| MATH 924 Section I Statistics - SUMMARY of classes 2-8 |
| Type of variable | Numerical (continuous) | Categorical |
| How are values obtained? | Measured | Counted for each category (minitab calls it attribute!) |
| SUMMARY STATISTICS | | Counts in Table, calculate proportions |
| Measures of central tendency | Sample mean population mean µ | n.a. |
| | Median | n.a. |
| Measures of dispersion | Sample standard deviation | n.a. |
| | Population standard deviation | n.a. |
| | Range = max - min | n.a. |
| | 1st, 3rd quartile | n.a. |
| GRAPHICAL REPRESENTATIONS | Dot plot | Bar graph |
| (incl. frequency distributions) | Box plot |
| | Histogram |
| STATISTICAL ESTIMATION |
| PROBABILITY DENSITY FUNCTIONS | Normal distribution | Binomial distribution |
| (Theoretical frequency distributions) | Student t distributions | (converges into normal distribution) |
| | | mean of binomial distribution: µ= np |
| | | variance of binomial distr.: σ2=np(1-p) |
| | | SD of binomial distribution: σ= √(np(1-p)) |
| SAMPLING DISTRIBUTION | (of mean values) | (of proportions) |
| Condition for normality of sampling distribution | n > 30 | np > 10 ; n(1-p) > 10 |
| Mean of sampling distribution | mean of mean values; = population mean | mean of proportions: µ=np |
| Standard error | (of the mean, SEM) | with σ= √(np(1-p)) |
| Margin of error (MOE) for a certain confidence level | MOE = z x SEM | MOE = z x SE (for normal approximation) |
| Confidence interval (CI) | C.I. = mean +/- MOE | 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 | · one proportion |
| | · comparing one experimental value to known (or hypothesized) value | · comparing one proportion to known (or hypothesized) value |
| | · [comparing two experimental mean values] (possible, but we didn't cover this in class) | · comparing two proportions |
| STATISTICAL DECISION |
| (HYPOTHESIS TESTING) |
| Purpose 1 | Compare experimental value to known or claimed/hypothesized value (like an established population mean) | Compare proportion to known or hypothesized value |
| Hypothesis test | One sample t test, z test | chi-square test for goodness-of-fit (not covered) |
| Null hypothesis | Experimental value is equal to a known value. |
| Purpose 2 | Compare 2 experimental mean values | test association between 2 categorical variables |
| Null hypothesis | Two experimental mean values are equal. | No association of the two variables; difference between observed and expected values = 0 |
| Test | 2 sample t test | Pearson chi-square test for association of 2 categorical variables |
| Purpose 3 | Compare a series of pairs of experimental values |
| Null hypothesis | Pairs are equal, no difference |
| Test | Paired t test |
| Connection between two variables | Correlation | Association |
| Testing for connection | Linear Regression | Pearson chi-square test for association |
| | Pearson correlation coefficient |
pbiner
COURSESUMMARYTABLE-allclasses.xlsx
