Elementary Statistics 2004
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| Data | Observations (such as measurements, genders, survey responses) that have been collected | ||||
| Statistics | A collection of methods for planning experiments, obtaining data and then organizing, summarizing, presenting, analyzing, interpreting, and drawing conclusions based on the data | ||||
| Population | The complete collection of all elements (scores, people, measurements, and so on) to be studied | ||||
| Population | it includes all subjects to be studied | ||||
| Census | The collection of data from every member of the population | ||||
| Sample | A subcollection of members selected from a population | ||||
| Sample data | must be collected in an appropriate way, such as through a process of random selection | ||||
| If sample data are not collected in a appropriate way, | the data may be so completely useless that no amount of statistical torturing can salvage them | ||||
| TYPES OF DATA??? | Parameter,Statistic , | ||||
| Parameter | A numerical measurement describing some characteristic of a population. | ||||
| Parameter | all of those votes to be the population considered, When Lincoln was first elected, he received 39.82% of the 1,865,908 votes cast which is 29.825. | ||||
| Statistic | A numerical measurement describing some characteristic of a sample | ||||
| Based on a sample | of 877 surveyed executives, it was found that 45% of them would not hire someone with a typographical error on their job application | ||||
| Quantitative data | Data consists of numbers representing counts or measurement | ||||
| Quantitative data | weights of supermodels | ||||
| Interval level of measurement | Temperature, Years | ||||
| Interval level of measurement | Data that can be arranged in order and for which differences between data values are meaningful | ||||
| Interval level | shoe sizes [US vs Europe] and temperature | ||||
| Interval data | can be either discreet or continuous | ||||
| Ratio level of measurement | Data that can be arranged in order, for which differences between data values are meaningful, and there is an inherent zero starting point. | ||||
| Ratio level of measurement | differences and ratios are meaningful | ||||
| Ratio level of measurement | prices of textbooks; $50 is half of $100 | ||||
| Ratio level of measurement | Height of students | ||||
| Ratio data | is continuous. | ||||
| Ratio level of measurement | HIGHEST LEVEL OF DATA | ||||
| Ratio level of measurement | can be either discreet or continuous. | ||||
| Quantitative (interval and ratio) data | can be further distinguished between discrete and continuous. | ||||
| Discrete Data | Data that results when the number of possible values is either a finite number or a “countable” numbers. | ||||
| Discrete Data | Counting-type things | ||||
| Discrete Data | number of eggs that hens lay | ||||
| Continuous (numerical) Data | thickness of paper; measurement of weight | ||||
| Continuous (numerical) Data | Results from infinitely many possible values that correspond to some continuous scale that covers a range of values without gaps, interruptions, or jumps. | ||||
| Continuous (numerical) Data | amounts of milk from cows | ||||
| Qualitative (or categorical or attribute) data | Can be separated into different categories that are distinguished by some nonnumerical characteristics. | ||||
| Continuous (numerical) Data | The genders (male/female) of professional athletes | ||||
| Nominal Level of Measurement | Characterized by data that consists of names, labels, or categories only | ||||
| Nominal Level of Measurement | Lowest form of data. Has groups, but no ordering to the groups | ||||
| Nominal Level of Measurement | cannot be arranged in an ordering scheme (such as low to high) | ||||
| Nominal Level of Measurement | Survey responses of yes, no, and undecided | ||||
| Nominal Level of Measurement | Colors of cars driven by college students (red, black, blue, etc. | ||||
| Ordinal Level of Measurement | (Categories & groups, but with some natural order to the groups.) | ||||
| Ordinal Level of Measurement | Course grades – Grades of A, B, C, D, or F | ||||
| Ordinal Level of Measurement | Ranking cities; those ranked 1st, 2nd, 3rd, etcBut, the differences between ranks are meaningless | ||||
| Money and Counting are | Discrete | ||||
| Temperature is | Interval | ||||
| Ages are | usually Discrete | ||||
| Man on the street samples are | always convenience sampling | ||||
| Misuses of Statistics | self-selected surveyBad samplesSmall samplesMisleading graphsPictographsLoaded Questions | ||||
| Misuses of Statistics | Order of Questions | ||||
| Misuses of Statistics | Precise NumbersPartial picturesDeliberate Distortions | ||||
| Randomness | typically plays a critical role in determining which data to collect. | ||||
| Observational Study | Observing and measuring specific characteristics without attempting to modify the subjects being studied. (Control group) | ||||
| Cross Sectional Study | Data are observed, measured, and collected at one point in time. | ||||
| Retrospective (or Case Control) Study | Data are collected from the past by going back in time. | ||||
| Prospective (or Longitudinal or Cohort) Study | Data are collected in the future from groups (called cohorts) sharing common factors. | ||||
| Experimental | Apply some treatment and then observe its effects on the subjects. (Experimental group.) Doing something to affect what happens. | ||||
| Experimental Key Elements | Control, Replication, Randomization | ||||
| control | Effects of variables through: blinding, blocks, completely randomized, experimental design, rigorously controlled experimental design | ||||
| Confounding | Occurs in an experiment when the experimenter is not able to distinguish between the effects of different factors. | ||||
| Blinding | Subject doesn't know if he or she is receiving a treatment or placebo | ||||
| Double-blind | Neither the subject nor the experimenter knows whether treatment or placebo is being administered | ||||
| Blocks | Groups of subjects with similar characteristics | ||||
| Completely Randomized Experimental Design | Subjects are put into blocks through a process of random selection | ||||
| Rigorously Controlled Design | Subjects are very carefully chosen so that those in each block are similar in the ways that are important to the experiment. | ||||
| Random Sample | Selection so that each has an equal chance of being selected | ||||
| Simple Random Sample | of size n | ||||
| Systematic Sampling | Select some starting point and then select every Kth element in the population | ||||
| systematic sampling | 7th person of a group of 10; i.e., 7, 17, 27, 37, etc., OR every 7th person i.e., 7, 14, 21, 28, etc | ||||
| Convenience Sampling | Use results that are easy to get, choosing the first 10 people who get off work | ||||
| Stratified Sampling | Subdivide the population into at least two different subgroups that share the same characteristics, then draw a sample from each subgroup (or stratum | ||||
| Cluster Sampling | Divide the population into sections (or clusters); randomly select some of those clusters; choose all members from selected clusters | ||||
| Sampling Error | The difference between a sample result and the true population result; such an error results from chance sample fluctuations | ||||
| Nonsampling Error | Sample data that are incorrectly collected, recorded, or analyzed (such as by selecting a biased sample, using a defective instrument, or copying the data incorrectly |
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