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Statistics Midterm 1
| Question | Answer |
|---|---|
| quantitative data | numerical values with magnitudes that can be placed in a meaningful order and consistent intervals |
| categorical data | names or labels with no logical order with inconsistent differences; can be qualitative |
| (quantitative) discrete | represents counts via integers. not all integer data is discrete |
| discrete examples | age, pets, number of siblings |
| (quantitative) continuous | measurement, any value in a given interval, integer, or decimal |
| continuous examples | exact age, height, weight, GPA |
| (categorical) nominal | groups have no natural ordering and no magnitude |
| nominal examples | residence hall, major, ethnicity, hometown |
| (categorical) ordinal | groups have natural order, but group distances unknown |
| ordinal examples | pain scale (low, med, high), app rating in stars |
| range | the two most extreme values into account; highly sensitive to outliers |
| sample variance | the average squared deviations of observations from their mean. squared units |
| sample standard deviation | the size of typical deviation from the mean. positive square root of variance |
| bar chart | categorical data; the height of each bar represents the absolute or relative frequency of that category |
| pie chart | categorical data; the area of the slice represents its relative frequency (%) |
| boxplots | quantitative data; shows the 5 num summary. two types: skeletal and modified (modified shows outliers) --> good for discrete data |
| histograms | quantitative data; display of frequency distribution |
| left (negative) skew for boxplots | the negative whisker extends much farther out than the positive whisker |
| right (positive) skew for boxplots | the positive whisker extends much farther out than the negative whisker |
| measures of central tendency | mean, median, and mode |
| what happens if distribution is symmetric and unimodal? | the mean, median, and mode should all be approx. the same |
| marginal distribution | the distribution of just one variable at a time, often found in the margins of the two-way table |
| conditional distribution | tells you how a variable is distributed within a specific group (think "given that...") |
| what do side-by-side barplots show us? | for CxC distributions; can use absolute or conditional relative frequencies |
| what do stacked barplots show? | conditional relative frequencies (more specific) |
| groupwise summaries | numerical Q summaries but done for each group in the C variable (split data into groups, then summarize each group) |
| side-by-side boxplots | visually compares 5 num summary for each group |
| how to read side-by-side boxplots | -look for overlap of boxes -if boxes are farther away, more significantly different data |
| what are we looking for when we have 2 Q variables? and what graph works best with QQ? | a relationship --> correlation (how strong are the variables related?) scatterplot works best |
| what is an outlier with high leverage? | it pulls linear trend away from the other points |
| what is pearson's correlation coefficient? | a measure of how linearly associated two QQ variables are. scaled from -1 to +1 |
| observational study | observe characteristics of a sample without intervening with a treatment (ex. ask students how many hrs of Netflix they watch and STAT exam scores. observe what happens) |
| experimental study | implement a treatment and observe how characteristics change. can conclude cause-and-effect. (ex. assign half of students to study method and observe stats exam grades) |
| double-blinded | to reduce bias, neither subjects nor designer know the assigned treatment (single-blinded is next best) |
| randomized | sampling AND treatment assignment are randomized |
| what do we sample for an observational study | the population of interest and observe those in the sample only |
| what do we sample for an experimental study | have a group of people who can participate and then assign those subjects to treatment |
| simple random sampling | subjects are randomly selected from the population with equal probability |
| systematic sampling | sample every nth subject of a population where n cannot equal 1 (ex. grabbing every 5th student walking into a classroom) |
| convenience sampling | subjects are chosen based on who is around and convenient to be involved in the study (ex. asking friends a question for a survey) |
| voluntary sampling | subjects volunteer/choose to be involved (can be form of convenience sampling) |
| stratified sampling | population divides into similar groups based on categorical variable; sample randomly from within each strata (ex. divide students by class year and choose 10 kids from each group) |
| cluster sampling | identify how a population clusters, randomly sample whole clusters and use all observations within |
| multi-stage sampling | use a combo of sampling methods applied at different stages (ex. choose 12 colleges at random > 3 res halls > 10 rooms > both students |
| blocked randomization | 1) sort similar subjects into blocks based on one/more variables 2) randomly assign treatment within the blocks (ex. stratify by hospital in multi-center study and randomize within hospital) |
| matched-pairs randomization | match subjects together that are very similar based on baseline measurements and randomly assign them to different treatments |
| selection bias | some members of the population are more likely than others to be selected for the sample (ex. call people @ home b/w 9am-5pm on weekdays for a survey) |
| measurement bias | method of observation produces values that are systematically different from the true value (ex. faulty scale, sensitive question) |
| non-response bias | not every subject selected to be in the sample provides a response to a survey |
| confounding variable | variables that affect the response but are not of interest and can lead to incorrect conclusions |