Parameter
A numerical characteristic of a population, such as a population mean �, a population standard deviation ?, a population proportion p, and so on.
Target population
The population for which statistical inferences such as point estimates are made. It is important for the target population to correspond as closely as possible to the sampled population.
Sampled population
The population from which the sample is taken.
Sampling distribution
A probability distribution consisting of all possible values of a sample statistic.
Sample statistic
A sample characteristic, such as a sample mean bar(x), a sample standard deviation s, a sample proportion bar(p), and so on. The value of it is used to estimate the value of the corresponding population parameter.
Finite population correction factor
the term ?((N-1)/(n-1)) that is used in the formulas for standard deviation of x bar and p bar whenever a finite population, rather than an infinite population, is being sampled. the generally expected rule of thumb is to ignore this when n/N ? .05
Simple random sample
Sample selected such that each possible sample of size n has the same probability of being selected.
Standard error
The standard deviation of a point estimator.
Point estimator
The sample statistic, such as bar(x), s, or bar(p), that provides the point estimate of the population parameter.
Central limit theorem
A theorem that enables one to use the normal probability distribution to approximate the sampling distribution of bar(x) whenever the sample size is large.
Point estimate
The value of a point estimator used in a particular instance as an estimate of a population parameter.
Unbiased
A property of a point estimator that is present when the expected value of the point estimator is equal to the population parameter it estimates.
Confidence interval
Another name for an interval estimate.
margin of error
The � value added to and subtracted from a point estimate in order to develop an interval estimate of a population parameter.
Confidence coefficient
The confidence level expressed as a decimal value. For example, .95 is the confidence coefficient for a 95% confidence level.
Degrees of freedom
A parameter of the t distribution. When the t distribution is used in the computation of an interval estimate of a population mean, the appropriate t distribution has n ? 1 degrees of freedom, where n is the size of the sample.
Confidence level
The confidence associated with an interval estimate. For example, if an interval estimation procedure provides intervals such that 95% of the intervals formed using the procedure will include the population parameter, the interval estimate is said to be c
Null hypothesis
The hypothesis tentatively assumed true in the hypothesis testing procedure.
Two-tailed test
A hypothesis test in which rejection of the null hypothesis occurs for values of the test statistic in either tail of its sampling distribution.
Alternative hypothesis
The hypothesis concluded to be true if the null hypothesis is rejected.
p-value
A probability that provides a measure of the evidence against the null hypothesis provided by the sample. Smaller p-values indicate more evidence against H0. For a lower tail test, the p-value is the probability of obtaining a value for the test statistic
Type I error
The error of rejecting H0 when it is true.
Type II error
The error of accepting H0 when it is false.
Level of significance
The probability of making a Type I error when the null hypothesis is true as an equality.
Critical value
A value that is compared with the test statistic to determine whether H0 should be rejected.
One-tailed test
A hypothesis test in which rejection of the null hypothesis occurs for values of the test statistic in one tail of its sampling distribution.
Dependent variable
The variable that is being predicted or explained. It is denoted by y.
Independent variable
The variable that is doing the predicting or explaining. It is denoted by x.
Simple linear regression
Regression analysis involving one independent variable and one dependent variable in which the relationship between the variables is approximated by a straight line.
Regression model
The equation that describes how y is related to x and an error term; in simple linear regression: y = ?0 + ?1x + ?.
Regression equation
The equation that describes how the mean or expected value of the dependent variable is related to the independent variable; in simple linear regression, E(y) = ?0 + ?1x.
Estimated regression equation
The estimate of the regression equation developed from sample data by using the least squares method. For simple linear regression: ? = b0 + b1x.
Scatter diagram
A graph of bivariate data in which the independent variable is on the horizontal axis and the dependent variable is on the vertical axis.
Coefficient of determination
A measure of the goodness of fit of the estimated regression equation. It can be interpreted as the proportion of the variability in the dependent variable y that is explained by the estimated regression equation.
Standard error of the estimate
The square root of the mean square error, denoted by s. It is the estimate of ?, the standard deviation of the error term ?.
Confidence interval
The interval estimate of the mean value of y for a given value of x.
Prediction interval
The interval estimate of an individual value of y for a given value of x.
Residual plot
Graphical representation of the residuals that can be used to determine whether the assumptions made about the regression model appear to be valid.
Time series
A sequence of observations on a variable measured at successive points in time or over successive periods of time.
Mean squared error (MSE)
The average of the sum of squared forecast errors.
Time series plot
A graphical presentation of the relationship between time and the time series variable. Time is shown on the horizontal axis and the time series values are shown on the vertical axis.
Horizontal pattern
Exists when the data fluctuate around a constant mean.
Moving averages
A forecasting method that uses the average of the most recent k data values in the time series as the forecast for the next period.
Stationary time series
A time series whose statistical properties are independent of time. For a stationary time series the process generating the data has a constant mean and the variability of the time series is constant over time.
Trend pattern
A trend pattern exists if the time series plot shows gradual shifts or movements to relatively higher or lower values over a longer period of time.
Smoothing constant
A parameter of the exponential smoothing model that provides the weight given to the most recent time series value in the calculation of the forecast value.
Seasonal pattern
A seasonal pattern exists if the time series plot exhibits a repeating pattern over successive periods. The successive periods are often one-year intervals, which is where the name seasonal pattern comes from.
Cyclical pattern
A cyclical pattern exists if the time series plot shows an alternating sequence of points below and above the trend line lasting more than one year.
Mean absolute error (MAE)
The average of the absolute values of the forecast errors.