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81 Cards in this Set
- Front
- Back
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The four parts of statistics
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It's the study of data analysis-defining the problem, collecting the data, analyzing and summarizing data, and drawing inferences from data.
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Distribution
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A list of the possible values of a variable together with how often each value occurs
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Types of data
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Quantitative and categorical
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Left Skewed
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The tail is on the left, mean is less than the median.
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Right Skewed
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Tail on the right, the mean is greater than the median
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Histogram and boxplot
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A right skewed histogram will match with a boxplot that has a long right whisker
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Outliers
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A data point that is quite a bit removed from the rest of the data
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Mean
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A measure of center. The "balance point". Computed by adding numbers and dividing by how many there are
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Median
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Measure of center, cuts the data in half. Order the data and find middle observation. Outliers have no affect on the median.
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Five number summary
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Each quartile is 25 percent. Minimum, median and maximum
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Standard Deviation
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Measures the variability of the data about the mean; in a sense, it is like the average distance of the date from the mean.
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Effects of outliers on standard deviation.
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Since outliers affect the mean and deviations from the mean are used to compute standard deviation, then outliers can make the standard deviation bigger than it should be.
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When to use five number summary or mean and standard deviation.
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Use the five-number summary in the presence of outliers.
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When can a normal distribution be used to model a data set.
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The Normal distribution can be used whenever the shape of the histogram of the data resembles the normal curve.
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How do you obtain a proportion or a probability for a value from a normal curve.
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First, convert the value to a z score and look the z score up in table A. Be sure that if you want the "greater than" percentage you subtract the probability given in the table from one.
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68-95-99.7 rule.
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68% of the observation are within one standard deviation, 95% within 2 st dev., 99.7 within three.
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Z-score
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The z-score tells how many standard deviations a value is from the mean. If a score from a test has a z score of 1.8 that means the score is 1.8 standard deviations above the mean.
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Explanatory Variable
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The variable we are assessing or testing in an experiment.
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Response Variable
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The variable we want to predict (y) and the explanatory variable is the x or the variable we use to do the predicting.
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Correlation
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Correlation is a measure of the linear relationship between the x and y variables. R is the symbol for correlation coefficient.
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Corellation (r)
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r is always between -1 and 1. Values close to zero indicate littler or no linear relationship. Values close to -1 show strong negative,+1 strong positive. r has no unit of measure. r only measures strenghth of linear relationships.
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Least squares regression line
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The line obtained by minimizing the sum of the squared residuals.
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Purpose of regression equations.
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Regression equations are used to model relationships between quantitative variables and also for prediction.
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Residual
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Observed y minus predicted y
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Slope in a least squares regression line.
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slope tells us the average increase(or deacrease if negative) in y for each one unit increase in x.
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Roles of x and y in regression
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X is the explanatory and y is the response variable
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r-squared
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Tells the percentage of total variation in the y's that can be explained by the x's
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Residual Plots
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1) Uniform scatter 2)outlers (normality) 3) Megaphone (equal variance) 4) A smile or frown (non linearity)
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Necessary Conditions for testing Significance using slope
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Normality-Variance is constant
Independent-Linear |
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Tests on slope
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Ho:B=0 versus Ha:B does not equal 0. 1. No linear relationship exists
2. A significant relationship exists. |
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s in regression output
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The s in regression output measures the standard deviation of the observed y's about the regression line.
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Extrapolation
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Using an x value outside of the range of the observed x's used to obtain the reqression equation to predict a y value.
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CI vs PI
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PI is wider
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Lurking Variable
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Affects the relationship between the response variable and explanatory variable but is not part of the study. They are dangerous because they can suggest relationships that do not really exist.
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Marginal Distribution
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row total divided by table total
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Conditional distrubtion
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cell count divided by the row.
* if the distributions are equal we say the variables are NOT related. |
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Voluntary response sample
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Samples obtained by having respondents call in or write in voluntarily
*biased, not probability sample |
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Convenience Sample
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Researchers contact subjects that are convenient to contact.
*biased, not probability sample |
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Population of interest vs. sample
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The entire group of interest-population
The subgroup of individual from the population about which the researcher actually obtains information-sample |
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Response Variable
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The observation recorded (measured) on each individual.
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Bias
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The amount that sample results systematically differ from what they should be. Bias can be eliminated by taking probability samples, using careful wording on survey questions etc.
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SRS
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Sampling from the entire population
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Stratified sampling
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Sampling from withing froups of a population or sampling from withing different populations
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Multistage
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First sampling groups and then sampling from within those groups.
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SRS & Stratified & Multistage
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All probability samples where every member of the population has a known non-zero chace of being selected. SRS gives each possible sample of size n an equal chance of being selected and a stratified sample gives each member of the stratea an equal chance within its strata of being selected.
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Cautions of surveying
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Uncercoverage, non-response, response bias, wording of questions
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Methods to reduce bias
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Using probability samples, avoiding undercoverage, reducing non response and avoiding poor wording on questions.
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Observational Study
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Studies where information is gathered on the population but nothing is inflicted on the subjects.
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Sample Surveys
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Observational studies not experiments.
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Advantage of experiment over observational study.
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You can establish causation
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Control group
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Those that recieve the placebo
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Completely randomized experiment
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An experiment where all experimental units are allocated at random among the treatment groups
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Replication
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having more than one experimental unit per treatment
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Double blind
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Niether the subjects nor the diagnostician know who is recieving the treatment or placebo.
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Matched Pairs
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Taking two measurements on each individual
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Completely random
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Two completely seperate groups. In the experiment. If individuals are randomly allocated to treatments you have a completely random design. In experiment if order in which treatments are applied to individuals is randomized you have a matched pairs.
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Sampling Distribution
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A list of the possible valued of the statistic together with the probabilities of each value. A collection of all statistics values from all possible samples.
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Increase preicision
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by increasing sample size
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x-bar
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sample mean
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P hat
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sample proportion
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When is Phat normal
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when np is greater than 10 and when n*1-P is greater than 10.
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Inferential Statistics
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Using information from a sample to draw inferences about a population.
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Two most used types of inferential statistics
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Confidence interval and test of hypothesis
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Confidence Interval
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Gives a range of plausible values of the parameter being estimated by the confidence interval
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95 % confidence means?
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The procedure provides intervals containing the parameter value for 95% of all samples. Confidence is in the procedure not the interval.
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p-value
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The probability of getting a test statistic as extreme or more extreme than the value actually ovserved if the null hypothesis were true.
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alpha
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The level of significance, probability of rejecting the null hypothesis when it is true or the largest risk the researcher is willing to take in rejecting a true null hypothesis.
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multiple analyses
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two or more tests of significance perforemd. Inflates the type 1 error rate
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Power
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Increasing alpha descreases beta and increases power. Increasing sample size decreases beta and increases power
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T distribution vs. Normal distribution
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t distribution is more spread out than normal.
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First rule in data analysis
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plot the data
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When are t procedures robust
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When there are no outliers.
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Chi-Square Hypothesis
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Ho: no relationship
Ha: relationship |
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Expected Count
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Coumng total times row total divided by table total
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When is using Chi-square appropriate
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Expected counts are greater than 5.
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DF for two way table
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(r-1)(c-1)
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What does Chi-Square test?
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Measures the amount of discrepancy between the observed counts and the expected counts where expected counts are computed assuming the null hypothesis of no relationship is true.
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Anova Hypothesis
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Ho: All means equal
Ha: at least one mean differs |
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When do you use ANOVA
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When the explanatory variable is categorical and the response variable is quantitative OR the problem says you are comparing three or more means.
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When do you use Chi-square
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When both variables are categorical.
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What symbols to use for means
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mu for means, p symbols for proportions, beta for slope in regression.
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