Ch. 17. DETERMINATION OF SAMPLE SIZE

Transcription

1 LOGO Ch. 17. DETERMINATION OF SAMPLE SIZE Dr. Werner R. Murhadi

2 Descriptive and Inferential Statistics descriptive statistics is Statistics which summarize and describe the data in a simple and understandable manner. inferential statistics is Using statistics to project characteristics from a sample to an entire population.

3 Sample Statistics and Population Parameters A sample is a subset or relatively small portion of the total number of elements in a given population. Sample statistics are measures computed from sample data. Population parameters are measured characteristics of a specific population. In other words, information about the entire universe of interest. Sample statistics are used to make inferences (guesses) about population parameters based on sample data.2 In our notation, we will generally represent population parameters with Greek lowercase letters for example, or and sample statistics with English letters, such as X or S.

4 Making Data Usable To make the data usable, this information must be organized and summarized. Methods for doing this include frequency distributions, proportions, measures of central tendency, and measures of dispersion. frequency distribution is A set of data organized by summarizing the number of times a particular value of a variable occurs. Proportion is The percentage of elements that meet some criterion. Central tendency can be measured in three ways the mean, median, or mode each of which has a different meaning.

5 Measures of Central Tendency Mean is A measure of central tendency; the arithmetic average. Median is A measure of central tendency that is the midpoint; the value below which half the values in a distribution fall. Mode is A measure of central tendency; the value that occurs most often.

6 Measures of Dispersion THE RANGE THE STANDARD DEVIATION Variance is A measure of variability or dispersion. Its square root is the standard deviation. standard deviation is A quantitative index of a distribution s spread, or variability; the square root of the variance for a distribution.

7 The Normal Distribution Normal Distribution is A symmetrical, bellshaped distribution that describes the expected probability distribution of many chance occurrences. Standardized Normal is distribution A purely theoretical probability distribution that reflects a specific normal curve for the standardized value, z

8 Population Distribution, Sample Distribution, and Sampling Distribution population distribution is A frequency distribution of the elements of a population. sample distribution is A frequency distribution of a sample. sampling distribution is 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 is The standard deviation of the sampling distribution.

9 Central-Limit Theorem central-limit theorem is The theory that, as sample size increases, the distribution of sample means of size n, randomly selected, approaches a normal distribution.

10 Estimation of Parameters confidence interval estimate is 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 is 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.

11 Sample Size Three factors are required to specify sample size: (1) the heterogeneity (i.e., variance) of the population; (2) the magnitude of acceptable error (i.e., some amount); and (3) the confidence level (i.e., 90 percent, 95 percent, 99 percent).

12 Estimating Sample Size for Questions Involving Means Once the preceding concepts are understood, determining the actual size for a simple random sample is quite easy. The researcher must follow three steps: 1. Estimate the standard deviation of the population. 2. Make a judgment about the allowable magnitude of error. 3. Determine a confidence level.

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