Essentials of Statistics - Triola
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Data are observations ( such as measurementrs, genders, survet responses ) that have been collected
Statistics is a collection of methods for planning studies and experiments, obtaining data and then organizing, summerizing, presenting, analyzing, interpreting and drawing conclusions based on the data.
A population is the complete collection of all elements ( scores, people, measurements and so on) to be studied. The collection is complete in the sense that it includes all subjects to be studied.
A census is the collection of data from every member of the population.
A sample is a subcollection of members selected from a population
A Parameter is a numerical measurement describing some characteristic of a population.
A statistic is a numerical measurement desribing some characteristic of a sample.
Quantitative Data consists of numbers representing counts or measurements.
Qualitative ( or categorical or attribute ) Data
Qualitative ( or categorical or attribute ) Data can be separated into different catagories that are distinguished by some nonnumeric characteristic.
Discrete Data result when the number of possible values is either a finate number or a "countable" number. ( That is the number of possible values is 0 or 1 or 2 or so on.)
Continuous (numerical) data
Continuous (numerical) data result from infinitely many possible values that correspond to some continuous scale that covers arange of values without gaps, interuptions or jumps.
NOMINAL LEVEL OF MEASUREMENT
- The nominal level of measurement is characterized by data that consists of names, labels or catagories only. The data cannot be arranged in an ordering scheme.
- Ex. student states
ORDINAL LEVEL OF MEASUREMENT
- Data are at the ordinal level of measurement if they can be arranged in some order, but differences between data values either cannot be determined or are meaningless.
- EX student cars types....compact to mid to full size
INTERVAL LEVEL OF MEASUREMENT
- The interval level of measurement is like the ordinal level, with the additional porperty that the differences between any two data values in meaningful. However, data at this level do not have a natural zero starting point ( where none of the quantity is present. )
- EX. campus tempertures
RATIO LEVEL OF MEASUREMENT
- The ratio level of measurement is the interval level with the additionla property that there is also a natural zero starting point, ( where zero indicates that none of the quantity is present). For values at this level, differences and ratios are both meaningful.
- Ex. student commuting distance to school.
VOLUNTARY RESPONSE SAMPLE
A voluntary response sample or self selected sample, is one in which the respondent themselves decide whether to be included.
- To find some percentage of an amount, drop the % symbol and divide the percentage value by 100. Then multiply
- 6% of 1200 responses = 6/100 X 1200 = 72
Fraction - percentage
to convert from a fraction to a percentage, divide the denominator into the numerator to get an equivalent decimal number, then multiply by 100 and affix the % symbol. This example show that the fraction 3/4 is equivalent to 75%.
3/4 = 0.75 0.75X 100% = 75 %
Decimal to percentage
To convert from a decimal to a percentage, multiply by 100%. This example shows that 0.250 is equivalent to 25.0%
0.250 to 0.250 x 100% = 25.0 %
Percentage to decimal
To convert from a percentage to a decimal number, delete the % symbol and divide by 100. This example shows that 85% is equivalent to 0.85
85% = 85/100 = .85
Survey questions can be loaded to elicit a desired response.
Order of questions
Sometimes survey questions can be loaded unintentionaly by such factors as order of items being considered.
A non response occurs when someone either refuses to respond to a survey question, or the person is unavailable.
Results can be sometimes be dramatically affected by missing data. Missing data can be random or due to special factors such as low income or homeless or in phone call surveys the number of people with out phones.
SELF INTERST STUDY
- Studies are sometimes sponsored by parties with intersts to promote.
- Ex MDs for pharmacuticals.
Some figures appear precise in their randomness when it is really an estimate.
Claims may be technically correct but may be misleading when not presenting complete results.
Deliberate distortion is when a company distorts the findings to show only how their company benifits and disreguards the rest of the data.
In an observational study, we observe and measure specific characteristics but we don't attempt to modify the subjects being studied.
In an experiment, we apply some treatment and then proceed to observe its effects on the subjects. Subjects in an experiment are called experimental subjects.
in a cross sectional study data are observed, measured and collected one point at a time.
RETROSPECTIVE ( OR CASE CONTROLLED ) STUDY,
In retrospective study data are collected from the past by going back in times through examination of records, interviews and so on.
PROSPECTIVE OR LONGITUDNAL OR COHORT STUDY
In a prospective longitudnal or cohort study data are collected in future from groups sharing common factors called cohorts.
Confounding occurs in an experiment when you are not able to distinguish among the effects of different factors.
In order to controll the effect of variables in an experiment blinding may be used, a techniques in which the subject doesn't know if he is recieving a treament or a placebo.
- A block is a group of subjects that are similar, but blocks are different in ways that may affect the outcome of the experiment.
- Ex A block of similar trees in one block has moist soil the other block has dry soil. They both get the same fertilizer
RANDOMIZED EXPERIMENTAL DESIGN
With a completly randomized experimental design subjects are assigned to different treatment groups through a process of random selection.
RIGOROUSLY CONTROLLED DESIGN
With a rigorously controlled design subjects are very carefully chosen so that those given each treatment are similar in ways that are improtant to the experiment.
Repitition on an experiment on sufficiently large groups of subjects is called Replication.
In a random sample, members from the population are selected in such a way that each individual mamber has an equal chance of being selected.
SIMPLE RANDOM SAMPLE
In a simple random sample of n subjects is selected in such a way that every possible sample of the same size n has the same chance of being chosen.
A probability sample involves selecting members from a population in such a way that each member has a known ( but not necessarily the same) chance of being selected.
In systematic sampling we select some starting point and then select every kth ( such as every 50th) element in the population.
With stratified sampling we subdivide the population inot at least two different subgroups ( or strat) so that the subjects with in the same subgroup share the same charactersitics, such as gender or age bracket, then we draw a sample from each subgroup or stratum.
In cluster sampling we first divide the population area into sections ( or clusters), then randomly select some of those clusters, and then choose all the members from those selected clusters.
MULTISTAGE SAMPLE DESIGN
In a multistage sample design involves the selection of a sample in different stages that might use different methods of sampling.
A sampling error is the difference between a sample result and the tru population result: such an error results from chance sample fluctuations.
A nonsampling error occurs when the sample data are incorrectly collected, recorded or analyzed (such as by selecting a biased sample, using a defective measure instrument, or copying the data incorectly).
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