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66 Cards in this Set
- Front
- Back
- 3rd side (hint)
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STATISTICS
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Technology that describes and measures aspects of nature from samples which quantifies uncertainty
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ESTIMATION
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Process of inferring an unknown quantity of a target population using sample data.
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PARAMETER
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A quantity describing a population, whereas an estimate is a related quantity calculated from a sample.
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HYPOTHESIS TESTING
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The process of determining how well a "null" hypothesis about a population fits a sample of data. (null like no, often takes negative or skeptical view)
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Example of Interest: Concept Sampling Bias-Raining Cats or "Feline High-Rise Syndrome (injuries/stories fallen)
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low number at 2 stories, more at 5 and surprisingly back to low 2 story level at 7 or more-cats at low end and high end don't go to vet, so sampling bias.
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POPULATION
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The entire collection of individuals or units that a researcher is interested in studying.
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SAMPLE
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Small set of individuals or units selected from population of interest for study.
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SAMPLING ERROR (one of two types of errors)-Bulls Eye - Grouped tightly-low error or dispersed- more error
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Chance difference between an estimate and the population parameter being estimated.Directly related to accuracy.
(Inversely related to precision) |
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PRECISION OF AN ESTIMATE
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The spread of estimates resulting from the sampling error
(Inversely related to sampling error) |
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BIAS (one of two types of errors)-Bull Eye - Mostly Centered so Precise or off Center so imprecise.
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Systematic discrepancy between estimates an the true population characteristic.
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4 STEPS TO CREATING RANDOM SAMPLE
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1.create list and give unit a number from 1 and the total population
2.n=? define Then 3. Use random number generator, gen. n integers bet w and the total population 4. Sample those units whose #s match the ones picked by random generator. |
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SAMPLE OF CONVENIENCE
DEFN: 3 EXAMPLES |
PG. 10
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GRAPHING CATEGORICAL DATA USING...
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FREQUENCY TABLES AND BAR GRAPHS PG. 25
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GRAPHING NUMERICAL DATA USING...
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HISTOGRAMS AND FREQUENCY TABLES
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5 CONCEPTS TO KEEP IN MIND TO DESCRIBE SHAPE OF HISTOGRAM
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PG. 30
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MODE
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PG 30
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INTERVAL WIDTH AND EXAMPLE
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PG 31
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STURGES RULE FOR # OF INTERVALS
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1+LN(N)/LN(2)
N IS NUMBER OF CHOICES AND LN IS THE NATURAL LOG (MOST ADD A FEW INTERVALS TO THIS NUMBER TO BE LESS CONSERVATIVE) |
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THE XTH PERCENTILE
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Value under which X percent of the individuals lie or the X/100 quantile..the 50th percentile is referred to as the .50 quantile.
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Week 1
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4 STEPS TO CREATING RANDOM SAMPLE
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1.create list and give unit a number from 1 and the total population
2.n=? define Then 3. Use random number generator, gen. n integers bet w and the total population 4. Sample those units whose #s match the ones picked by random generator. |
Week 1
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Example of Interest: Concept Sampling Bias-Raining Cats or "Feline High-Rise Syndrome (injuries/stories fallen)
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low number at 2 stories, more at 5 and surprisingly back to low 2 story level at 7 or more-cats at low end and high end don't go to vet, so sampling bias.
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RANDOM SAMPLE
(minimizing bias when done well and this minimizing makes possilbe meausre of sampling error) |
Each member of a population has an equal AND independent chance of being selected.
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INDEPENDENT
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Adjective used to describe the sample unit. It is a condition that the selection of one unit/member of the population must NOT influence the selection of any other unit/member of the population
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How to take a random sample?
5 STEPS |
1LIST EVERY UNIT IN POP AND APPLY # 1 THROUGH TOTAL POP 2.DECIDE N=?
3.USE RANDOM NUMBER GENERATOR TO GENERATE THE N RANDOM VALUES BET 1 AND TOTAL # UNITS POP (OR GROUP WITHIN POP) 4. SAMPLE THE UNITS WHOSE #'S MATCH DESIGNATED COMPUTER SAMPLE REQUEST 5. |
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SAMPLE OF CONVENIENCE
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Collection of individuals that are easily available to the researcher. (Injury Rate of Cats/Cod Fishery collapse and using estimate of population from sea only overestimated/Literary Digest Poll false projection of Election got pop from magazine lists (left out poor)/samples that might end up being friends
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Volunteer Bias
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systematic difference bet/ pool of volunteers and population (polio vaccine more parents with kids without polio so infection rate higher than expected
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List several reasons for Volunteer Bias
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1.healthier/proactive 2.low income if paid. 3. sicker if study has risk 4. telephone surveys attract people older and unemployed because home 4.more angry5.less prudish talk about sex
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2 Types of data and variables (Define)
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1)Categorical (named characteristics of a population w/ out magnitude on a numerical scale ( can be scale/grouped data with numbers ) 2)Numerical (measurements are quantitative and have magnitude on numerical level).
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Categorical Data - 2 types
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Nominal and Ordinal
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What are the two types of numerical Data -2 types
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1) Discrete : come in individual counts
2) Continuous: numerical data take on any real number value within some range with infinite number of values possible. |
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Variables
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Characteristics that differ among individuals
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Frequency Distribution
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A distribution which describes the # of times each value of a variable occurs in a sample.
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Week
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Probability Distribution
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A distribution of a variable in the whole population.
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normal Distribution
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A distribution used for a continuous variable (like beak length) which approximates the frequency distribution occurring in real life.
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Experimental Study
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A study for which the researcher assigns treatment randomly to individuals
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Observational Study
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A study for which nature assigns treatment or values of an explanatory variable (not the researcher!)
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Response Variable
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Variable being predicted
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Explanatory Variable
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Variable being used to predict the response
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Experimental Studies
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Researcher assigns subjects randomly to different treatments or groups
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Observational Studies
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Researcher does not assign subjects to treatment but observe individuals to understand the affect treatment had on them.
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Relative Frequency Distribution
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A distribution which describes the fraction of occurrences of each value of a variable.
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Frequency Table
(example: Causes of Teenage Death) |
Text display of number of occurrences of each category in the data set.
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Bar Graph
(example: Causes of Teenage Death-Accidents main one) |
Graph which uses the height of rectangular bars to display the frequency distribution ( or relative frequency distribution) of a categorical variable.
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Rules for Bar Chart Data
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Ordinal Castagorical Data: present in natural order on horizontal axis (severity ex:minimal, moder...)
Nominal: frequency of occurrence ordered (descending...) |
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Two ways of representing frequency distributions
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Histogram or Frequency Tables
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5 Descriptors of shape for histograms
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1. mode (highest peak)
2.Bimodal (frequency dn w/ 2 peaks) 3.Symmetry (semetric-pattern to right or left of peak mirrors each other. 4. Skew-asymmetry in shape of a frequency distribution in s numerical variable (Left/Right) 5. Outliers-observation well outside the range of values of other observations in the data set. |
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Histogram Construction- 5 guidelines
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1)Bar Spacing:Diff. from bar in that no separtion between adjacent bars (numerical scale reinforced)-2)Cut Off Value Decision (lower or higher bar when at cut off?)3)Sturges Rule4)use readable breakpoint numbers 5) label n=X in legend
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Week 1: A) Displaying Data
1.Displaying Frequency Distributions |
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Sturge's Rule of Thumb
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intervals= 1+ln(n)/ln(2) with n=observations and ln=natural logarithm.*rounding up is traditional
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Week 1: A) Displaying Data
1.Displaying Frequency Distributions |
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Cumulative Frequency Distribution
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x axis:Species Abundance and y axis:Cumulative Relative Frequenty (google moreexamples) Defined as graph of all quantiles of a numerical variable
+'s |
Week 1: Displaying Data
2.) Quantiles of a Frequency Distribution |
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Cumulative Relative Frequency
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fraction of observations less than or = to that same measurement pg 34
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Week 1: B) Displaying Data
2.) Quantiles of a Frequency Distribution |
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Contingency Tables
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A frequency table for two or more categorical variables
(explanatory in column and response variable (predicted one) in rows. |
Week 1: Displaying Data
3) Associations bet/ Categorical Variables |
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Grouped Bar Graph
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Graph that uses the height of rectangular bars to display the frequency(or relative freq.) distribution of two or more categorical variables. (space explanatory variable(treatment/no treatment) and response (Malaria/No Malaria) ones more than bars between groups
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Week 1: Displaying Data
3) Associations bet/ Categorical Variables |
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Mosaic Plot
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similar to grouped bar graph but stacked and only shows relative frequency and not true numerical number for frequencyNote: 1)width of bar is proportional to percent of n represented by the response variable 2) order bars for ordinal data
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Week 1: Displaying Data
3) Associations bet/ Categorical Variables |
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Compare Grouped bar (GB), contingency(C) and mosaic plot (MP)
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GB>CT easier to compare between groups for bar height and area (yet not so true if multiple categories for variables.
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Week 1: Displaying Data
3) Associations bet/ Categorical Variables |
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Stacked Vertical Histograms
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Compare histograms between groups with same scale.
Experiment: high alt>low O>high hemoglobin (binds with O so less O more H) Result: Only Andes not Ethiopia or Tibet pops showed increased hemoglobin so no physiological attributes presently universally compensating for high altitude. |
Week 1: Displaying Data
4)Comparing Numerical Variables bet/ Groups (only one variable need be numeric) 4A)Histograms |
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Grouped Cumulative Frequency Distributions
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Y Axis: Cumulative Relative Frequency X Axis: Measured Indicator (Response Variable?) pg. 40
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Week 1: Displaying Data
4)Comparing Numerical Variables bet/ Groups (only one variable need be numeric) 4B)Comparing Cumulative Frequencies |
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Scatter Plot (SP)
associations no magnitude or frequency |
Graphical Display of two numerical variables in which each observation is represented as a point on a graph with two axes.
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Week 1: Displaying Data5) Displaying Relationships bet/ pair of numerical variables
5A)Scatter Plot |
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Line Graph Described/Compared to SP
Famous Example: Cyclic Fluctuations in Lynx Numbers (Hudson Bay Company from 1752-1819) |
Dots connected by line segments to display trends in time or other ordered series .Different than scatter plot as only one y measurement appears for a particular x-observation.
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Week 1: Displaying Data
5) Displaying Relationships bet/ pair of numerical variables 5B)Line Graph |
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Map
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spatial equivalent of a line graph which displays a numerical response measurement at multiple locations on a surface
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Week 1: Displaying Data
5) Displaying Relationships bet/ pair of numerical variables 5C)Maps |
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5 Principles of Graphical Display
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1. Show the data (Bees-curve and dot)
2.represent magnitudes properly(Educational Spending Bar Graph 50 % visual but 20 % actual) 3.minimize clutter 4. maximize ease of interpretation (color/ shapes/labels) 5. use clear graphical elements |
Weel 1: Week 1: Displaying Data
5) Principles of Effective Display |
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Graph vs. Tables
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Graphs show pattern/exceptions
Tables show more quantitative aspects of the data |
Week 1: Displaying Data
5) Principles of Effective Display |
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Sample Mean
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Average measurement of the sample
Sum of all the observations divided by number of observations |
Week 1: Describing Data
1. Arithmetic Mean & Standard Deviation |
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Standard Deviation
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X
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Principles of Effective Display
1. Arithmetic Mean & Standard Deviation |
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Variance
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X
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Principles of Effective Display
1. Arithmetic Mean & Standard Deviation |
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Sum of Squares
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x
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Principles of Effective Display
1. Arithmetic Mean & Standard Deviation |
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Coefficient Variation
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X
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Principles of Effective Display
1. Arithmetic Mean & Standard Deviation |
