1 / 14

Statistical Control in Sampling: Types and Testing Procedures

Explore various types of sampling methods and testing procedures in statistical control, including hypothesis testing and confidence intervals. Learn how to determine sample size and conduct statistical tests effectively.

rbouley
Download Presentation

Statistical Control in Sampling: Types and Testing Procedures

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Types of Control I. Measurement Control (Reliability and Validity) II. Statistical Control (External Validity) III. Experimental Control (Internal Validity)

  2. Statistical Control - Sampling I The Vocabulary of Sampling II Types of Samples III Testing Samples IV Determining Sample Size

  3. Statistical Control - Sampling I. The Vocabulary of Sampling • A. The Universe (The Theoretical Concept) • B. The Population (The Indicator Concept) • C. The Sampling Frame (The Operational Procedure) • D. The Sample (The Observational Set)

  4. Statistical Control - Sampling II. Types of Samples • A. Non-Probability • B. Probability

  5. Statistical Control - Sampling II. Types of Samples • A. Non-Probability (Good for Exploratory Research) 1. Convenience Sampling 2. Referral Sampling 3. Quota Sampling

  6. Statistical Control - Sampling II. Types of Samples • A. Non-Probability • B. Probability (Good for Explanatory Research) 1. Simple Random Sample 2. Systematic Random Sample 3. Stratified Random Sample 4. Cluster or Area Sample

  7. Statistical Control - Sampling III. Testing a Single Sample Mean A. The Central Limit Theorem - When random samples of Size N are repeatedly taken from a population (no matter what shape the population is, the resulting sampling distribution of means is normal in shape with a mean equal to the population mean and a standard deviation equal to the population S.D. divided by the square root of N. B. The Normal Curve

  8. Statistical Control - Sampling III. Testing Samples (cont.) - Hypothesis Testing: • A. State the Hypotheses • The Null Hypothesis (i.e. Ho) • The Alternative or Research Hypothesis (i.e. Ha) B. Specify the Distribution (e.g. Normal Distribution) C. Set the Decision Criteria Type I error – Alpha or Critical Region D. Calculate the Outcome (e.g. determine Z-value) E. Make the Decision Reject Ho or Do not Reject Ho

  9. Statistical Control - Sampling III. Testing Samples (cont.) - Single Sample Statistical Tests The z-test is called for when both the population mean and variance are known and a point (mean value) is being evaluated Example The t-test is called for when the mean, but not the population variance, is known and a point (mean value) is being evaluated. Example Confidence Intervals are used when neither the mean nor variance of the population are known and an interval estimate is being evaluated. Example

  10. Statistical Control - Sampling IV. Sample Size (Three Components) A. Error in Prediction B. Confidence Level C. Variability in Population Click here to see formulae

  11. Determining Sample Size Consider the confidence interval Solving for the sample size N we get If Then Observe now the three parentheses that define N: 1) our confidence level (z); 2) the population variance; and 3) the margin of error. Back to Beginning End Presentation

  12. Single Sample z-test Problem: Suppose you want to test the idea that CSUN student GPAs are higher this year than in the past. If records indicate that the past GPA is 2.50 with a S.D. of .5, can you conclude that a sample of 25 students, whose GPA is 3.00, is significantly higher? Solution: Use the five step hypothesis testing procedure Step 1 State the hypotheses: Ho: = 2.50 H1: > 2.50 Step 2: Specify the distribution: Normal (Z-distribution) Step 3: Set alpha (say .05; one tail test therefore Z= 1.65) = .5/.1 = 5.0 Step 4: Calculate the outcome: Step 5: Draw the conclusion: Reject Ho: 5.0 > 1.65 Students have a better GPA today. Back

  13. Single Sample t-test Problem: Given historical data, documenting the time it takes students at CSUN to complete the undergraduate degree, yields an average of 6.5 years. Could you conclude that students this semester take significantly longer to graduate if your sample of 64 students this semester, yields a mean of 7.5 years, with a unbiased standard deviation of 1.6 years? Solution: Use the five step hypothesis testing procedure Step 1 State the hypotheses: Ho: = 6.50 H1: > 6.50 Step 2: Specify the distribution: Student’s t-distribution Step 3: Set alpha (say .05; one tail test; therefore since N>30, t= 1.65) = 1.0/.2 = 5.0 Step 4: Calculate the outcome: Step 5: Draw the conclusion: Reject Ho: 5.0 > 1.65 Students today take longer. Back

  14. Confidential Intervals Problem: Suppose you reject the null hypothesis in the z-test example and now do not have a specific value of the population to use. Can we estimate an interval within which we can be a certain degree assured that the actual population falls? Solution: Construct a confidence interval to estimate the population mean. If the formula for the z-test is: Then solving for the population mean we get the following: Thus, in the previous example the 95% confidence interval would be: Thus, we can be 95% sure the true population mean falls between the values 2.804 and 3.196 Back

More Related