1 4 aspects of a good sample Random Independent Covers entire population 2 unbiased Difference between qualitative nominal ordinal quantitative variables continuous discrete BIOM301 REVIEW SHEET Chapter 1 Statistics 3 Definition of terms a Population b Sample c Experimental unit d Variable e Data value f Data g Statistic h Parameter Chapter 2 Descriptive Analysis and Presentation of Single Variable Data 1 Qualitative data Circle bar graphs 2 Quantitative Stem Leaf plot Frequency diagrams Frequency histogram Relative Frequency histogram 3 Describing graphs a Uniform b Symmetric c Skewed right left d J shaped e Bimodal f Normal uniform symmetric bell shaped Measures of Central tendency Quantitative data 4 a Mean b Median c Mode d Midrange 5 Measures of Dispersion a Range b Variance c Standard Deviation 6 Statistics vs Parameters x sample mean Population mean s sample standard deviation Population standard deviation s2 sample variance 2 Population variance 7 68 95 99 7 Rule 8 Z score Establishes the position of a value x measured in the number of standard deviations from the mean z your value population mean x population standard deviation Example Exam score 1 your score 79 class mean 85 standard deviation 6 meaning your score was 1 standard deviation below the mean z 79 85 1 6 Chapter 3 Descriptive Analysis and Presentation of Bivariate Data 1 Bivariate Data a Occurs when 2 variables are measured on same experimental unit b Data come in pairs 1 pair experimental unit c Assumes each pair of observations was collected independently and without bias 2 Scatter Plot 3 Linear Correlation a A correlation exists between 2 variables when one of them is related to the other in a linear manner b Linear Correlation Analysis measures the direction and strength of the linear relationship between 2 quantitative variables c Described by Linear Correlation Coefficient r d No Correlation if y does not change when x changes r 0 e Positive Correlation if y increases when x increases r is positive f Negative Correlation when y decreases when x increases r is negative 4 Linear Correlation Strength a Strength of linear relationship shown by r value b r 1 perfect positive correlation c Perfect negative correlation r 1 d 5 Regression Intermediate relationships when r is between 1 and 0 and 1 a R2 value the amount of variability in the dependent variable y explained by the variability in the independent variable x b Varies from R2 0 no relationship between x and y to R2 1 perfect relationship e g straight line for linear regression 6 Correlation vs Regression Correlation a Not causation b r Correlation Coefficient varies between 1 and 1 c Does not generate a predictive relationship between x and y variables d Never extrapolate beyond range of data e Linear relationship only Regression f Generates a predictive relationship of y variable as a function of x variable equation of the regression line g R2 value that tells how much of variation in y variable is explained by the x variable Varies between 0 and 1 h May be causal but be careful of interpretation i Never extrapolate beyond range of data j Can generate nonlinear regression equations Chapter 4 Probability 1 Probability uses population info to make predictions about samples 2 Definition Example An experiment process that yields 1 result or observation In the problem above the experiment is spinning the spinner outcomes all the possible results The possible outcomes are landing on yellow blue green or red An event is one outcome of interest We might be interested in landing on blue Probability is the measure of how likely an event is The probability of landing on blue is 1 out of 4 1 4th 3 3 ways to to find the probability of an event occurring a Empirically b Theoretically c Subjectively 4 Empirically Prime notation used for Empirical Probabilities P Probability and P Empirical Probability A specific outcomes can use any letter e g B C etc n A number of times the event A has occurred n total number of times the experiment is attempted Law of Large Numbers expected theoretical probability As With repetition empirical results will approach the 5 Theoretically a Sample Space S a list of all possible outcomes that could occur for some experiment b Determined by your experimental question c Outcomes must all be equally likely d Denoted by S e The number of outcomes in S n S f If all outcomes in a sample space are equally likely then you can calculate the probability of an event as the proportion of times your event occurs out of the total g P A of times event A occurs in sample space of outcomes in sample space h P A n A n S 6 Subjectively a These are based on personal judgement b example Meteorologists using their expert knowledge to estimate the probability of rain 7 The probability of an event is between 0 and 1 a The probability of an impossible event 0 b The probability of a certain event 1 8 The sum of all possible outcomes 1 9 Complement 10 Odds 11 P A or B a Equation Odds for an event are a to b b Then probability of event a a b a The Complement of A probability that Event A does NOT occur b The probability of the complement P A 1 P A a When thinking about whether one outcome OR another occurred we are thinking about 2 events that are Mutually Exclusive meaning only 1 event can occur b Example of mutually exclusive if you have a baby you can only have a Boy OR a Girl c To calculate the probability of a mutually exclusive event you add the P A P B to find out the P A or B d Might seem counterintuitive but since more than 1 outcome can meet the requirements the probability should go up addition e P A or B P A P B P A and B f 12 P A and B If events are mutually exclusive then P A and B 0 a P A and B P A P B b 2 events are independent c So to calculate the probability of Independent Events you end up multiplying the probabilities d This makes sense since you need not just 1 but 2 events to occur e Since it is less likely that 2 events will occur the probability should go down 13 Conditional Probabilities a P B A the probability that B will also occur given that A has occurred b P B A P A and B c If event A is independent of event B then the P A P A B P A Chapter 5 Discrete Probability Distributions 1 A random variable is simply a variable x whose value depends on the outcome of a chance operation random variable 2 So for a a Outcome based on chance operation b 1 outcome per run of the chance operation c Every outcome is independent of every other