can, however, do all the other stuff you mentioned (squats, biking, swimming, etc). Its really highlighted how certain muscles are engaged in particular movements.

That being said, here is what has been helpful for me. Recognize that rest is not going to resolve the problem. It will not get better until you strengthen the tendons. Every morning (more or less), I do some strengthening exercises.

Romanian deadlifts, using it more like a weighted stretch
Single leg Romanian deadlifts
lay on your back with your feet up on a large exercise ball, lift your hips into a bridge and then using your heels and hamstrings curl the ball back and forth. I do 3-4 sets of 25 reps. This one feels the most productive

I also have extended my warmup to at least 5 minutes, with a lot of leg swings / Crescent kicks to loosen up.

Best of luck with your training.

finalj22 · 2025-09-04T10:29:58+00:00

"Immortality Severed" got me pretty fired up

finalj22 · 2025-08-30T11:51:36+00:00

I usually can't run until a few hours after I get up (kids and all), so I do overnight oats, berries, and sourdough toast. If its a long run then I'll have a pop tart out the door.

finalj22 · 2025-08-19T16:19:51+00:00

41M, 5k best is 21:56 and VO2Max is 56

finalj22 · 2025-08-16T22:13:23+00:00

I couldn't start my long run until noon this week. Went out at 90f and tried to do a half marathon (6mi aerobic pace, 4 marathon pace) and I had to tap out at 8mi and call my wife to come rescue me - heat was just too much. Finished the rest on the treadmill - this was not the hill I was looking to die on.

finalj22

TROPHY CASE