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| methods for oragnizing, summarizing, and interpreting data |
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| tables, graphs, or numbers that organize or summarize a set of data |
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| a descriptive statistic for a sample |
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| a descriptive statistic for an entire population |
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| mathematical techniques that allow us to make decisions, estimates, or predictions about a larger group of individuals (a population) on the basis of data collected from a much smaller group |
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| we are confident that the results we see for our sample will hold true for 1. most other samples drawn from the same populations, and thus 2. for the entire populations from which the sample was drawn |
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| a set of units (people, objects, events) we are interested in studying |
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| any subset of the population |
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| a subset of the population that exhibits the important characteristics, the diversity of the target population |
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| unrepresentative (biased) sample |
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| a subset of the population that does not have the characteristics typical of the target population |
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| one in which every individual in the population has an equal chance of being chosen in the sample |
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| to ensure that particular groups within a population are adequately represented in a sample, we can randomly select individuals from each group in our sample equals the proportion of the group in the larger population |
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| occurs whenever the sample is selected based on the ease of collecting data, rather than using a random or representative sampling method |
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| voluntary response sampling |
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| a type of convenience sample in which only those who volunteer are in the sample |
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| repeating the study, with essentially the same methodology, on a new sample |
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| any characteristic we can measure that may assume more than one value |
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| (of a variable) describes exactly how a variable will be measured |
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| categorical / qualitative variable |
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| are not naturally numerical; responses are usually words (yes or no; spring, summer, fall, winter) |
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| measuring on this scale involves assigning people or objects into categories that describe how they differ on a variable; the categories cannot be meaningfully ordered |
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| measuring on this scale allows us to rank order people or objects; to put them into categories that fall along a continuum |
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| numerical / quantiative variables |
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| measuring on this scale yields a numeric value for each person or object and the distances between values on the measurement scale are equal |
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| are naturally numeric; the distance between values on the scale are equal; and they DO have an absolute zero point |
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| produce numerical responses, typically from a counting process, and therefore tend to take only a finite number of real values (1,2,3...12,493,568). Include your age in years and calendar year |
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| produce numerical responses, typically from a measuring process, and therefore can assume an infinite number of real values. height, distance, temperature |
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| one of the categories into which qualitative data can be classified |
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| number of observations in the data set falling in a particular class |
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| class relative frequency (CRF) |
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| the proportion or percentage of observations falling in a class |
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| typically used to present categorical data and the separation between bars communicates to the viewer that each bar represents a distinct category |
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| a circular chart divided into slices illustrating the relative frequency of each class |
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| shows each individual measurement in a set of data as a single dot placed along a numerical scale |
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| a graphic representation for numerical data sorted into evenly spaced measurement classes |
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| evenly spaced intervals into which we can place quantitative data for summary tables and graphs |
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| measures of central tendency |
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| a value around which other measurements in a data set cluster; it is a single numerical measure used to represent an entire set of scores |
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| average; the most often used and often the best measure of central tendency |
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| the middle number in a set of measurements, arranged from smallest to largest |
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| the most frequently occurring score in a set of scores |
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| unusually high or low scores |
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| a graph that shows how scores are distributed along a measurement scale |
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| a symmetric distribution; mean = median = mode |
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| skewed right distribution |
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| high outliers; mean > median > mode |
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| low outliers; mean < median < mode |
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| indicates how alike or different are the scores in a dataset -- whether they cluster together around the mean or whether they are widely dispersed |
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| the highest score minus the lowest score |
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the sum of the squared deviations of each score from the mean divided by n-1
s2 = ∑(x - x̅ ) / n-1 |
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| the approximation of the average distance of each score from the mean |
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68% of measurements will fall within 1 SD of mean
95% of measurements will fall within 2 SD of mean
99.7% of measurements will fall within 3 SD of mean |
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| measures of relative standing |
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| indicates how a particular score compares to the other scores in a data set |
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| the percentage of scores that are less than a given score |
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| the number of standard deviations away from the mean a score falls |
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| standard normal distribution |
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| summation sign -- add up everything to the right of ∑ (capital sigma) |
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| sum of squares -- square all individual scores (x) and sum the squares |
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| square of the sum -- sum all individual scores and square the sum |
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| sample mean -- pronounced "x-bar" |
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| sample variance -- it is the square of standard deviation |
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| sample standard deviation |
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| population mean -- pronounced "mew" |
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| population variance (lowercase sigma squared) -- it is the square of standard deviation |
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| population of standard deviation (lowecase sigma) |
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| z-score -- a measure of relative standing |
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| all bell-shaped and symmetrical; can differ in shape because they differ in mean and standard deviation |
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| bell-shaped, perfectly symmetrical and has a certain degree of "peakedness"; areas beneath the normal probability curve that has been recorded in tables for the sake of convenience in estimating event probabilities |
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| standard normal distribution (SND) |
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| a normal distribution that has been standardized so that the mean = 0 and Standard Deviation = 1 |
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| distribution of sample means (DSM) |
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| shows the means of many samples drawn from one particular population |
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| the standard deviation of all sample means |
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| when a distribution of sample means is created from large samples (N≥ 30), the DSM will resemble a normal distribution regardless of whether the samples were drawn from a population that was distributed normally or non-normally (skewed left, skewed right, bimodal) |
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| standard deviation of a distribution of sample means (DSM), also called standard error |
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| mean of a distribution of sample means (DSM) |
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