DESCRIPTIVE STATISTICS - CHAPTERS 1 & 2 1
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1 DESCRIPTIVE STATISTICS - CHAPTERS 1 & 2 1 OVERVIEW STATISTICS PANIK...THE THEORY AND METHODS OF COLLECTING, ORGANIZING, PRESENTING, ANALYZING, AND INTERPRETING DATA SETS SO AS TO DETERMINE THEIR ESSENTIAL CHARACTERISTICS... HYPERSTAT...IN THE BROADEST SENSE, "STATISTICS" REFERS TO A RANGE OF TECHNIQUES AND PROCEDURES FOR ANALYZING DATA, INTERPRETING DATA, DISPLAYING DATA, AND MAKING DECISIONS BASED ON DATA...
2 DESCRIPTIVE STATISTICS - CHAPTERS 1 & 2 2 DESCRIPTIVE - SUMMARIZE ESSENTIAL FEATURES OF DATA (CENTRAL TENDENCY, VARIABILITY, DISTRIBUTION) INFERENTIAL - ESTIMATES, PREDICTIONS, PREDICTIONS, FORECASTS, GENERALIZATIONS PANIK...INDUCTIVE STATISTICS, INFERRING SOMETHING ABOUT THE WHOLE FROM THE EXAMINATION OF ONLY ONE PART...
3 DESCRIPTIVE STATISTICS - CHAPTERS 1 & 2 3 POPULATION DANIEL...LARGEST COLLECTION OF ENTITIES FOR WHICH WE HAVE AN INTEREST AT A PARTICULAR TIME... HYPERSTAT...ENTIRE SET OF OBJECTS, OBSERVATIONS, OR SCORES THAT HAVE SOMETHING IN COMMON...EXAMPLE, A POPULATION MIGHT BE DEFINED AS ALL MALES BETWEEN THE AGES OF 15 AND 18...THE DISTRIBUTION OF A POPULATION CAN BE DESCRIBED BY SEVERAL PARAMETERS SUCH AS THE MEAN AND STANDARD DEVIATION... ESTIMATES OF THESE PARAMETERS TAKEN FROM A SAMPLE ARE CALLED STATISTICS...
4 DESCRIPTIVE STATISTICS - CHAPTERS 1 & 2 4 CENSUS...COUNT EVERY ENTITY IN THE POPULATION... SAMPLE...PART OF A POPULATION... HYPERSTAT...SUBSET OF A POPULATION...SINCE IT IS USUALLY IMPRACTICAL TO TEST EVERY MEMBER OF A POPULATION, A SAMPLE FROM THE POPULATION IS TYPICALLY THE BEST APPROACH AVAILABLE...
5 DESCRIPTIVE STATISTICS - CHAPTERS 1 & 2 5 PARAMETER (POPULATION) HYPERSTAT...NUMERICAL QUANTITY MEASURING SOME ASPECT OF A POPULATION OF SCORES...EXAMPLE, THE MEAN IS A MEASURE OF CENTRAL TENDENCY...PARAMETERS ARE RARELY KNOWN AND ARE USUALLY ESTIMATED BY STATISTICS COMPUTED IN SAMPLES...
6 DESCRIPTIVE STATISTICS - CHAPTERS 1 & 2 6 STATISTIC (SAMPLE) HYPERSTAT..."STATISTIC" IS DEFINED AS A NUMERICAL QUANTITY (SUCH AS THE MEAN) CALCULATED IN A SAMPLE. SUCH STATISTICS ARE USED TO ESTIMATE PARAMETERS... HYPERSTAT..."STATISTICS" SOMETIMES REFERS TO CALCULATED QUANTITIES REGARDLESS OF WHETHER OR NOT THEY ARE FROM A SAMPLE...EXAMPLES, BATTING AVERAGE, "GOVERNMENT STATISTICS"
7 DESCRIPTIVE STATISTICS - CHAPTERS 1 & 2 7 QUANTITATIVE (TEMPERATURE) QUALITATIVE (GENDER) THE QUALITATIVE-QUANTITATIVE DEBATE HYPERSTAT...QUALITATIVE VARIABLES ARE SOMETIMES CALLED "CATEGORICAL VARIABLES"...QUANTITATIVE VARIABLES ARE MEASURED ON AN ORDINAL, INTERVAL, OR RATIO SCALE...QUALITATIVE VARIABLES ARE MEASURED ON A NOMINAL SCALE...
8 DESCRIPTIVE STATISTICS - CHAPTERS 1 & 2 8 DISCRETE (NUMBER OF HOSPITAL ADMITS IN A DAY) CONTINUOUS (HEIGHT) HYPERSTAT...SOME VARIABLES (SUCH AS REACTION TIME) ARE MEASURED ON A CONTINUOUS SCALE...THERE IS AN INFINITE NUMBER OF POSSIBLE VALUES THESE VARIABLES CAN TAKE ON...OTHER VARIABLES CAN ONLY TAKE ON A LIMITED NUMBER OF VALUES AND SUCH VARIABLES ARE CALLED "DISCRETE" VARIABLES...
9 DESCRIPTIVE STATISTICS - CHAPTERS 1 & 2 9 LEVELS OF MEASUREMENT NOMINAL (GENDER, ETHNICITY, RACE) HYPERSTAT NOMINAL MEASUREMENT CONSISTS OF ASSIGNING ITEMS TO GROUPS OR CATEGORIES... NO QUANTITATIVE INFORMATION IS CONVEYED AND NO ORDERING OF THE ITEMS IS IMPLIED... NOMINAL SCALES ARE QUALITATIVE RATHER THAN QUANTITATIVE... FREQUENCY DISTRIBUTIONS ARE USUALLY USED TO ANALYZE DATA MEASURED ON A NOMINAL SCALE... MAIN STATISTIC COMPUTED IS THE MODE... REFERRED TO AS CATEGORICAL OR QUALITATIVE VARIABLES
10 DESCRIPTIVE STATISTICS - CHAPTERS 1 & 2 10 ORDINAL (ATTITUDE SCALE: 0, 1, 2, 3,4 5) HYPERSTAT ORDERED IN THE SENSE THAT HIGHER NUMBERS REPRESENT HIGHER VALUES... INTERVALS BETWEEN THE NUMBERS ARE NOT NECESSARILY EQUAL... NO "TRUE" ZERO POINT FOR ORDINAL SCALES SINCE THE ZERO POINT IS CHOSEN ARBITRARILY
11 DESCRIPTIVE STATISTICS - CHAPTERS 1 & 2 11 INTERVAL (TEMPERATURE) HYPERSTAT ONE UNIT ON THE SCALE REPRESENTS THE SAME MAGNITUDE ON THE TRAIT OR CHARACTERISTIC BEING MEASURED ACROSS THE WHOLE RANGE OF THE SCALE... NO "TRUE" ZERO POINT RATIO (HEIGHT) HYPERSTAT RATIO SCALES ARE LIKE INTERVAL SCALES EXCEPT THEY HAVE TRUE ZERO POINTS
12 DESCRIPTIVE STATISTICS - CHAPTERS 1 & 2 12 RANDOM SAMPLING RANDOM SAMPLE...EACH MEMBER OF A POPULATION HAS THE SAME CHANCE OF BEING SELECTED... SIMPLE RANDOM SAMPLE...EACH SAMPLE OF SIZE N IS SELECTED SUCH THAT EACH SUCH SAMPLE OF SIZE N HAS THE SAME CHANCE OF BEING SELECTED...
13 DESCRIPTIVE STATISTICS - CHAPTERS 1 & 2 13 OTHER SAMPLE TYPES SYSTEMATIC... Nth ENTITY STRATIFIED... RANDOM ENTITIES WITHIN STRATA (GENDER, AGE GROUP, COUNTY) CLUSTER... ALL ENTITIES WITHIN RANDOMLY SAMPLED CLUSTERS (COUNTY, CENSUS TRACT, ZIP CODE) CONVENIENCE... WHATEVER
14 DESCRIPTIVE STATISTICS - CHAPTERS 1 & 2 14 CRITICAL THINKING CHAPTER 1 AVERAGE AGE AT DEATH FOR VARIOUS OCCUPATIONS STUDENTS...MEAN = 20.7 MOST DANGEROUS OCCUPATION = STUDENT???
15 DESCRIPTIVE STATISTICS - CHAPTERS 1 & 2 15 DESCRIBING & COMPARING DATA TRIOLA...ONE DATA SET TO ILLUSTRATE CONCEPTS IN CHAPTER SERUM COTININE LEVELS IN BLOOD (PRODUCED BY NICOTINE)...INDICATOR OF EXPOSURE TO CIGARETTE SMOKE FIVE (WELL, THREE + TWO) IMPORTANT CHARACTERISTICS OF DATA... CENTER VARIATION DISTRIBUTION OUTLIERS TIME
16 FROM TRIOLA, CHAPTER 2 COTININE: METABOLITE OF NICOTINE - WHEN NICOTINE IS ABSORBED BY THE BODY, COTININE IS PRODUCED SMOKER: REPORTED TOBACCO USER ETS: NON-SMOKERS EXPOSED TO 2ND HAND SMOKE NOETS: NON-SMOKERS, NO EXPOSURE TO 2ND HAND SMOKE
17 DESCRIPTIVE STATISTICS - CHAPTERS 1 & 2 16 FREQUENCY DISTRIBUTIONS DATA VALUES GROUPED INTO INTERVALS CHOICE OF INTERVALS AFFECTS HOW YOU (OTHERS) SEE (INTERPRET) YOUR DATA...NO ONE RIGHT ANSWER AS TO WHAT INTERVALS ARE APPROPRIATE USER-DEFINED QUARTILES NATURAL BREAKS STURGES RULE SOFTWARE-DEFINED TABLES OR GRAPHICS
18 DESCRIPTIVE STATISTICS - CHAPTERS 1 & 2 17 Using Statcrunch Histograms
19 DESCRIPTIVE STATISTICS - CHAPTERS 1 & 2 18 Using Statcrunch Stem-and-Leaf Dot plot Variable: SMOKER 0 : : : : : : : 1 3 : 4 : 4 : 89
20 DESCRIPTIVE STATISTICS - CHAPTERS 1 & 2 19 Using Statcrunch Boxplots No Fences With Fences
21 DESCRIPTIVE STATISTICS - CHAPTERS 1 & 2 20 Using SAS * * * * * * * * *--+--* * * 0 + *-----* *--*--* group ETS NOETS SMOKE
22 DESCRIPTIVE STATISTICS - CHAPTERS 1 & 2 21 OTHER GRAPHICS SCATTER PLOTS (2 VARIABLES) TIME SERIES (TREND LINES) OGIVE (CUMULATIVE FREQUENCY) MISCELLANEOUS (USER CREATIVITY!!!)
23 DESCRIPTIVE STATISTICS - CHAPTERS 1 & 2 22 MEASURES OF CENTER MEAN MEDIAN MODE SUM OF ALL VALUES DIVIDED BY THE NUMBER OF VALUES (VERY SENSITIVE TO EXTREME VALUES) MIDPOINT - NOTHING TO DO WITH THE VALUES THEMSELVES (NOT SENSITIVE TO EXTREME VALUES) MOST FREQUENTLY OCCURRING VALUE (POSSIBILITY OF MULTIPLE MODES, BIMODAL NOT UNCOMMON) RELATIONSHIP OF MEAN, MEDIAN, MODE (SYMMETRIC AND SKEWED DISTRIBUTIONS)
24 DESCRIPTIVE STATISTICS - CHAPTERS 1 & 2 23 MEASURES OF VARIATION RANGE STANDARD DEVIATION VARIANCE COEFFICIENT OF VARIATION DIFFERENCE BETWEEN MINIMUM AND MAXIMUM VALUES MEASURE OF VARIATION OF VALUES AROUND THE MEAN AVERAGE SQUARED DEVIATION OF A VALUE FROM THE MEAN (SQUARE OF STANDARD DEVIATION) - DENOMINATOR, N VERSUS N-1 AND BIAS STANDARD DEVIATION EXPRESSED AS A PERCENTAGE OF THE MEAN
25 DESCRIPTIVE STATISTICS - CHAPTERS 1 & 2 24 STANDARD DEVIATION AND 'TYPICAL VALUES' EMPIRICAL RULE - IN A BELL-SHAPED DISTRIBUTION... 68% OF VALUES FALL WITHIN 1 STANDARD DEVIATION OF THE MEAN...95% OF VALUES FALL WITHIN 2 STANDARD DEVIATIONS OF THE MEAN % OF VALUES FALL WITHIN 3 STANDARD DEVIATIONS OF THE MEAN ACCEPTED CONCEPT OF 'TYPICAL VALUES' --- WITHIN 2 STANDARD DEVIATIONS OF THE MEAN
26 DESCRIPTIVE STATISTICS - CHAPTERS 1 & 2 25 CHEBYSHEV'S THEOREM REGARDLESS OF THE SHAPE OF A DISTRIBUTION, THE PROPORTION OF DATA LYING WITHIN K STANDARD DEVIATIONS OF THE MEAN IS AT LEAST...1-1/K 2 AT LEAST 3/4 (75%) OF ALL VALUES LIE WITHIN 2 STANDARD DEVIATIONS OF THE MEAN AT LEAST 8/9 (89%) OF ALL VALUES LIE WITHIN 3 STANDARD DEVIATIONS OF THE MEAN RATIONALE FOR STANDARD DEVIATION (AND VARIANCE)
27 DESCRIPTIVE STATISTICS - CHAPTERS 1 & 2 26 RELATIVE STANDING Z-SCORES QUARTILES STANDARDIZED SCORES USING MEAN AND STANDARD DEVIATION (UNUSUAL VALUES - JORDAN, LOBO, BOGUES - OUTSIDE OF +/- Z=2) Q1, Q2, Q3 MEDIAN, MEDIANS OF UPPER AND LOWER HALF INTERQUARTILE RANGE (Q1 AND Q3)
28 DESCRIPTIVE STATISTICS - CHAPTERS 1 & 2 27 EDA (EXPLORATORY DATA ANALYSIS - JOHN TUKEY, 1977) EDA IS DETECTIVE WORK (NUMERICAL, COUNTING, GRAPHICAL) EDA CAN NEVER BE THE WHOLE STORY, BUT NOTHING ELSE CAN SERVE AS THE FOUNDATION STONE, AS THE 1ST STEP SEARCH FOR PATTERNS, GROUPS, UNEXPECTEDLY POPULAR VALUES, UNUSUAL VALUES, OUTLIERS TRIOLA 5-NUMBER SUMMARY (MINIMUM, Q1, MEDIAN, Q3, MAXIMUM) STEM-AND-LEAF PLOTS, BOX PLOTS
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