Social Science Statistics Exam 2 (chapters 4-6)

Raw score formula for standard deviation

(chapter 4) 1. square each raw score 2. add squared scores 3. obtain mean 4. square mean 5. find sample variance 6. find the standard deviation

Variability

(chapter 4) AKA spread, width, or dispersion. Index of how scores are scattered around the center of the distribution. Serves both as a descriptive measure and as an important component of most inferential statistics.

Distance

(chapter 4) In both cases of range and standard deviation/variance, variability is determined by:

Standard Deviation

(chapter 4) Measure of variability. Distance of any given raw score from the mean. (subtract mean from raw score, X-X*) Useful for calibrating the relative standing of individual scores within a distribution (allows for comparison between a given raw score in a set against a standardized measure). Measures the standard (average) distance between a score and the mean. Represents the average variability in a distribution. Reflects the effect of all scores. = s

Range

(chapter 4) Measure of variability. Measure of variation in interval-ratio variables. Difference between highest and lowest scores in a distribution. Quick, easy computation. Gives merely crude index of the variability of a distribution. R = H - L

Variance

(chapter 4) Measure of variability. Purpose is to provide a measure of variability (diversity) Mean of the squared deviations from the mean. s^2 = EX^2/N - x^2 --> Sum of the squared raw scores divided by the total number of scores minus the mean squared. = S^2

Variance as a descriptive statistic

(chapter 4) Measures the degree to which the scores are spread out or clustered together in a distribution.

Goal for variability

(chapter 4) Obtain an objective measure of how spread out the scores are in a distribution.

Variance as an inferential statistic

(chapter 4) Provides a measure of how accurately any individual score or sample represents the entire population.

Greater; larger

(chapter 4) The _______________ the variability around the mean of a distribution, the ____________ the range, standard deviation and variance.

variability; standard deviation

(chapter 4) The greater the ______________ around the mean of the distribution, the larger the _______________________

One-sixth

(chapter 4) The size of the standard deviation is approximately _____ of the size of the range.

Interval

(chapter 4) Variance and Standard Deviation assume ___________ data.

Range

(chapter 4) What is a preliminary or rough index of the variability of a distribution? Quick, but not reliable. Can be applied to interval or ordinal data.

Probability Distribution

(chapter 5) Based on theory (probability theory), rather than on what is observed int he real world (empirical data). Specify the possible values of a variable and calculate the probabilities associated with them. Directly analogous to a frequency distribution. Theoretical or ideal, portrays what the percentages should be in a perfect world.

Multiplication Rule

(chapter 5) Combination of independent outcomes equals the product of their separate probabilities, applied when "both" or "and" statements are implied.

Expected value

(chapter 5) Mean of a probability distribution. Greek letter mu

Theoretical probabilities

(chapter 5) Reflect the operation of chance or randomness, along with certain assumptions we make about the events.

Probability

(chapter 5) Relative likelihood of occurrence of any given outcome. Method for measuring and quantifying the likelihood of obtaining a specific sample from a specific population. Defined as a fraction or a proportion. # of times the outcome or event can occur/ total # of times any outcome or event can occur

Addition Rule

(chapter 5) Rule of probability Determines cumulative probability, applied when "either - or" statements are implied.

Converse Rule

(chapter 5) Rule of probability Determines the probability that something will NOT occur

Z score

(chapter 5) Standard score Indicates the direction and degree than any given raw score deviates from the mean of a distribution on a scale of sigma units. Computed by the score minus the mean of the distribution divided by the standard deviation. Use Table A in appendix C. Values for one side of the normal curve given because of symmetry.

Empirical probabilities

(chapter 5) Those probabilities for which we depend on observation to determine or estimate their values. Essentially percentages based on a large number of observations.

Purpose of reliability

(chapter 5) Whenever the scores in a population are unpredictable, it is impossible to predict with perfect accuracy exactly which score(s) will be obtained when you take a sample from the population.

Decision making

(chapter 5) process of testing hypotheses through analysis of data. cornerstone is probability.

Normal Curve

(chapter 5) theoretical or ideal model that was obtained from a mathematical equation. Can be used for describing distributions of scores, interpreting the standard deviation, and making statements of probability. Smooth, symmetrical curve. Bell shaped. Unimodal. Asymptotic. Mean/Median/mode coincide.

alpha value

(chapter 6) 1 - Level of confidence

Confidence Interval using t computation

(chapter 6) 1. find the mean of the sample 2. obtain the standard deviation 3. calculate the standard error of the mean 4. determine the value of t from Table C 5. Determine your margin of error ( t x standard error) 6. find the interval within which we are 95% confident the population mean falls

Characteristics of Sampling Distribution of means

(chapter 6) 1. sampling distribution of mean approximates a normal curve 2. mean of a sampling distribution of means (mean of means) is equal to the true population mean 3. the standard deviation of a sampling distribution of means is smaller than the standard deviation of the population.

Central Limit Theorem

(chapter 6) 1. the mean of the distribution of sample means is called the expected value of mean and is always equal to the population mean mu. 2. standard deviation of the distribution of sample means is called the standard error of Mean. 3. shape of distribution of sample means tends to be normal, guaranteed to be normal if either the population from which the samples are obtained is normal or the sample size is n=30 or more

Sampling

(chapter 6) Allows researcher to generalize. Integral to social science research.

Standard Error of mean

(chapter 6) Can calculate the range of mean values in which population mean is likely to fall. 1. write out formula 2. determine SD of original distribution 3. determine sample size (N) 4. find square root of the sample size 5. divide SD by the square root of the sample size

Sampling Error

(chapter 6) Error between a sample statistic and the corresponding population parameter. Measure of the discrepancy between the sample and the population.

Nonrandom samples

(chapter 6) Every member (or element) of the population is NOT given an equal chance of being included in the sample.

Random samples

(chapter 6) Every member of the population has the same chance of being included, every member must be identified.

Central Limit Theorem

(chapter 6) Mathematical relationship that states whenever many random sample are drawn from a population, a normal distribution is formed, and the center of the distribution for a variable equals the population parameter.

Sampling distributions of means as normal curve

(chapter 6) Most sample means will fall close to the true population mean, within 3 standard deviations units above and below mu. Standard deviation of sampling error is denoted. Shows theoretical probability, standard deviation among all possible sample means.

Degrees of Freedom (dF)

(chapter 6) N-1

Purposive sampling

(chapter 6) Nonrandom sampling Researcher uses their common sense or better judgement to select a sample.

Quota sampling

(chapter 6) Nonrandom sampling Sample specific characteristics of the population based on the proportions they occupy in the population.

Convenience sampling

(chapter 6) Nonrandom sampling Selects elements from the population based primarily on what is convenient for the researcher.

Confidence Interval

(chapter 6) Probability that population mean falls within range of mean values.

Systematic sampling

(chapter 6) Random sampling Predetermine a number that we will consistently use to select members from the population.

Stratified sampling

(chapter 6) Random sampling Researcher first identifies a set of mutually exclusive and exhaustive categories, divides the sampling frame by the categories, and then uses random selection to select case from each category.

Simple random sampling

(chapter 6) Random sampling Use a mathematical and structured technique to determine who will be in the sample

Cluster sampling

(chapter 6) Random sampling Uses multiple stages and is often used to cover wide geographic areas in which aggregated units are randomly selected and thens ample are drawn from the sampled aggregated units, or clusters.

Distribution of sample means

(chapter 6) Set of means from all the possible random samples of a specific size (n) selected from a specific population. Has well-defined (and predictable) characteristics that are specified in the Central Limit Theorem

Three basic properties of probability

1. cannot be a negative number 2. probability ranges from 0 to 1.0 (o = impossible, 1 = certainty) 3. probabilities of all possible events sum to one (1)

Four Assumptions

Of the total # of events: 1. each even is equally likely to occur 2. different events are mutually exclusive 3. the different events are mutually independent 4. total # of events exhausts all the possible events