Z scores can be more than 1. The approximate limits are often considered +/-3.49, but the asymptotic nature of the distribution means any value of z is possible (just not probable)

@@charlesvanliew9927 Thank you for the clarification. I thought it was b/n +/-1.

Because the SD is the square root of the variance (and variance cannot be negative), SD can be greater than variance if the variance is between 0 and 1.

The mean is obtained by adding the scores and dividing by the number of scores. Here, the sum of the scores is 1 + 2 + 3 + 4 + 5 = 15. 15 divided by 5 (the number of scores) is 3. So, M = 3.

AI...a great example of the usefulness of statistical models

You would do that simply by putting the "xx - xx" (which I assume refers to the lower class and upper class limit, respectively) in the Label area. The Value entry does not permit multiple values. I hope that helps!

@@cavanliew Thank you so much for your prompt response! it helped!! thanks!!!!!

Without going into the details of why, multiple R is always positive. The sign of the correlation is what will tell you the direction of the relationship accurately. You will also note that the sign of the slope in the regression table will match the sign of the correlation coefficient.

Technically, yes. However, there are many free resources online (as well as statistical programs) that will find these values for you rather than using the distributional formula "by hand". For example, graphpad.com/quickcalcs has an "r to p" calculator. You can find others by doing a quick web search. My channel also has videos with such examples. I hope that helps.

Perfectly normal would have 0 skewness and kurtosis. A rule of thumb that is sometimes suggested for "fairly" normal is within plus or minus 3. Positive values of skewness indicate a positive skew (tail to right) and negative means negative (tail to left).

@@cavanliew Thank you so much!

No, the alternate hypothesis cannot contain a statement of equality in classical, frequentist hypothesis testing. Saying "no relationship" is the null (null means "none" basically), and it contains the statement of equality (such as r = 0) in the context of the correlation between two variables. The alternate is that there is a relationship of some kind.

You can, but Likert scale data is technically ordinal which is not perfectly in line with the assumptions of Pearson's correlation. As such, a more "technically correct" approach would be to use Spearman's rho for testing correlation in this case -- shown here: kzbin.info/www/bejne/gWO0fn6kdpidjrM. That said, the two methods will generally yield similar results and, in practice, it is rather common to treat Likert scale data "as if" it were interval-ratio data in many disciplines that use applied statistics.

In classical hypothesis testing using "frequentist" approaches, the "null" is the assumption we make to start. The "null" is generally going to be a statement of "no effect" -- null means "having or associated with the value zero". Unless there is some context given that makes it clear that the null hypothesis should be a value other than 0 based on some knowledge regarding the assumptions being made about the population, the assumption in correlation (or regression) is that the null hypothesis expects there to be "no relationship" (i.e., the correlation [or slope] coefficient is 0). The "alternative" (or research) hypothesis is the one that expects a relationship. Given the correlation coefficient is the numeric representation of the "relationship" between the two variables, the alternative would therefore mean that mathematically the correlation coefficient does not equal 0 (as a non-directional hypothesis example). If you have a reason to expect a particular type of relationship (positive or negative), you might be more specific and say that the correlation coefficient is "greater than" or "less than" zero, but this would only be if you are making a directional hypothesis. (The default in most "real-world" applications is to use non-directional hypotheses, but some classes or books will have you practice with directional ones, too.)

If the p value is 0.08 and you set alpha at 0.05 (or are using this as the "conventional" alpha), you would retain the null hypothesis because 0.08 > 0.05 (i.e., p > alpha). Your obtained p value must be less than or equal to alpha to reject the null hypothesis.

@@cavanliew thank you so much for the quick reply. You really really helped me for my last minute study for stats exam that's in a couple of hours

You can do it one by one if what you want to know is the "bivariate correlation" of each independent variable with the dependent variable. If you want to know how all three variables relate to the outcome "controlling for the others," you would want to use a multiple independent variable approach. The simplest way to do this in Excel is to use regression and select the multiple independent variables all at once. Which approach to use (3 bivariate correlations or 1 multiple regression) depends mostly on your question. For example, if you want to know whether one variable "adds" to your ability to predict the dependent variable above and beyond the others, you would want to use a multiple regression. If you just want to know whether each variable is related to the dependent variable in its own, you would use several bivariate correlations. Hope that helps!

@@charlesvanliew9927 thank you so much sir for your response and great answer! It helps me a lot 😊

For correlation, you select both X and Y (there is only one input box). Excel will expect that one column contains X and one contains Y. When you do regression, you have to select X and then select Y (and there are input boxes that identify which one to put where ("Y Input Range" and "X Input Range").

@@cavanliew thank you