STAT 210/ STUDY GUIDE/ TEST 1INTRODUCTION AND BASIC DEFINITIONSSTATISTICS- EXTRACTION OF INFO FROM NUMERICAL DATA FROM AN EXP. OR SAMPLE. INVOLVES DESIGN OF PROCEDURE, COLLECTION, AND ANALYSIS.POPULATION- WHOLE GROUP, “ALL”. EX: ALL CITIZENS, ALL STUDENTS, ALL SECTIONS PARAMETER- CHARACTERISTIC OF POP THAT RESEARCHER WANTS TO MEASURE. “PROPORTION, AVERAGE,” ETC. -MEAN USES U (“MU”), PROPORTION OF POP THAT ARE SUCCESSES USES PI.EX: PROPORTION OF CITIZENS, AVERAGE HEIGHTSAMPLE- SUBSET OF POP. USED FOR INFORMATION.EX: IF POPULATION IS ALL MALE STUDENTS IN UNIV, THEN SAMPLE CAN BE ALL MALE STUDENTS IN THIS CLASS.STATISTIC- DESCRIPTIVE MEASURE FROM A SAMPLE. IS NUMERIC. -X-BAR= SYMBOL FOR MEANEX: POP= ALL MALE STUDENTS IN UNIV, SAMPLE= ALL MALE STUDENTS IN THIS CLASS, STATISTIC= AVERAGE HEIGHT OF MALE STUDENTS IN THIS CLASSINFERENCE- STATEMENT ABOUT A POP. BASED ON SAMPLE DATA. USUALLY ESTIMATES A POP. PARAMETER.EX: USING AVERAGE HEIGHT OF MALES STUDENTS IN THE CLASS TO EST. AV. HEIGHT OF ALL MALE STUDENTS AT UNIV.DISTRIBUTION- A LIST OF THE VALUES OF A CHARACTERISTIC AND ITS #/% OF OCCURRENCE.EX: GENDER= MALE OR FEMALE, # OF EACH= DISTRIBUTION. EX: IF A TEST IS WORTH 100 POINTS- # OF STUDENTS IN EACH 10 POINT INTERVAL COULD BE ANEX OF DISTRIBUTION.DESCRIPTIVE STATISTICS- THE NUMERICAL AND GRAPHICAL STATISTICS OF A POP, ALSO COMPARES CHARACTERISTICS IN THOSE POP.INFERENTIAL STATISTICS- USING DATA AND STAT FROM A SAMPLE TO MAKE INFERENCES, USUALLY FROM DESCRIPTIVE STATISTICS.REPLICATION/REPETITION- TO ASSURE ACCURACY BY REPEATING MEASUREMENTS SEVERAL TIMES.CONSTANT- WHEN THE MEASUREMENTS OF A CHARACTERISTICS DON’T CHANGE WITH REPETITION. EX: NUMBER OF DAYS IN JAN (ALWAYS 31), OR NUMBER OF MINUTES IN HOUR (ALWAYS 60)VARIABLE- IF MEASUREMENTS OF A CHARACTERISTIC VARY WITH REPETITION.EX: GRADES ON TESTSQUALITATIVE OR CATEGORICAL VARIABLE- VARIABLE THAT IS DIFFERENT IN NAME BUT NOT VALUE BECAUSE THEY HAVE NO VALUES.EX: GENDER (MALE OR FEMALE), EYE COLOR (BLUE, GREEN, BROWN, ETC.), SOCIAL SEC. #QUANTITATIVE VARIABLE- VARIABLE WITH DIFFERENT VALUES WITH TRIALS.EX: WEIGHT OF A STUDENT, NUMBER OF STUDENTS IN A CLASS, GRADES ON A TEST 1)DISCRETE QUANT VARIABLE- VARIABLE THAT CAN ONLY BE COUNTED EX: NUMBER OF ___, GRADES 2)CONT QUANT VARIABLE- VARIABLE WITH DIFFERENT VALUES IN A LINE INTERVAL, IS USUALLY CALCULATED, LIKE RATES, PROPORTIONS, AND PERCENTAGESEX: WEIGHT OF A STUDENT, PERCENTAGE OF STUDENTSPRODUCING DATAREPRESENTATIVE- IF A SAMPLE’S CHARACTERISTICS ARE NEARLY THE SAME AS THE CHARACTERISTICS IN THE POP.EX: POP OF STUDENTS: 60% FEMALE, 40% MALE, SAMPLE CAN BE REP IF IT IS ALSO 60% FEMALE AND 40% MALE.BIAS- WHEN SUBJECTS/OUTCOMES ARE FAVORED MORE THAN OTHERS. 1)SELECTION BIAS- WHEN ONE OR MORE TYPES OF SUBJECTS ARE EXCLUDED FROM SAMPLE. WHEN AN INFERENCE CANNOT BE MADE TO WHOLE POP BUT ONLY A SUBSET, IT IS CALLED UNDERCOVERAGE.2)NONRESPONSE BIAS- WHEN INDIVIDUALS CANNOT BE CONTACTED OR DON’T RESPOND. HAPPENS IN SURVEYS AND POLLS. 3)RESPONSE BIAS- WHEN INACCURATE INFO IS GIVEN OR IF INTERVIEW INFLUENCES SUBJECT TO RESPOND A CERTAIN WAY (USUALLY WITH LEGAL OR SOCIAL ISSUES). EX: SOCIAL PRESSURES FROM RISKY QUESTIONS, OR QUESTIONS THAT ONLY MENTION ACERTAIN THING (EX: A QUESTION ABOUT DELTA AIRLINES, INSTEAD OF INCLUDING ALL AIRLINES)HAPHAZARD SAMPLES- CHOOSING A SAMPLE OUT OF CONVENIENCE, DOESN’T INCLUDE RANDOMIZATION.EX: SURVEYING STUDENTS ONLY IN ONE SPECIFIC BUILDING- NO EQUAL CHANCES FOR OTHER STUDENTSVOLUNTEER RESPONSE SAMPLES- WHEN PEOPLE VOLUNTEER TO BE A PART OF A STUDY. PROBLEM= OVERREPRESENTATION CAUSE THOSE WHO DO VOLUNTEER WANT VOICE TO BE HEARD. USUALLY TELEPHONE POLLS, INTERNET SURVEYS (MOSTLY CONVENIENCE/NOT RANDOM SAMPLES)PROBABILITY SAMPLING DESIGNS- EACH MEMBER OF POP. HAS EQUAL CHANCES OF SELECTION. REDUCES BIAS AND CHOOSES SUBJECTS RANDOMLY.SIMPLE RANDOM SAMPLING- MAKE A LIST OF ALL POSSIBLE INDIV. IN THE POP AND RANDOMLY CHOOSE SAMPLE SIZE (LOWERCASE “n”), SO THAT EVERY SAMPLE SIZE SET HAS AN EQUAL CHANCE TO BE IN THE SAMPLE. INTERVIEWER HAS NO CHOICE WHO IS IN SAMPLE. -IS MOST USED, DOESN’T GUARANTEE A REP SAMPLE, MIGHT FAVOR A SUBJECT OVER ANOTHER BECAUSE % MIGHT BE BIGGER FOR THAT SUBJECT. STRATIFIED RANDOM SAMPLE CANGET RID OF OVER/UNDER REPRESENTING.-THIS TEST CAN BE EXPENSIVE, TIME-CONSUMING, AND INCONVENIENT.TABLE OF RANDOM DIGITS- USUALLY USES A COMPUTER PROGRAM, SUCH AS A TABLE OF RANDOM DIGITS. TO USE, 1) KNOW THE POPULATION NUMBER (CALLED “N”). 2) LABEL POP 1 TO N. 3) CHOOSE “n” DEPENDING ON # OF DIGITS IN “N” (TWO DIGIT FROM 1 TO 80, THREE DIGIT FROM 001 AND 636, ETC.) DUPLICATES AND #S OUTSIDE RANGE= OMITTED.1)FROM THE LINE YOU ARE TOLD TO ENTER FROM, WRITE THE TWO DIGIT #S DEPENDING ON DIGITS OF POP. 2)THEN CHOOSE THE SAMPLE # OF TWO DIGIT #S THAT IS UNDER THE POP NUMBER (AKA “N”). SO IF THE SAMPLE NUMBER IS 8 AND THE POP NUMBER IS 50, CHOOSE 8 OF THE TWO DIGIT NUMBERS THAT IS UNDER 50. STRATIFIED RANDOM SAMPLING- POP IS DIVIDED INTO GROUPS OF SIMILAR SUBJECTS (STRATA). SIMPLE RANDOM SAMPLE IS CHOSEN FROM EACH GROUP, AND THEN COMBINED FOR COMPLETE SAMPLE. # CHOSEN FROM EACH GROUP SHOULD BE THE SAME AS THE TOTAL POP IN EACH GROUP FOR A MORE REP SAMPLE. -YOU LOSE A LITTLE BIT OF RANDOMIZATION BUT IT IS MORE REPRESENTATIVE, AND THEREFORE, MORE RELIABLE. EX: 1) AFTER POP IS DIVIDED INTO ITS GROUPS, MAKE SURE A NUMBER OF THE CORRECT PROPORTION IS CHOSEN FROM EACH GROUP. FOR EXAMPLE, IF SAMPLE SIZE IS 200, MAKE SURE 200 IS DIVIDED ACCORDING TO THE PROPORTION OF EACH GROUP. (USUALLY DO TOTAL POP/SIZE OF GROUP, THEN TURN THAT # INTO A DECIMAL. 2) FOR THE # EACH GROUP SHOULD HAVE IN THE SAMPLE, MULTIPLY THE NUMBER BY THE SAMPLE SIZE (THIS IS THE # IN THE SAMPLE). THIS NUMBER IS HOW MANY YOU SHOULD CHOOSE IN THE TABLE OF RANDOM DIGITS (IF GROUP SIZE’S DIGITS IS 4 AND THE # IN THE SAMPLE IS 60, CHOOSE FIRST 60 4 DIGIT NUMBERS BETWEEN 1 AND THE GROUP SIZE).-THIS TEST CAN BE EXPENSIVE, TIME-CONSUMING, AND INCONVENIENT.STRATA- WHEN POP IS DIVIDED INTO GROUPS OF SIMILAR SUBJECTS.MULTISTAGE RANDOM SAMPLING- POP IS DIVIDED INTO GROUPS OF INDIVIDUALS, THEN USE SIMPLE RANDOM SAMPLING TO SELECT SOME GROUPS. THEN DIVIDE THESE GROUPS TO CHOOSE SUBGROUPS AND USE SIMPLE RANDOM SAMPLING ON THESE.-THERE HAS TO BE AT LEAST TWO RANDOMIZATION STAGES.-NOTE: THE NUMBERS IN EACH STAGE MULTIPLIED TOGETHER= THE SAMPLE #.DESIGN OF EXPERIMENTS 1)EXPERIMENTAL UNITS- THE INDIVIDUALS OR UNITS THAT MEASUREMENTS ARE MADE