“There are three types of lies: Lies, Damn Lies and Statistics” - Mark Twain

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

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

I. The Vocabulary of Sampling Statistical Control- 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)

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

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

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

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 Statistical Control- Sampling

Statistical Control 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 - 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 The t-test is called for when the mean, but not the population variance, is known and a point (mean value) is being evaluated. Confidence Intervals are used when neither the mean nor variance of the population are known and an interval estimate is being evaluated. - SamplingStatistical Control Example

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

Determining Sample Size Solving for the sample size N we get IfThen Consider the confidence interval 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 BeginningEnd Presentation

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) Step 4: Calculate the outcome: =.5/.1 = 5.0 Step 5: Draw the conclusion: Reject Ho: 5.0 > 1.65 Students have a better GPA today. Back

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) Step 4: Calculate the outcome: = 1.0/.2 = 5.0 Step 5: Draw the conclusion: Reject Ho: 5.0 > 1.65 Students today take longer. Back

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. Back 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 and 3.196