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Reasons to Sample over census
- -cheaper
- -quicker
- -large populations may be inaccessible
- -destructiveness of the observation
- --carefully obtained sample is better than sloppily conducted census
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Sampling Error
- -due solely to particular units that have been selected
- -chance
- -sampling bias(usually the result of poor planning)
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Protection Against Sampling Error
- -chance->use a large enough sample
- -sampling bias->have a good plan
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Non Sampling Error
- -can occur in census or sampling
- -results solely from the manner in which observations are made
- -ex. inacurate measurement from malfunctioning instruments
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Types of Sampling(list)
- -convenience
- -representative
- -random(with and without replacement)
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Convenience Sampling
- -usually self selected (people that phone in to give opinion)
- -bad type of sampling
- -results regarded with caution
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Representative Sampling
- -represent the characteristics of a population as closely as possible
- -more reliable than convenience
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Random Sample
- -most important type of sample
- -people recruited for use are totally random(can be with or without replacement)
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Canadian Census
- -every 5 years
- -last one was May 10, 2011
- -employ about 34,000 temp workers for it
- -must be filled out by law
- -first one taken in 1871(had 211 questions)
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Agriculture Census
- -started in Manitoba in 1896, Sask and Alberta joined in 1906
- -every 5 years
- -separate from regular census
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Element
-specific subject(object) about which the info is collected
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Variable
-characteristic under study for each element
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Observation/measurement/data value
-value OF a variable FOR an element
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Data/Data set
-collection of observations on one or more variables
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Quantitative Variables
- -can be measured numerically
- -math can be performed on the results
- -can be continuous or discrete
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Continuous Variables
- -variable that can assume any numerical value
- -blood pressure, time, distance
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Discrete Variables
- -countable units
- -you can have 3 dogs, but not 2.3 dogs
- -the variable cannot assume any number in its range, only full units
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Qualitative Variables
-must be defined in non-numerical categories
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Raw Data
-data recorded in the sequence in which it was collected
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Frequency Distribution
-lists the number of the data occurrences for each category of data
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Relative Frequency Distribution
-shows the percent of observations that belong to each category
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Pareto Chart
-bar graph that shows the bars in decreasing order of frequency (can be frequency or relative frequency)
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Continuous Histograms
-similar to bar graph, but no gaps between the bars
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Discrete Histograms
-similar to bar graph but does have gaps between the bars (versus continuous)
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Parameter
-descriptive measure of a population
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Statistic
-descriptive measure of a sample
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Mean
- -average of the data
- -can be of sample or population
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Median
- -the middle term of data points that have been arranged in a ranked order (increasing or decreasing)
- -if you have an even number of terms, average the 2 middle terms
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Mode
- -the number which occurs with the highest frequency
- -can be unimodal, bimodal or multimodal
- -only measure of central tendency for qualitative data
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Range
- -difference between the highest and lowest data points
- -influenced by outliers
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Standard Deviation
- -tells you how closely the values of the data set are clustered around the mean
- -low value= data is closer to mean than a large SD
- -calculated by taking the square root of the variance
- -always in same unit as data
- -can never be negative, may be zero
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5 Number Summary
-include the lowest value, quartile 1 boundary, median, quartile 3 boundary and highest value
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law of large numbers
- -the long run relative frequency of repeated independent events gets closer to the relative true frequency as the number of trials increases
- -the more times you flip a coin the closer you will get to 50/50 results
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Sample Space
-the set of all possible outcomes of the experiment
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Event
- -any collection of outcomes from an experiment
- -denoted using capital letters such as A
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Simple Event
-includes only one of the final outcomes for an experiment and is denoted Ei
-can only be achieved one way
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Compound Event
- -collection of more than one outcome for an experiment
- -can have multiple ways of achieving the requirement
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Classical Probability
-done when all outcomes from an event are equally likely
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Relative Frequency Probability
-used when all possible outcomes do not have an equal chance to occur
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Subjective Probability
-probability assigned to an event based on subjective judgement (experience, information and belief)
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Marginal Probability
- -probability of an event without considering any other event
- -also called simple probability
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Conditional Probability
-probability that an event will occur given than another event has already occured
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Mutually Exclusive Events
- -events that cannot occur together
- -events have no shared elements
- -in a venn diagram the circles will not overlap
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Mutually Non Exclusive Events
-where observing one thing does not rule out the other, they can both occur, or one or the other
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Complimentary Events
-two always mutually exclusive events that taken together include all the outcomes for an experiment
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