This subreddit is aimed at an intermediate to master level, generally in or around graduate school or for professionals ... I'm currently working on my thesis which I am using a moderation analysis for. Based on my readings, it seems that for moderation analysis, a null hypothesis is "moderator ... More on reddit.com

The null hypothesis says "there is nothing going on here". Let's say you rolled a die three times and it always came up six. You conclude the die is probably loaded, and that becomes your hypothesis. The null hypothesis is the die is not loaded, and your results were due to chance or experimental error. After all, there is a 1 in 216 chance you would expect to see that on a fair die. You would next design an experiment to drive the likelihood of the null hypothesis so low that it can be ignored. If you rolled the dice ten times and got all sixes, that would represent a 1 in 60 million longshot, and strong evidence the null hypothesis is not true. Note that evidence against the null hypothesis is evidence something is going on, but not necessarily evidence for your hypothesis. Your hypothesis could have just as easily been "I am controlling the die with my telekineses", and eliminating the null hypothesis certainly would not support that conclusion. Further experiments would be required to determine exactly when the die always rolls sixes. The null hypothesis is often tied to the placebo effect. When people receive treatment, they tend to report improvement even when there is none. The null hypothesis remains "there is nothing going on here", and that any results were due to chance and/or the placebo effect. More on reddit.com

With Null Hypothesis Significance Testing, you assume the null hypothesis is true And 2) try to find evidence against it This method is similar to the " reductio ad absurdum " method in logic/philosophy. You assume the null is true, show that something ridiculous follows from that assumption and then conclude that since that happened, the null probably isn't true. 0.05 is a (pretty arbitrary) cutoff that we use for "statistical significance". But in reality, choosing a cutoff (our alpha value) is more about controlling our Type I error rate (falsely rejecting the null) than about telling us whether our p-value is good "evidence". If we choose alpha = 0.05, then if the null is true, we will only falsely reject it 5% of the time if we repeated this experiment over and over. Ronald Fisher once said (and I'm paraphrasing) that p-values don't tell you anything about the probability of what is true in the real world; they're instead a measure of how much you should distrust that the null hypothesis is correct. P-values tell is in a kind of hand wavy way whether there's evidence against the null. Within one experiment, a p of 0.00001 provides stronger evidence against the null than p = 0.001 but there's no real way to calibrate that between experiments. A p = 0.001 could represent different amounts of evidence in different studies. (Side note, though there's some difficulties with Bayes frameworks as well, this is one reason why Bayes is cool; it CAN provide you with a measure of "evidence" that is comparable between experiments). Confidence intervals are pretty heavily misunderstood. Confidence intervals can be thought of in two(related) ways: you can think of these values as "values we can't rule out based on our data and statistical tests". if you think about the confidence interval as a process, then if a 95% confidence interval procedure is repeated a BUNCH of times, 95% of them will contain the true population mean. However, this does NOT mean that there's a 95% chance that YOUR confidence interval contains the mean, as it is no longer a random variable. But this is useful if you're worried about controlling your Type I error rate. If you work at Guiness' beer factory measuring the quality of hops they put in a batch of beer, and you do this could continually, you could say that you want your quality to be about an average of 7 (I have no clue how they measure that), and so you take a sample of each batch of hops, calculate the mean quality and it's 6.75. do you throw out this batch? You could calculate a 95% confidence interval and say "as long as it contains 7, I'll consider this batch good", then if the batches are actually good, you'll only get a confidence Interval that doesn't contain the value 7 (which causes you to throw out he batch) 5% of the time. If you calculated a 99% confidence interval then you'd only mistakenly throw out a batch 1% of the time. More on reddit.com

Gaussian I.e normal distribution: You would use a two tailed z-score to test a hypothesis in which you cannot tell the direction. If you know what your testing is going to be positive or negative, then you know to use a one tailed test to check against your critical value.

A Poisson distribution is not normally distributed so you can't just do a two tailed hypothesis and expect the same results. Normal distribution has the parameters of mu and sigma. Poisson has the parameter of lambda.

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