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128 Cards in this Set
- Front
- Back
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inference
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the process of learning about a population by studying a sample
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sample regression
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estimates the association between x and y in the entire population
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regression line
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an estimate from a sample trying to describe the true regression line from the population
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observational study
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a statistical study in which the subjects are not modified (just observed) so that researchers can measure and record certain characteristics
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experiment (experimental study)
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A statistical study in which a "treatment" is applied to the subjects (i.e. they are modified) and researchers measure the effect of the treatment
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lurking variable (confounding variable)
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-other variables that may influence the response that are not studied
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explanatory variable
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variable that explains or causes the differences in another variable, ( "x" or independent variable)
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response variable
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variable which is thought to depend on the value of the explanatory variable, ("y", dependent variable)
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study question
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the question about the population that the study is attempting to answer
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population
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the complete set of all individuals/objects the study is attempting to answer a question about, the whole group of individuals we are interested in
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study subjects
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the individuals actually measured in the study (i.e. the selected sample of individuals/objects from the population)
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treatment
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what the research does/gives to some or all of the study subjects; the factor whose effect is under study; also called the explanatory variable
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response variable
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the quantity or characteristic that is measured to determine the treatment effect
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control group
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group of subjects that have the same sources of variability as those receiving the treatment but does NOT receive treatment; sometimes called the placebo group
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confounding factor
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any factor other than the experimental treatment that can affect the response variable in the experiment
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completely randomized design
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a design in which the treatments in the experiment are randomly assigned to the experimental units without using matched pairs or blocks
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researchers
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people who make measurements
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single blinding
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subject doesn't know if he/she is in the treatment or control group
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double blinding
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neither RESEARCHERS nor SUBJECTS know where the participants are assigned between the control and treatment group
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matched pair design
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makes two measures on each subject
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blocking design
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-extension of completely randomized design
- put similar subjects into blocks, expect the blocks to differ with respect to the response variable -then do a completely randomized experiment within each block |
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block
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a group of subjects that are similar in some way
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"blocks" refers to ...
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individuals
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"experimental units" refers to...
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repeated time periods in which the blocks receive the varying treatments
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scatter plot
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used to compare variables
-must measure two variables on a common individual (an individual can be a person, place, or even time) -then plot the two variables |
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positive association
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this type of association occurs when the value of one variable tends to increase as the value of the other variable increases
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negative association
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this type of association occurs when the value of one variable tends to decrease as the value of the other variable tends to increase
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non-linear association
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this type of association occurs when there is no linear relationship between two values
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correlation
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a number that indicates the strength and the association of a straight-line relationship between two quantitative variables
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strength of correlation
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determined by the absolute value of the correlation, indicates the overall closeness of the points to a straight line
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direction of the correlation
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determined by the sign of the correlation
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magnitude of r
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absolute value of r, indicates the strength of the relationship
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r = 1 or r = -1
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indicates that there is a perfect linear relationship and all data points fall in the straight line
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squared correlation, r²
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this is the proportion of variation in the response variable that is explained by the explanatory variable. It is positive between 0 and 1.
Referring to a correllation |
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r
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correlation coefficient, used to measure linear relationship between x and y
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the line of best fit
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-this estimates the average value of y when you know x and individual's values will vary around the predicted value
- can be used to give a prediction of a value of y, given a specific value of x |
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randomization test
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a test on two groups when paired data is NOT available
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sampling frame
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a list of all individuals in the population
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in hypothesis testing, population parameter =
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null value
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null hypothesis
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-the statement being tested
-a statement that describe some aspect of the statistical behavior of a set of data -this statement is treated as valid unless the actual behavior of the data contradicts this assumption |
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null value
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-the specific # the parameter equals if the null hypothesis is true
- value of population parameter being tested in the null hypothesis |
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alternative hypothesis
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- a statement that something is happening
- researchers want to prove this - it may be a statement that the assumed status quo is false, or that there is a relationship, or there is a difference |
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two types of alternative hypothesis
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one sided test, two sided test
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one-sided test
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when Ha specifies a single direction
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two-sided test
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when Ha includes values in both directions
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p-value
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the probability of obtaining a test statistic at least as extreme as the one that was actually observed, assuming Ho is true
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level of significance
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(α) is the border line for deciding that the p-value is low enough to justify choosing the alternative hypothesis
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hypothesis testing about paired differences
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matched pairs design
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matched pairs design
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taking two measures on the same subject to see if there is a difference between the two measurements
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paired t-test
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a one-sample t-test used on the sample of differences to examine whether the sample mean difference is significantly different from 0
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sampling distribution
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-describes the possible values the statistic might have when random samples are taken from a population
the distribution of statistics ("xbar" or "p hat") for all possible samples from the same population of a given sample size (n) |
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statistical inference
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gives us methods for drawing conclusions about a population based on data from samples
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confidence interval
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an interval of values computed from sample data that is likely to include the true population
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standard error
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is the estimated standard deviation of the sample distribution of the statistic
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confidence level
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proportion of samples for which the confidence interval will capture the true parameters, % of time we expect the procedure to work, determines how frequently the observed interval contains the parameter
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standard error of sample mean
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(s) is the sample standard deviation
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statistic
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a number summarized by the same characteristic of the sample data, computed from the sample values, a known value that varies from sample to sample
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is the distribution of possible values of the statistic for repeated samples of the same size taken from the same population
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sampling distribution
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mean of a sampling distribution
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the average of all possible values of the statistic for repeated samples of the same size from a population
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the standard deviation(SD) of a sampling distribution
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measures the average distance of the possible values of the statistic from the mean of the sampling distribution, roughly speaking
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there is a difference between N and n!
N= n= |
n= sample size (number of values in one sample/subgroup)
N= number of samples (number of subgroups) |
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Law of Large Numbers (LLN)
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as you average more observations, sample mean settles down at population mean
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graphs used for categorical variables
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1. pie chart
2. bar graph |
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graphic representations for quantitative variables
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1. histogram
2. stem-and-leaf plot 3. box plot |
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standard deviation
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a value that measures the variability (spread) of data.
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density curve
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the outline of the histogram which approximates the overall pattern of a distribution
1. Its always on or above the horizontal axis 2. It has area of exactly 1 underneath it |
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standard normal distribution
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-this is a normal distribution with a mean of 0 and a standard deviation of 1
-all other normal distributions are compared to this |
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z-score
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(a standardized value) that is the distance between a specified value and the mean, measured in number of standard deviations
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observation (individual)
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an individual or the value of a single measurement
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variable
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a characteristic that can differ from one individual to the next
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categorical variables
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the observational units are being divided into units, there is no special ordering of the categories
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ordinal variables
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the observational units are being divided into categories which have an order
basically a categorical variable with ordered categories |
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quantitative variables
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-variables that take numerical values
- you should be able to do mathematical operations with these numbers such as adding, multiplying, etc. (A social security number would not be one of these) |
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graphs for quantitative variables
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1. Histogram
2. Stem-and-Leaf Plot 3. Dot Plot |
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Pie Chart
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each slice of a pie corresponds to a category and the size of the angle of the slice shows the percentage of the individuals in the corresponding category
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Bar Graph
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-each category is presented as a bar
- the height of the bar represents the number (or percentage) of individuals in the corresponding category |
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range
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highest value subtract the lowest value
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histogram
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bar graphs for a quantitative range of possible value are broken into categories
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frequency
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actual number of individuals who fall into each interval (of a histogram)
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relative frequency
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proportion or percentage that are in an interval (of a histogram)
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stem and leaf plot
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every individual data value is shown
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dot plot
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display a dot for each observation along a number line
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distribution
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the overall pattern of how often the possible values occur
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shape of a distribution
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shows how values are distributed in a distribution
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center
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location, average, mean and median measure this
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outlier
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unusual values that do not fit with the rest of the pattern
(may be due to data entry errors or may be actual unusual values) |
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symmetric distribution
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one half of the distribution is the mirror image of the other (bell shape)
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bimodal distributions
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has two peaks which can be caused by two or more groups of values in the sample
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multimodal distribution
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distribution with several peaks
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median
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the middle number of the data when it is ordered, 50% of the data is above it and 50% of the data is below it
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two measures of the center
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mean and median
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symmetric distribution
(mean ? median) |
mean = median
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right skewed distribution
(mean ? median) |
mean>median
mean is greater than median |
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left skewed distribution
(mean ? median) |
mean<median
mean is less than median |
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First Quartile (Q1)
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25% of the data is at or below this number
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Third Quartile (Q3)
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75% of the data is at or below this number
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Inter-Quartile Range (IQR)
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A value describing the spread over approximately the middle 50% of the data
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the five number summary includes
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1) maximum
2) minimum 3) Q1 4) median 5) Q3 |
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boxplot
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a graphical representation of the 5 number summary
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1.5*IQ Rule
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an outlier is any value that lays more than one and a half times the length of the box
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variance
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measures the distance of all individuals from the mean
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strata
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sub groups of population which might have different responses to the question of interest
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stratified sample
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is a collection of samples taken in each stratum of the population
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cluster samples
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sampling technique used when natural groups are evident in a statistical population
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systematic samples
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select ever k-th individual from the sampling frame
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under coverage
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sampling frame does not include all the population
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over coverage
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sampling frame includes individuals who are not in the population being examined
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data entry errors
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person recording the data makes mistakes
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question wording error
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the set up of the question can have a big influence on the answers
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definition of statistics
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a collection of procedures and principles for gathering data and analyzing information to help people make decisions when face with uncertainty
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individuals
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the objects described by the data set
(each student in the class is an observational unit or individual) |
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variables
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characteristics of the individuals
(max speed, sex of the students, height, time of sleep) |
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sample
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subgroup of the population examined to measure the variables and gather information
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parameter
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a number that describes a characteristic of the population. It is mostly a summary of a population. It's value is unknown.
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statistic
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summary of a sample, the value of this is usually known
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census
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taken to measure ALL individuals in the population
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selection bias
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this method of selection of participants favors a particular outcome
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non response bias
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some part of the individuals in the sample cannot be reached or do not respond, this creates a bias because respondents may differ in meaningful ways from non-respondents.
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response bias
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participants give incorrect information
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response rate
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the proportion of the sample that responded to the question
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non-response rate
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the proportion of the sample that didn't respond to the question
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convenience samples
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investigators choose individuals that are easy to reach
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volunteer response samples
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individuals decide whether to answer the questions or not
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simple random sample
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definition?
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statistical significance
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a result is unlikely to have occurred just by chance
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practical significance
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the difference from the claimed value we observe is actually meaningful
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numbers in"stem"column of stem and leaf plot
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first digit of each number in the data set
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numbers in"leaf"column of stem and leaf plot
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contains only the last digit of the # regardless of whether it falls before or after the decimal point
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