Please enable JavaScript.
Coggle requires JavaScript to display documents.
Chapter 8: Introduction to Hypothesis Testing - Coggle Diagram
Chapter 8: Introduction to Hypothesis Testing
Hypothesis test- is a statistical method that uses sample data to evaluate a hypothesis about a population. Used when not possible to collect data for every individual in the population of interest.
State the hypothesis about the population.
Before selecting a sample, you use the hypothesis to predict characteristics that the sample should have.
Obtain a random sample from the population.
Compare the obtained sample data with the prediction that was made from the hypothesis. If the sample mean is consistent with the prediction, we conclude that the hypothesis is reasonable. If there is a big discrepancy, then the hypothesis is wrong.
Compute the z score that describes exactly where the sample mean is located relative to the hypothesized population mean from H0.
Z-statistic (z = (x-μ)/σ): if z is positive, the z statistic gets larger when the numerator gets larger, or when the denominator gets smaller. The denominator gets smaller when the population standard deviation gets smaller, or when the sample size (n) gets bigger.
3 changes that can increase the value of the z statistic: 1. the obtained difference (M-m) increases. 2. The population standard deviation decreases. 3. The sample size (n) increases.
z = sample mean - hypothesis population mean/standard error between M and m.
Alpha level or level of significance - is a probability that is used to define the concept of "very unlikely" in a hypothesis test
Critical Region - composed of the extreme sample values that are very unlikely (as defined by alpha level) to be obtained if the hypothesis is true. Use alpha levels and the unit normal table.
Null Hypothesis - states that the treatment has no effect. H(subscript 0). H= hypothesis and 0 = zero-effect hypothesis
If a null hypothesis is true, then you should NOT reject it. If the null hypothesis is false, then you SHOULD reject it.
If you fail to reject a null hypothesis and it was true, that is a TYPE I error. If the null hypothesis is false and you DON'T reject it, that is a TYPE II error.
When you reject the null hypothesis, you say the results are significant (or statistically significant).
Scientific or Alternative Hypothesis - predicts that the independent variable (treatment) does have an effect on the dependent variable. H subscript 1.
Hypothesis test first determines the probability that the pattern could have been produced by chance alone. If the probability is large the pattern could be explained by chance. If the probability is small, we can rule OUT Chance as a plausible explanation.
Factors that influence a Hypothesis test: If the z-score is large enough to be in the critical region, we reject the null hypothesis and conclude there is a significant treatment effect. A BIG mean difference indicates that the treated sample is noticeably different from the untreated population. Z-score is also influenced by the standard error, which is determined by the variability of the scores (standard deviation or variance) and the number of scores in the sample.
1 tailed test (directional hypothesis test) - used when you do predict the direction of change. 2 tailed test is used when you do not predict the direction the scores will change.
1- tailed test: specify the increase or a decrease in the population mean. First step, state the statistical hypotheses. 2 hypotheses are mutually exclusive and cover all possibilities (population).
Critical region is defined by sample outcomes that are very unlikely to occur if the null hypothesis is true.
Cohen's d measures effect size = mean difference/standard deviation
Size of a treatment effect: d = .2 small effect; d= .5 medium effect; d= .8 large effect
Power
of a statistical test is the probability that the test will correctly reject a false null hypothesis. Power is the probability that the test will identify a treatment effect if one really exists.
Increasing the alpha level increases power. 2. A one-tailed test has greater power than a 2-tailed test. 3. A large sample results in more power than a small sample.