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Blair Lusby Holes and Goals Statistics Glossary Alpha: the likelihood that the population lies outside of the confidence interval Alternative Hypothesis: the hypothesis that your observations are influenced by a nonrandom cause Back-to-back Stemplots: a graphic way to compare data from two populations; there is a center column called the stem with a vertical line on either side of the column, there are leaves on the left and right side of the column each side representing a different population Bar Chart: made up of columns or rows on a graph; the length of the column or row represents the size of the group defined by the column or row label Bernoulli Distribution(binomial distribution): the probability distribution of a binomial random variable Bias: the tendency to over or under estimate the population parameter Biased Estimator: when the mean of the sampling distribution of a statistic is not equal to a population parameter Bimodal Distribution: a distribution of data with two clear peaks Bivariate Data: when a study is done with two variables Blinding: when you do not tell subjects whether they are getting a placebo or the actual treatment Boxplot: used for quantitative data; data is split into quartiles (Q1, Q2, Q3) in a box; Q2 line is drawn at the median in the box, there are two “whiskers” one that goes from Q1 to the smallest non-outlier and one that goes from Q3 to the largest non-outlier Central Limit Theorem: if the sample size is large enough then the sample distribution will always be normal or near normal Clusters: when the population is in separate groups Cluster Sampling: random sample of clusters is selected and the research is conducted on those clusters Combination: a selection of all or part of a set of objects Complement: the event does not occur Completely Randomized Design: the subjects are randomly assigned to either the placebo or the experiment Conditional Probability: the probability that even B occurs given that event A occurred Confidence Interval: used to express ones uncertainty with the sample statistics Confidence Level: the likelihood that the population lies within the given confidence interval Confounding: occurs when the experimental controls do not allow the experimenter to reasonably eliminate plausible alternative explanations for an observed relationship between independent and dependent variables Blair Lusby Holes and Goals Continuous Value: when a variable can take on any value between its minimum and maximum value Control Group: the group in a study that is the baseline and does not receive the treatment Convenience Sample: a sample of people who were easy to reach Correlation: the strength of association between two variables Critical Value: used to compute the margin of error Decision Rule: used by researchers to decide whether or not to keep the null hypothesis Dependent Variable: the “effect” of the independent variable Deviation Score: the difference between a raw score and the mean Discrete Variable: data that can be listed or placed in order Dotplot: a graphic display used to compare frequency counts within categories or groups Double Bar Chart: has two pieces of information for each category instead of one like normal bar charts Double Blinding: when the subject and the analysts both do not know who is the control group and who is the treatment group Effect Size: the difference between the critical value and the value specified in the null hypothesis Estimation: when there are inferences made about population, based on information obtained from a sample Estimator: the process of estimation Event Multiple: a grouping of two or more independent events Expected Value: the mean of the discrete random variable Experiment: a controlled study in which the researcher attempts to understand cause-andeffect relationships Experimental Design: a plan for assigning subjects to treatment conditions Frequency Count: a measure of the number of times an event occurs Geometric Distribution: a negative binomial distribution where the number of successes is equal to one Geometric Probability: the probability that a negative binomial experiment will result in only one success Histogram: columns plotted on a graph Hypothesis Test: sample data that statisticians use to determine whether to reject a null hypothesis Independent: when the occurrence of one event does not affect the probability of the other event occurrence Independent Variable(Factor): the variable that is manipulated by the experimenter to determine its relationship to an observed phenomenon Influential Point: an outlier that greatly affects the slope of the regression line Blair Lusby Holes and Goals Interquartile Range: a measure of variability, based on dividing a data set into quartiles(Q1, Q2, Q3) Interval Estimate: two numbers, between which a population parameter is said to lie Interquartile Range(IQR): a measure of variability, based on dividing a data set into quartiles Joint Frequency: entries in a table that are only in the body of the table Lurking Variable: an extraneous variable Margin of Error: the max expected difference in the true population parameter and a sample estimate of that parameter Marginal Distribution(Marginal Frequency): in a table these are the entries that go in the total rows or total columns Mean: an average score; denoted by X(with a line over top) Measurement Scales: used to categorize and/or quantify variables Median: a measure of the central tendency; to find you arrange values from smallest to largest and you choose the middle value or two middle values to be your median Mode: the most frequent value in a sample Mutually Exclusive: when two events have no sample points in common Nominal Scale: a measurement scale where values are assigned to variables which represent a descriptive category, but have no inherent numerical value with respect to magnitude Non-probability sampling: the probability that each element will be included in the sample cannot be specified Normal Distribution: a probability distribution that associates the normal random variable X with a cumulative probability Null Hypothesis: the hypothesis that your observations occur by chance Null Set: a set that has no elements in it Observational Study: a study trying to understand cause-and-effect relationships but cannot control how subjects are assigned to groups or which treatments each group receives One-Sample t-Test: used to test if a population mean is significantly different from some hypothesized value One-Sample z-Test: used to test if a population parameter is significantly different from some hypothesized value One-Tailed Test: a statistical hypothesis test where the region of rejection is on only one side of the sampling distribution One-Way Table: when a table only has data for one categorical variable Outlier: a data point that diverges greatly from the overall pattern of data Parameter: a measurable characteristic of a population; examples: mean or standard deviation Blair Lusby Holes and Goals Pearson Product-Moment Correlation: measures the strength of the linear association between variables Percentage: a way to express a proportion Percentile: if a data set are rank ordered from smallest to the largest, then the values that divide a rand-ordered set of elements into 100 equal parts are percentiles Permutation: an arrangement of all or part of a set of objects, with regard to the order Placebo: a neutral treatment that has no “real” effect Point Estimate: a single value used to estimate the population parameter Population: the total set of observations that can be made Precision: how close estimates from different samples are to each other Probability: a measure of the likelihood that the event will occur Probability Distribution: a table or an equation that links each outcome of a statistical experiment with its probability of occurrence Probability Sampling: every element of the population has a know probability of being included in the sample Proportion: the fraction of the total P-Value: measures the strength of evidence in support of a null hypothesis Qualitative Data: categorical data Quantitative Data: numerical data Quartile: divide a rank-ordered data set into four equal parts Random Number Table: a list of numbers that are arranged in no predictable order Random Number: a number determined totally by chance Random Sampling: a procedure for sampling from a population in which the selection of a sample unit is based on chance and every element of the population has a know, nonzero probability of being selected Random Variable: when the value of a variable is the outcome of a statistical experiment Randomization: the practice of using chance methods to assign subjects to treatments Range: a simple measure of variation in a set of random variables Ratio Scale: a type of measurement scale that is characterized by equal intervals between scale units and an absolute zero Region of Acceptance: the range of values that leads the researcher to accept the null hypothesis Region of Rejection: the range of values that leads the researcher to reject the null hypothesis Replication: the practice of assigning each treatment to many experimental subjects Representative: a good sample Residual: the difference between the observed value of the dependent variable and the predicted value Blair Lusby Holes and Goals Residual Plot: a graph that show the residuals on the vertical axis and the independent variable on the horizontal axis Response Bias: the bias that results from problems in the measurement process Sample: a set of observations drawn from a population Sample Point: an element of a sample space Sample Space: a set of elements that represents all possible outcomes of a statistical experiment Sample Survey: a study that obtains data from a subset of a population Sampling: the process of choosing a sample of elements from a total population of elements Sampling Error: the error that results from taking one sample rather than taking a census of the entire population Sampling Fraction: the proportion of a population to be included in a sample Sampling Method: a procedure for selecting sample members from a population Scatterplot: a graphic tool used to display the relationship between two quantitative variables Selection Bias: the bias that results from an unrepresentative sample Set: a well defined collection of objects Significance Level: the probability of committing a Type I error, which occurs when the researcher rejects a null hypothesis when it was true Skewness: when there are more observations on one side of the graph than the other Slope: a measure of the steepness of a line Standard Deviation: a numerical value used to indicate how widely individuals in a group vary Standard Error: a measure of the variability of a statistic Standard Score(z score): indicated how many standard deviations an element is from the mean Statistic: a characteristic of a sample; used to estimate the value of a population parameter Statistical Hypothesis: an assumption about a population parameter Stemplot: used to display quantitative data; a vertical line with numbers on the left being stems and the numbers on the right being leaves Symmetry: used to describe the shape of a data distribution that is able to be cut in half and the two pieces are mirror images of each other t-Test: any hypothesis test in which the test statist follows Student’s distribution if the null hypothesis is true Two Sample t-Test: used to test the difference between two population means Two Tailed Test: the region of rejection is on both sides of the sampling distribution Type I Error: occurs when researcher rejects a null hypothesis that was true Blair Lusby Holes and Goals Type II Error: occurs when researchers accept a null hypothesis that is false Unbiased Estimator: what a statistic is when the mean of the sampling distribution of a statistic is equal to a population parameter Undercoverage: a type of selection bias; occurs when some members of the population are inadequately represented in the sample Uniform Distribution: a probability distribution for which all of the values that a random variable can take on occur with equal probability Unimodal Distribution: a distribution of data with one peak Univariate Data: when a study is done with one variable Variable: an attribute that describes a person, place, thing, or idea Variance: a numerical value used to indicate how widely individuals in a group vary Voluntary Response Bias: occurs when sample members are voluntary samples Voluntary Sample: made up of people who self-select into the survey Y Intercept: the value of y when x equals zero on the Cartesian coordinate system z Score(Standard Score): indicates how many standard deviations an element is from the mean