Comm 150 week 8
Comm 150 week 8 Communication Studies 150
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Communication Studies 150
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Popular in Communication Studies
This 7 page Class Notes was uploaded by Alyssa Notetaker on Sunday November 22, 2015. The Class Notes belongs to Communication Studies 150 at University of California - Los Angeles taught by PJ Lamberson in Fall 2015. Since its upload, it has received 47 views. For similar materials see Methodologies in Communication Research in Communication Studies at University of California - Los Angeles.
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Date Created: 11/22/15
Week Eight Lecture 13 Data Analysis Why To express or quantify uncertainty 0 Are the differences between the test and control groups real Statistically significant Or could they be due to chance 0 So data analysis9 know how certain we are that the results are significant actually re ect reality 0 Are the results real or due to chance To measure quantify relationships between independent and dependent variable 0 Is there a relationship or not Is the relationship real Modeling uncertainty Sample space set of all possible things that could happen 0 Ex ipping a coin sample space Q heads tails 0 Ex rolling a dice sample space Q 1 2 3 4 5 6 0 Can be infinite I EX height set of all possible heights infinite I Ex income Outcomes Elements of the sample space the individual things that can happen Events sets of outcomes 0 Ex event A is rolling an odd number so event A is comprised of the outcomes 1 3 and 5 I A 1 3 5 Notations o A 5 B I quotA is a subset of Bquot I Every outcome in A is also in B I So if event A happens an outcome in A occurs then B also happens I quotA union Bquot I Event consisting of all outcomes in A or B or both quotorquot is inclusive in statistics quotA or Bquot means quotA or B or bothquot A B AUB A U B is everything purple AAIl B I quotA intersect Bquot O I Set of outcomes that are in both A and B o A or AC I quotA complementquot I Set of all outcomes in the sample set EXCEPT for A Event A white A complement is red o A and B are mutually exclusive if APE Q A B I No intersection Probability 0 To capture uncertainty about the likelihood an event occurs 0 We call PA quotthe probability that A happensquot I The probability that some outcome in A happens I Example Roll a die A 1 2 3 and PA probability of rolling either a 1 2 or 3 o The Probability Axioms aka the axioms of probability I 1 PA 3 0 The probability of an event occurring has to be greater than or equal to zero I 2 P 1 The probability that anything in the sample space happens so that something happens is 1 100 Basically says that the maximum probability is 1 or 100 I 3 If A and B are mutually exclusive then PAUB PA PB The sum of the probability of A and the probability of B happening is the same as the probability of A union B IFF they re mutually exclusive 0 08 I In this case they re mutually exclusive So PAUB PAPB I in this case they re not mutually exclusive So PAUB PAPB PAnB 0 Rules of Probability I 1 Subsets IfA is a subset of B then PA 5 PB IfA is a subset of B the probability ofA is less than or equal to the probability of B I 2 Complements PA 1PA Probability of A complement is 1 minus the probability of A I 3 Unions PAUB PA PB PAnB Venn Diagrams U O I A blue and pink I Bpink and orange I AnB pink I AnB blue pink and orange u A O I PA area ofAarea of I Pinkpurple I The U in the picture 1 omega What is a probability 0 A subjective estimate of our uncertainty about an event 0 Longrun frequencies I Idea with more trials the probability will get closer to the truth I With thousands of rolls of a dice the chance of getting one of the numbers will get closer and closer to 16 I Controversy some things you can t do lots of times EX how to estimate the probability of Hillary Clinton winning the 2016 presidential election 0 Probability tree helps keep track of sequences of probabilities I quotUncertainty nodes or quotchance nodes locations at which there s a choice an uncertainty as to what one will do The first 3 black circles below I Terminal nodes the end of each branch of the tree where there s no more uncertainty no choice to be made The last 4 black circles 3 pm n B swamquot p39quot 3quot pm p B A quotquot0 pm 0 B if a pligh pliBllz rx pm n B PIE xvi BIA pm n B I Conditional Probabilities o Idea our uncertainty can change when we learn new information o PA B quotprobability of A given B I The probability that A happens if we know that B happens PAB PAnB PB U 0 What s PAB 0 Well given B we know it has to be in orange or pink this is the new sample space I So the only way A can happen is if it s in pink I PAB pinkorangepink Examples A B testing aka split testing compares 2 versions of a web page to see which performs better 5p 0ch ck7 55m 01255 b m f A o 5 r 4 39rau y f sIAgt g g2 L 1 l quot l r cl2k n M5 quot4 39VKIWWLg f An 3 0 One ad test Pclick and Psign up 0 Psign up is a subset of Pclick since you have to click the quotlearn more button before signing up I Probability tree for this example 0 The last branches show conditional probabilities PBA where B is the site Visitor signs up and A is the site Visitor clicks probability of the Visitor both clicking and signing up probability of the Visitor just clicking PBA PAnBPA Without water plant dies 90 of the time The probability the friend waters the plant is 30 What is the probability the plant survives vf 1 I V 5 50 5w s gw f 39Iquot tWW by Wm 0mm 3 3 5 1quot f 1J1fd quot 7 f M will 7 furv39w 3 I 07 l I f Gni id r lgj I 24 07 31 Lecture 14 Conditional Probabilities and different ways to write the equation P AB PAnB PB PAnB PAB X PB More examples 0 Pwaters3 Pdieswater2 Pdiesno water 9 What is the probability that your friend waters the plant it dies 0 Don t know if the friend waters the plant also don t know if it will die I So it s not really conditional I The and indicates it s a question about intersection Looking for Pwaters 11 dies PAnB PAB X PB Pwaters 11 dies P waters X Pdieswaters o 3 X 2 06 What is the probability the friend forgets to water the plant and the plant dies 0 Looking for P no water 11 dies 0 P no water 11 dies Pno water X Pdiesno water I 7 X 9 What is the probability the plant dies 0 Looking for Pdies I P no water n dies u water n dies I P no water n dies P water n dies 06 63 69 A Fourth Probability Rule Whenever there s an event A we can divide it into the probability A happens when B happens the probability A happens when B does not happen 0 PA PAnB PAnBC O I Pink blue Finding the reverse probabilities What is the probability your friend failed to water the plant given that you came home from your trip and it was dead 0 We know Pno water plant dies 9 Pwith water plant dies 2 P friend waters the plant 3 0 We re looking for P no water dies 0 Bayes rule I Purpose to turn conditional probabilities around I 1 PBA PBnAPA I 2 PAnB PAB X PB insert number 2 into the top equation keeping in mind AnBBnA PBAPAB X PfBD PfA PAB X PB PAnB PAnBC 39 30 PBIA PAIB X PB PAIB X PB PABc X P039 Shortcut if possible short Bayesquot without the denominator broken up PBA PAB X PB PA Even shorter PBA PAnB PA o Pno water dies Pdies no water X Pno water Pdies I 9 X 7 69 63 69 913 Bayes Rule example We know a woman who is 4050 years old has no family history of breast cancer and she has a positive mammogram What are the chances she has breast cancer 0 Probability a 4050 year old woman with no family history of breast cancer has breast cancer 008 o If a person has breast cancer the probability of a positive test 9 o If person does not the probability of a positive test false positive 07 What we know and want to know 1 P cancer in woman like this 008 2 P positivel cancer 9 3 P positivel no cancer 07 We are looking for P cancerl positive test I So opposite of 2 I P cancerl positive P cancer n positive P positive I P cancerl positive P positive cancer x P cancer P positive I P cancerl positive P positive cancer x P cancer P positivel cancer x P cancer P AB x PB I P cancerl positive 9 x 008 9 x 008 07 x 992 I 0072 07664 0939 0000 Definitions Independence two events A and B are independent if the probability of A n B PA x PB o When PAnB PA x PB I Because if they are independent PAB PA x PB PB B happening doesn t have any effect on A so the PB s cancel out and o If two events are independent PAB PA I The likelihood one happens has nothing to do with the likelihood the other happens I If they re independent we can say that PAnB PA x PB and that PAB PA A random variable is an uncertain quality 0 Usually use capital letters from the end of the alphabet X Y Z etc The probability distribution distribution for short of a random variable is a list of all possible values along with the probability that each value occurs 0 Ex for rolling a die it s 16 with 16 as the probability for each I X 12 34 56 I PX 16 16 16 16 16 16