Question

Can someone help me quickly in explaining differences in R value, R^2, Adjusted R^2, and p-value for stats? Thanks so much

Answer 1

When you conduct the test for the estimators in a linear (both simple and multiple) regression model, the \(R^2\) value is an indicator of how well the model accounts for variation between the predicted values (according to the regression line) and the actual observed data.

In some cases, particularly for a multiple linear regression, the test you conduct may not accurately reflect one or more estimator's contribution to the prediction model. That's where the adjusted \(R^2\) value comes into play. It's a "better" reflection of the model because it considers the relative sizes of the sample data and the number of parameters/independent variables used in the model.

The \(p\) value is essentially the probability that a calculated test statistic falls outside the rejection region. In terms of an experiment, the \(p\) value tells you whether you have enough evidence to accept or reject some null hypothesis, depending on the significance level of the test.

I'm not sure about the \(R\) value... it could be referring to the correlation coefficient, or it could have something to do with the \(R^2\) value. I'll see if I have any notes on this.

In any case, take what I say with a grain of salt. I am by no means an expert on regression theory and analysis. Everything I've listed here has been a sort of personal interpretation of what I've learned about it.

Answer 2

I think you have the best help in SithsAndGiggles. I know next to nothing about stats.

Answer 3

If I have a p-value of less than 0.01 does that mean the data/hypothesis/correlation they are attempting to prove is false? I am unsure? I am critiquing a research paper

Answer 4

That would depend on the significance level of the test (usually denoted \(\alpha\)). If it's not explicitly stated, the standard sig level is \(\alpha=0.05\). If the \(p\) value is smaller than \(\alpha\), you would say the data provides significant statistical evidence to reject the null hypothesis.

Answer 5

What is a null hypothesis?

Answer 6

Suppose you want to test a theory that buying some product will achieve a desired effect, like a sleeping pill that will help you fall asleep faster and for longer.

You want to be able to assess the ability of the product by comparing two main ideas, the null and alternative hypotheses. The null hypothesis, in general, is designed to say something along the lines of, "The product has no (significant) effect." The alternative hypothesis is basically the opposite, but exactly how it's phrased can differ depending on the theory you want to test.

For example, if you believe the sleeping to pill to work adversely and hence not help people fall asleep as effectively, you could say, "The sleeping pill makes it (significantly) harder to sleep." If you believe it does indeed work, you could instead say, "The pill makes it (significantly) easier to sleep." Yet another way is to avoid any directional claim, so you'd say something to the effect of, "The pill (significantly) alters sleep habits."

Of course, when it comes to phrases like making it "easier" or "harder" to sleep, you have to be able to represent that sort of trend numerically. Let's consider a sample of people suffering from insomnia and their sleeping habits by looking at their average number of hours of sleeping at night. Let's make our claim concrete and say that we think the sleeping pill makes sleeping easier, which in this case means people will, on average, sleep longer. The corresponding null hypothesis would be that the mean number of hours spent sleeping does not change (significantly).

Answer 7

Stats has never really made sense to me. Sorry. I think I'm just going to find another article I guess. The research is so strange and the only way to see if the experiment worked well is to analyze the statistics derived from a questionnaire. I think I'm just going to switch articles last second and find another research one on Pubmed or something. It's my midterm. It's due in a day. thanks so much for the time and effort you placed in helping me though. IN my opinion the article makes no sense and I can falsify and critique a lot of it but I can't fully convey that if I don't understand the results. Thank you for your time though

Answer 8

No problem

Answer 9

I'm so stressed lol