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If each person took a pre-test and a post-test, and assuming your outcome metric is numeric, then you could use a paired t-test where you compare the difference (post minus pre) among the two groups (control vs. treatment).

@@danielm9463 thanku so much, If my population is larger, do I still need to use a paired t-test over a z-test?

Don't hesitate to post any questions you have about your work or what you're studying!

ditto

@@mayawen Yep, that's a typo

its the same in reverse

samsmets is correct; all of our calculations would come out in the opposite direction. The fact that we use a *positive* test charge is a matter of convention. We could have picked positive or negative, but for purposes of consistency, we need to pick something and then stick with it so that results can be understood and interpreted in this field.

You have to study perturbation theory as a linguistics student?!?! Could you share some links on how that's used?

Agreed! In many cases, one will simply decide to treat the discrete data either as categorical or continuous, and then use traditional parametric approaches. For example, see this post: www.theanalysisfactor.com/likert-scale-items-as-predictor-variables-in-regression/ However, some of the non-parametric methods could also be used, not only for discrete data but similarly for ordinal data. Some good choices can include the Mann-Whitney test, the Kruskal-Wallis test, Spearman's rank correlation coefficient, the Cochran-Armitage trend test, ordered logistic regression, etc. However, those methods are really out-of-scope for this video, which was designed as an overview/intro for high schoolers who (a) have no prior experience in stats yet (b) were expected to do stats in their IB Biology course.

You're still assuming the null hypothesis is correct even when it says p=0.05. The whole point is that p=0.05 is an extremely bad way to explain your experimental results. That is, the null hypothesis is a bad assumption if the only way it can explain your experimental results is by calling them a highly rare one-in-twenty occurrence. Imagine you place 10 plants on the south side of your home and 10 identical plants on the north side of your home. You find that the 10 plants on the north side grow 20% taller over the course of a year. Your friend comes along and says "it's incorrect for you to conclude that plants grow taller on the north side of your house because your results are just a statistical fluke. If you repeated this experiment 19 more times, you'd get no difference between the northern and southern plants on average." You probably wouldn't believe this friend, and you would reject their hypothesis. We do the exact same thing to the null hypothesis when it says "your experimental results are just a one-in-twenty fluke and p=0.05." Our response is "that's a bad way to explain the results of my experiment. I reject the null hypothesis and I reject the idea that my data are a highly rare one-in-twenty occurrence."

Kepler's 3rd law was published between 1609 and 1619 (i.e., some time in the early 17th century), which was well before Newton published the Principia in 1687. Kepler's work was very well known at the time when Newton was formulating his universal theory of gravitation, and before Newton published in 1687, it had even been posited that Kepler's 3rd law implied an inverse square force pulling on the planets--but it was Newton who suggested that this inverse square force was gravity, i.e., the same phenomenon that causes objects to fall toward the surface of the earth. And perhaps more importantly, Newton derived Kepler's 3rd law for elliptical orbit, which others thought was impossible and (if I recollect correctly) required him to invent some calculus for the full proof.

Here's a good article with some of the history: engines.egr.uh.edu/episode/3015

Correct! It says at 3:05 that we would reject the null hypothesis that case.

Yes! Inferential statistics is used across an extremely wide range of subjects. But this is very much an introductory video, so it's just important to know that the deeper you go into a subject, the more specific and advanced the statistics will generally become.

You have my permission :) Good luck in your thesis! I made this originally in powerpoint if you want to try re-creating the original diagram.

PS -- what's the topic of your thesis/

Thank you Daniel! I’m doing “Solar Power in Space” :) and I’m using your illustration to explain about solar constant.

This is a great question and a very common misunderstanding. Let's focus on this statement: "meaning the height difference of 4 Inches occurs 1 time and the heights are same the remaining 999 times." This is not quite true. Here's what we should say instead: "meaning the [the null hypothesis can only explain your data by claiming it is an extremely rare event, because a] height difference of 4 Inches occurs 1 time and [the null hypothesis is saying that, if you repeated your experiment 999 times, you would realize that your results are just pure luck.]" Pretend I'm the null hypothesis. I flip a coin 100 times in a row, and it comes up heads all 100 times. You say "that is not a fair coin." I respond "it IS a fair coin--it's just that the experiment is an extremely rare fluke." This would be an absurd response. Every time I flip the coin and it comes up heads again, my statement ("this is a fair coin and these results are extremely unlikely...") becomes less believable. The null hypothesis is the exact same. It's like me saying "no, it's actually a fair coin, and you just have extremely unlikely results." At some point, that's less believable than the alternative--the coin is not fair and has heads on both sides.

Highlight one column, then click Ctrl on your keyboard (or Cmd if you're using a Mac). While holding Ctrl (or Cmd), click and drag to select the second column

What about for the iPad

I could not agree more!!