Chapter 13

• Sample Statistics


  Variables in a sample or measures computed from sample data
• Population Parameters


  Variables in a population or measured characteristics of the population
• Descriptive Statistics


  Describe characteristics of populations or samples
• Inferential Statistics


  Make inferences about whole populations from a sample
• Frequency Distribution


  A set of data organized by summarizing the number of times a particular value of a variable occurs
• Percentage Distribution


  A frequency distribution organized into a table (or graph) that summarizes percentage values associated with particular values of a variable
• Probability


  The long-run relative frequency with which an event will occur
• Proportion


  The percentage of elements that met some criterion
• Top-Box Score


  Proportion of respondents who chose the most positive choice in a multiple choice question
• Mean


  A measure of central tendency; the arithmetic average
• Median


  A measure of central tendency that is the midpoint; the value below which half the values in a distribution fall
• Mode


  A measure of central tendency; the value that occurs most often
• Range


  The distance between the smallest and the largest values of a frequency distribution
• Deviation Scores


  Indicate how far any observation is from the mean
• Variance


  A measure of variability or dispersion. Its square root is the standard deviation
• Standard Deviation


  A quantitative index of a distribution's spread, or variability; the square root of the variance for a distribution
• Normal Deviation


  A symmetrical, bell-shaped distribution [normal curve] that describes the expected probability distribution of many chance occurrences
• Standardized Normal Deviation


  A purely theoretical probability distribution that reflects a specific normal curve for the standardized value, z
• Normal Distribution


  • Symmetrical, bell-shaped distribution (normal curve) that describes the expected probability distribution of many chance occurrences
  • 99% of its values are within ± 3 standard deviations from its mean
• Standardized Normal Distribution


  • Purely theoretical probability distribution that reflects a specific normal curve for the standardized value, z
• The normal distribution is also called "bell curve"
• The normal distribution is the curved shape of a graph that is highest in the middle and lowest on the sides
• Characteristics of a Standardized Normal Distribution

  • It is symmetrical about its mean
  • The mean identifies the normal curve's highest point (the mode) and the vertical line about which this normal curve is symmetrical
  • The normal curve has an infinite number of cases (it is a continuous distribution), and the area under the curve has a probability density equal to 1.0
  • The standardized normal distribution has a mean of 0 and a standard deviation of 1
• Standardized Values


  Used to compare an individual value to the population mean in units of the standard deviation
• Population Distribution


  A frequency distribution of the elements of a population
• Sample Distribution


  A frequency distribution of a sample
• Sampling Distribution


  A theoretical probability distribution of sample means for all possible samples of a certain size drawn from a particular population
• Standard Error of the Mean

  The standard deviation of the sampling distribution
• Three Important Distributions


  • Population Distribution
  • Sample Distribution
  • Sampling Distribution
• Central-Limit Theorem


  The theory that, as sample size increases, the distribution of sample means of size n, randomly selected, approaches a normal distribution
• The mean distribution of any distribution approaches normal as n increases
• The distribution of sample means for samples of various sizes and population distributions
• Hypothetical toy expenditures population distribution
• Calculation of population mean
• Arithmetic means of samples and frequency distribution of sample means
• Point Estimate


  An estimate of the population mean in the form of a single value, usually the sample mean
• Confidence Interval Estimate


  A specified range of numbers within which a population mean is expected to lie; an estimate of the population mean based on the knowledge that it will be equal to the sample mean plus or minus a small sampling error
• Confidence Level


  A percentage or decimal value that tells how confident a researcher can be about being correct; it states the long-run percentage of confidence intervals that will include the true population mean
• Confidence Interval


  A range of numbers within which a population mean is expected to lie
• Traditionally, researchers have used the 95% confidence level (a 5% tolerance for error)