And, because we know that z-scores are really just standard deviations, this means that it is very unlikely (probability of \(5\%\)) to get a score that is almost two standard deviations away from the mean (\(-1.96\) below the mean or 1.96 above the mean). Thus, there is a 5% chance of randomly getting a value more extreme than \(z = -1.96\) or \(z = 1.96\) (this particular value and region will become incredibly important later). ![]() We can also find the total probabilities of a score being in the two shaded regions by simply adding the areas together to get 0.0500. Then, using an online calculator, a handheld graphing calculator, or the standard normal distribution table, we find the cumulative. This might be useful if your audience does not understand quantiles but is comfortable with z-scores. First, we transform Mollys test score into a z-score, using the z-score transformation equation. For lognormal, you wont have something familiar like z 1.96 quantile 0.975, but if you get that youre at the 0.975 quantile of your distribution, you could report that as being a z-score equivalent of z 1.96. What did we just learn? That the shaded areas for the same z-score (negative or positive) are the same p-value, the same probability. Given an assumption of normality, the solution involves three steps. ![]() \( \newcommand\), that is the shaded area on the left side.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |