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DSST Principles of Statistics
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Terms in this set (50)
Frequency distribution
A table that shows the number of data observations that fall into specific intervals
Nominal data
Data assigned to categories with no mathematical comparisons between observations
Ordinal data
All the properties of nominal data with the additional capability of arranging the observations in order
Interval data
All the properties of ordinal data with the additional capability of calculating meaningful differences between the observations
Ratio data
All the properties of interval data with the additional capability of expressing on observation as a multiple of another; includes "true zero point"
True zero point
A 0 data value that indicates the absence of the object being measured
Descriptive statistics
Organizing and summing data
Inferential statistics
Drawing conclusions from "good" data
Qualitative data
Result of categorizing or describing attributes of a population
Quantitative data
Numerical data (either discrete or continuous)
Discrete quantitative data
Data that is counted
Continuous quantitative data
Data that is measured
Continuous random variable (CRV)
A random variable (RV) whose outcomes are measured
Discrete random variable
A random variable (RV) whose outcomes are counted
Sampling methods
Stratified sample
Cluster sample
Systematic sample
Convenience sample
Convenience sample
Use results that are readily available
Stratified sample
Divide the population into groups called strata and then take a sample from each stratum
Cluster sample
Divide the population into strata and then randomly select some of the strata
Systematic sample
Randomly select a starting point and take every nth piece of data from a listing of the population
Sampling without replacement
A method of sampling where each chosen member of the population is not put back into the population
Sampling with replacement
A method of sampling where each chosen member is replaced back into the population
Common statistical errors
Non-representative
Self-selected samples
Sample size issues
Undue influence
Non-response
Causality (just correlation)
Self-funded / self-interest studies
Misleading use of data
Confounding
Lurking variable
An explanatory variable that was not considered in the a study but that affects the value of the response variable in the study
Confounding
When the effects of multiple factors on a response cannot be separated
Relative frequency
The fraction of times an answer occurs
Cumulative relative frequency
Accumulation of the previous relative frequencies
Cross-sectional studies
Observational studies that collect information about individuals at a specific point in time, or over a very short period of time
Case-control studies
These studies are retrospective, meaning that they require individuals to look back in time or require the researcher to look at existing records
Cohort studies
This study first identifies a group of individuals to participate in the study (the cohort); it is then observed over a long period of time where various characteristics are recorded; this study is considered prospective
Matched-pairs design
An experimental design in which the experimental units are paired up such that they are somehow related
Randomized block design
An experimental design where the units are divided into homogeneous groups called blocks; within each block, the experimental units are randomly assigned to treatments
Interquartile Range (IRQ)
The distance between the third quartile (Q3) and the first quartile (Q1).
Outlier
An observation that does not fit the rest of the data
Percentile
A number that divides order data into hundredths (not necessarily one of the actual data points).
Quartiles
The numbers that separate the data into quarters.
Median
The number (not average) that splits the data in half. Its location is the (n + 1)/2.
Mode
The most frequently repeated value in the data set
Law of Large Numbers
If you take samples of larger and larger size from any population, then the mean x of the sample gets closer and closer to µ.
Sampling distribution
Essentially is a relative frequency distribution with a great many samples
Standard deviation
A measurement of how far data values are from their mean
Variance
The average of the squares of the deviations
Sample standard deviation (variable)
s
Population standard deviation (variable)
σ
Empirical Rule
Approximately 95% of the samples will be within two standard deviations of the population mean µ.
Correlation Coefficient
A measure developed by Karl Pearson that gives the strength of association between the independent variable and the dependent variable
Influential observation
An observation that significantly affects the least-squares regression line's slope and/or y-intercept, or the value of the correlation coefficient
Probability Distribution Function (PDF)
A mathematical description of a discrete random variable (RV), given either in the form of an equation (formula) , or in the form of a table listing all the possible outcomes of an experiment and the probability associated with each outcome.
Law of Large Numbers
...
Binomial Probability Distribution
...
Bernoulli Trials
...
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Verified questions
QUESTION
A randomly chosen subject arrives for a study of exercise and fitness. Describe a sample space for this case. You measure the maximum heart rate (beats per minute).
STATISTICS
Find the indicated area under the standard normal curve. If convenient, use technology to find the area. Between z = 0 and z = 2.95
PROBABILITY
A university plans on conducting a survey of its recent graduates to determine information on their yearly salaries. It randomly selected 200 recent graduates and sent them questionnaires dealing with their present jobs. Of these 200, however, only 86 were returned. Suppose that the average of the yearly salaries reported was $75,000. (a) Would the university be correct in thinking that$75,000 was a good approximation to the average salary level of all of its graduates? Explain the reasoning behind your answer. (b) If your answer to part (a) is no, can you think of any set of conditions relating to the group that returned questionnaires for which it would be a good approximation?
PROBABILITY
Consider n independent trials, each of which results in one of the outcomes $$ 1 , \ldots , k $$ with respective probabilities $$ p _ { 1 } , \ldots , p _ { k } , \quad \sum _ { i = 1 } ^ { k } p _ { i } = 1 $$ . Show that if all the $$ p_i $$ are small, then the probability that no trial outcome occurs more than once is approximately equal to exp(-n(n-1) $$ \sum _ { i } p _ { i } ^ { 2 } / 2 ) $$