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# Statistics (BNAD 276) Study Guide Exam 1 BNAD 276 001

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This 24 page Study Guide was uploaded by Jianna LoCricchio on Tuesday October 4, 2016. The Study Guide belongs to BNAD 276 001 at University of Arizona taught by Dr. Suzanne Delaney in Fall 2016. Since its upload, it has received 215 views. For similar materials see Statistic Inference in Management in Statistics at University of Arizona.

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Date Created: 10/04/16

BNAD 276 Study Guide Terms Statistics- is the “science of collecting, organizing, presenting, analyzing, and interpreting data to assist in making effective decisions” validity - the extent to which a test measures what it intends to measure. Does it measure what it says it's measuring? reliability - the extent to which a test yields consistent results. Do you get the same results every time you do it? dependent variable - the variable being measured. The Data independent variable - the factor that is being manipulated by the experimenter. The groups. between participant design - each subject participates in only one level of independent variable within participant design - each subject participates in every level of independent variable random assignment - any subject had an equal chance of getting assigned to either condition True experiment - there was random assignment. Cause and effect quasi experiment - there was NO random assignment. Co-occurrences but not causality. Without random assignment, you can’t say correlation implies causation Placebo effect- a neutral treatment that has no real effect on the subject, even though the subject has a positive response to it. random sampling - each person in the population has an equal chance of being selected to be in the same sample population - the entire group of people about whom a researcher wants to learn sample - the subgroup of people who actually participate in the study ratio data - scale has equal size intervals with a "true zero" ratio data examples - All have a true zero calories, height, odometer, number of kids, temperature (K) interval data - numeric data because interval sizes are meaningful and insistent but does not have a "true zero" interval data examples - GPA, SAT Scores, Shoe Size, temperature (C and F), all have 0, but it isn't a true 0 ordinal data - categories are ordered, ordering in intrinsic to the concept, however, the interval sizes are not necessarily the same ordinal data examples - grades (A, B, C), sports rankings, military rank, place in a race all follow an order where one is better than another nominal data - categories with no intrinsic ordering and no numeric properties. (Names) nominal data examples - phone number, type of dog, favorite car, political party, nationality. None have numbers or orders, they are basically just names and titles discrete data - measured in whole units and measurements cannot be made more precise by more careful measurement. Ex. political party, type of dog, place in a race, grade (A, B, C) continuous data - measured in infinitely precise units. Ex. calories, race times, height, time, salary, population, GPA experimental question - considers both the independent and dependent variables simultaneously single blind experiment - participant doesn't know what group they are in double blind experiment - experimenter nor participant know the group they are in, to help eliminate error and bias. theoretical constructs - concepts like humor or satisfaction, they are hard to measure on their own categorical data - also called quantitative data. A set of observations where any single observation is a word or a number that represents a class or category numerical data - also called quantitative data. A set of observations where any single observation is a number that represents an amount or count time series design - each observation represents a measurement at some point in time. repeated measurements allows us to see trends cross sectional design - each observation represents a measurement at some point in come, comparing across groups allows us to see difference census - measures each person in the specific population parameter - measurement of characteristic of POPULATION, represented by Greek letter statistic - numerical value calculated from a SAMPLE descriptive statistics - organizing and summarizing data inferential statistics - generalized beyond actual observations making inferences based on data collected simple random sampling - each person from the population has an equal probability of being included hard to do, must have a list of everyone in a population sample frame - how you define a population. ex. population of UA football team systematic random sampling - a probability sampling technique that involves selecting every nth (you pick the number) from a sampling frame. Ex. every 10th voter stratified sampling - sampling technique that involves dividing sample into subgroups or strata, and then selecting samples from each of those groups. Sampling technique can maintain ratios for the different groups cluster sampling - sampling technique divides a population into subgroups (clusters) by region or physical space. Can measure everyone or select samples for each cluster convenience sampling - involves sampling people nearby snowball sampling - non-random where one or more members of a population are located and used to lead the researcher to other members of the population. Find someone and ask them to introduce you to others like them judgment sampling - involves sampling people who an expert says would be useful correlation - measure of how two variables co-occur and cab also be used for prediction. Range between -1 and 1 weak correlation - close to zero -.2 or .2 (1, 2, 3) no correlation – 0 moderate correlation - 4, 5, 6 or negative of those strong correlation - 7, 8, 9 or negative of those perfect correlation score - 1 or -1 positive correlation - as values of one variable go up, so does the other. If you study more, your grades will increase Strong positive correlation Weak positive correlation negative correlation - as values of one variable go up, the other goes down. If you brush your teeth more, you will have less cavities Strong negative correlation Weak negative correlation No correlation perfect correlation - one variable perfectly predicts the other linear relationship - can be described best with a straight line curvilinear relationship - can be described best with a curved line pareto chart - categories are displayed in defending order of frequency stacked bar chart - bar height is the sum of several subtotals simple line chart - often used for time series data (continuous data). The space between two data points implies a continuous flow pie charts - general idea of data that must sum to a total central tendency - where are the data values concentrated? what are the typical/middle data values dispersion - how much variation is there in the data, how spread out are the values? shape - are the values distributed symmetrically mean - adding up all observations and diving by the number of observations. median - the middle value when observations are ordered from least to most mode - the value of the most frequent observation (most often) bimodal ditribution - if there are two modes mode is for - nominal and ordinal data (anything really). median is for - ordinal data mean is for - interval or ration data measures of central tendency - describes how scores tend to cluster toward the center of distribution positively skewed - the Mean is the largest mode<median<mean negatively skewed - the Mean is the smallest mean<median<mode Range - the difference between the largest and the smallest observations. Xmax-Xmin deviation score - difference from the mean. The amount by which observations deviate on either side of their mean sum of deviation scores will always - equal zero variance - standard deviation squared degrees of freedom - n-1, you lose a DOF for every parameter you estimate sum of squares - the numerator in the equations How to find standard deviation - find the mean subtract the mean from each score (deviation) square the deviation add up the squared deviations divide the squared deviations by N take the number above and square root it 1 standard deviation up and down - 68% 2 standard deviations up and down - 95% 3 standard deviations up and down - 99.7% Describe what is meant by a z-score and how area under the curve relates to a particular z-score What is the probability that a score will fall above a z of 0 (50%) What is the probability that a score will fall between -1 and +1 standard deviation of the mean? - 68% What is the probability that a score will fall between -1 or +1 standard deviation of the mean? - 34% notice, z = 1 What is the probability that a score will fall between -2 and +2 standard deviation of the mean? - 95% What is the probability that a score will fall between -1 or +1 standard deviation of the mean? – 47.5% notice, z = 2 What is the probability that a score will fall between -3 and +3 standard deviation of the mean? - 99.7% What is the probability that a score will fall between -1 or +1 standard deviation of the mean? – 49.85% - notice, z = 3 Chebyshev’s Theorem similar to empirical rule but can be applied to all distributions (not just normal curves) The probability that a score will fall within 2 standard deviations of the mean is at least 75% (Jaggia, pg 85) The probability that a score will fall within 3 standard deviations of the mean is at least 89% (Jaggia, pg 85) z score - how many standard deviations raw score - the actual number associated with the z-score Convert z scores to x scores raw score = mean + (z score)(standard deviation) Convert x scores to z scores (consider how the formula vary between samples and population) z score = raw score – mean / Standard deviation how to calculate z score - (raw score - mean)/standard deviation if you are within 2 standard deviations your score is - not unusual if you are beyond 2 standard deviations your score is – unusual if your score is beyond 3 standard deviations, your score is - an outlier if your score is beyond 4 standard deviations, your score is - an extreme outliar empirical probability - relative frequency approach. number of observed outcomes divided by number of observations. Deals with real data classical probability - a priori probability based on logic rather than on data or experience. All options are equally likely. Ex. Flipping a coin, lottery subjective probability - based on someone’s personal judgment to draw the probability. Bob is 90% sure he can swim across the river because of how confident he is with his swimming probability - the relative likelihood that an event will occur. Must lie within the interval from 0 to 1. 0 will not occur, 1 must occur compliment - compliment of A, just means the probability of not A P(A) + P(A') = 100% two mutually exclusive characters - if the occurrence of any one of them automatically implies the non-occurance of the remain characteristic. Two events are _________ if they happen at the same time collectively exhaustive events - if their union is the entire sample space. A car is either covered by car insurance or its not, there is no in-between union - of two event means event A or event B will happen P(A U B) intersection - of two events means event A and event B will happen P(A n B) conditional - probability that A has occurred given that B has occurred P (A I B) = (P(A n B))/ P(B) evaluating investment - the standard deviation refers to the volatility or risk of the investment. more risk=larger the standard deviation sharpe ration - also called reward. Mean for investment - mean for risk free all divided by standard deviation Larger sharpe ratio - means it offers more reward per unit of risk

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