| MATH 924 SUMMARY | up to Class 5 |
| Type of variable | Numerical | Categorical |
| How are values obtained? | Measured | Counted |
| SUMMARY STATISTICS |
| Measures of central tendency | Sample mean population mean µ |
| | Median |
| Measures of dispersion | Sample standard deviation |
| | Population standard deviation |
| | Range = max - min |
| | 1st, 3rd quartile |
| GRAPHICAL REPRESENTATIONS | Dot plot |
| (incl. frequency distributions) | Box plot |
| | Histogram |
| STATISTICAL ESTIMATION |
| PROBABILITY DENSITY FUNCTIONS | Normal distribution |
| (Theoretical frequency distributions) | Student t distributions |
| SAMPLING DISTRIBUTION | (of mean values) |
| Condition for normality of sampling distribution | n > 30 |
| Mean of sampling distribution | mean of mean values; = population mean |
| Standard error | (of the mean, SEM) |
| Margin of error for a certain confidence level | MOE = z x SEM |
| Confidence interval (CI) | C.I. = mean +/- MOE |
| Conversion of a value x to a z-score | z=(x-µ)/σ |
| Use confidence intervals for: | · one experimental mean value |
| | · comparing one experimental value to known value |
| | ·[comparing two experimental mean values] (possible, but we didn't cover this in class; |
| | instead, we use hypothesis testing) |
| STATISTICAL DECISION |
| (HYPOTHESIS TESTING) |
| Purpose 1 | Compare experimental value to known or claimed value (like an established population mean) |
| Hypothesis test | One sample t test, z test |
| Null hypothesis | Experimental value is equal to the known value. |
| Purpose 2 | Compare 2 experimental values |
| Hypothesis test | 2 sample t test |
| Null hypothesis | Two experimental mean values are equal. |
| Purpose 3 | Compare a series of pairs of experimental values |
| Hypothesis test | Paired t test |
| Null hypothesis | Pairs are equal, no difference |
pbiner
COURSESUMMARYTABLEuptoclass5.xlsx
