HYPOTHESIS TESTING Four Steps Statistical Significance Outcomes Sampling Distributions

Step 1: State the Null Hypothesis No difference, effect, or correlation (Ho) No difference, effect, or correlation (Ho) Ho is assumed to be true Ho is assumed to be true Burden of proof on the researcher Burden of proof on the researcher The researcher’s hypothesis (Alternative Hypothesis) is only tested indirectly

Step 2: Set the Criterion How strong does the evidence have to be to reject the Null? How strong does the evidence have to be to reject the Null? alpha (  ) alpha (  ) Conventional alpha level is.05. Conventional alpha level is.05. We are conservative about rejecting Ho. We are conservative about rejecting Ho.

Step 3: Compute the Test Statistic The test statistic is an inferential statistic that allows us to calculate the probability of our results occurring if Ho is true The test statistic is an inferential statistic that allows us to calculate the probability of our results occurring if Ho is true The statistic does not know whether we have collected the data in an appropriate way The statistic does not know whether we have collected the data in an appropriate way

Step 4: Evaluate the Ho Reject Ho if it is very unlikely (p <.05) you could get these results assuming Ho is true Reject Ho if it is very unlikely (p <.05) you could get these results assuming Ho is true Fail to Reject Ho if it is reasonably likely (p >.05) that you could get these results assuming Ho is true Fail to Reject Ho if it is reasonably likely (p >.05) that you could get these results assuming Ho is true Ho is never “accepted” Ho is never “accepted”

Statistical Significance The result is statistically significant if we reject Ho (p <.05). The result is statistically significant if we reject Ho (p <.05). The result is not statistically significant if we fail to reject Ho (p >.05). The result is not statistically significant if we fail to reject Ho (p >.05).

Outcomes There are four possible outcomes, based on two dimensions: There are four possible outcomes, based on two dimensions: The researcher’s decision about Ho. The researcher’s decision about Ho. Whether Ho is really true or false. Whether Ho is really true or false. The probability of each outcome can be determined. The probability of each outcome can be determined.

Ho trueHo false TRUE STATE OF THE WORLD DECISION Reject Ho Fail to Reject Ho Type I error  Correct 1 -  Correct 1 -  (power) Type II error  (beta)

Determining the Probabilities  is set by the researcher  is set by the researcher 1-  depends on  1-  depends on 

Determining the Probabilities Factors Increasing Power: Factors Increasing Power: higher alpha higher alpha larger sample larger sample lower variability lower variability larger effect size larger effect size Anything that increases power decreases beta

Sampling Distributions We usually sample only a small part of the population, but still wish to generalize. We usually sample only a small part of the population, but still wish to generalize. Making statements about the population is a probability game. Making statements about the population is a probability game. We make these probability judgments using a sampling distribution. We make these probability judgments using a sampling distribution.

What is a Sampling Distribution? Hypothetical Hypothetical A frequency distribution of sample statistics from an infinite number of samples. A frequency distribution of sample statistics from an infinite number of samples.

Imagining a Sampling Distribution 1.Take a random sample. 2.Compute the mean. 3.Take another random sample and compute the mean. 4.Do this an infinite number of times. 5.Put the resulting sample means in a frequency distribution.

Three Nice Things 1. The mean is the hypothesized population mean. 1. The mean is the hypothesized population mean. 2. The standard deviation can be calculated (standard error). 2. The standard deviation can be calculated (standard error). 3. The shape is usually normal. 3. The shape is usually normal.

Central Limits Theorem The sampling distribution becomes more normal as the sample size increases. With a sample size of 30 or more, the sampling distribution becomes very close to exactly normal.

Standard Error The standard deviation of a sampling distribution. The standard deviation of a sampling distribution. If it is a sampling distribution of the mean, the standard deviation is called the standard error of the mean. If it is a sampling distribution of the mean, the standard deviation is called the standard error of the mean.

Why These Are “Nice” Things If you know the  and  of a distribution, you can compute z-scores. If you know the  and  of a distribution, you can compute z-scores. In a normal distribution, you can look up the proportion of scores above or below any z score. In a normal distribution, you can look up the proportion of scores above or below any z score. For any sample mean in the sampling distribution, we can find the proportion of sample means above or below it. For any sample mean in the sampling distribution, we can find the proportion of sample means above or below it.

Making Inferences There are three distributions used when we make an inference: There are three distributions used when we make an inference: sample distribution sample distribution sampling distribution sampling distribution population distribution population distribution The sampling distribution is the “bridge” from the sample to the population. The sampling distribution is the “bridge” from the sample to the population.