2What is a Hypothesis Test? A hypothesis test is a statistical method that uses sample data to evaluate a hypothesis about a population
3Falsifiability A good hypothesis is one that is falsifiable You cannot prove something that cannot be disprovedBetter yet, you cannot support a hypothesis if you cannot disconfirm itWhat are some examples of hypotheses that cannot be falsified?What are examples of ones that can?
4What Are The Steps For Hypothesis Testing? First we state the null hypothesis H0.What is the null hypothesis?This states that in the general population there is no change, no difference, or no relationship.Basically it says the opposite of what we are hoping to show.
5Hypothesis Testing Continued Then we state the alternative hypothesisWhat is the alternative hypothesis?This states that there is a change, a difference, or a relationship for the general populationThis is where we state what we believe (hypothesize) to be true
6Why Do We Do This?There is no way to PROVE a hypothesis. You can only support a hypothesis, or reject it. If you support it 100,000 times, and then on the 100,001st time you reject it, the hypothesis is not true.So, we seek to reject the null, and thus, conversely we support the alternative.
7The Next Step (Hypothesis Testing) Set the evaluation criteriaBy this, we are looking to assess an acceptable level of error by chanceWhat do we think is an acceptable probability that the data we are looking at is “different”
8Alpha Levels Usually we use α = .05. This corresponds to p = .05. The alpha level or the level of significance is a probability value that is used to define the very unlikely sample outcomes if the null hypothesis is true. In this case we would expect to obtain this “outlier” sample in only 5% of the samples simply by chance.This corresponds to p = .05.In other words, the probability of obtaining this difference by chance is 5%.
9Critical RegionThe critical region is composed of extreme sample values that are very unlikely to be obtained if the null hypothesis is true. The boundaries for the critical region are determined by the alpha level. If sample data fall in the critical region, the null hypothesis is rejected.
12The Next Step (Hypothesis Testing) Collect DataCompute sample statisticsCompute test statistics
13What Are the Relevant Sample Statistics? The mean (M)The sample size (n)
14What Are the Relevant Population Parameters? μσWhere do we get these parameters?From our hypotheses
15Now We Calculate the Test Statistic The formula for a z-statistic isz = (M – μ) / σmFirst we calculateσm = σ/√nThe we use the values to get zFinally we make a decision based on the z statistic and the alpha level we have chosen
16Decision?Given the calculations we have performed, and the alpha levels chosen, are we going to accept or reject the null hypothesis?We fail to reject the null
18Type I and Type II Type I Type II Occurs when a researcher rejects a null hypothesis that is actually trueOccurs at the rate of the alpha level we setType IIOccurs when a researcher fails to reject a null hypothesis that is really falseNo easy calculation. How do we know if we have made this type of error? It is NOT the converse of Type IWe must estimate beta
20What Is Meant by Significance? A result is said to be significant or statistically significant if it is very unlikely to occur when the null hypothesis is true. That is, the result is sufficient to reject the null hypothesis.What factors influence significance?The size of the difference.The variability of the scores.The number of scores in the sample.Is there a difference between significance and meaningfulness?
21Assumptions For Hypothesis Tests With z-Scores All statistical tests are based on a certain set of assumptions that, when violated, may bias the statistic, and give us misleading resultsAssumptions for hypothesis tests with z-scoresRandom SamplingIndependent ObservationsThe Value of sigma is unchanged by the treatmentNormal sampling distribution
22Random SamplingIt is assumed that the subjects used to obtain the sample data were selected randomly
23Independent Observations The values in the sample must consist of independent observations.Two events are independent if the occurrence of the first event has no effect on the probability of the second event.
24Sigma Unchanged Because sigma is unknown we must make an assumption We assume that the standard deviation for the unknown population (after treatment) is the same as it was for the population before the treatmentIn other words, the treatment affects the mean, not the standard deviation
25Normal Sampling Distribution The distribution of sample means must be normal since we have been using the unit normal table to identify probabilities
26Directional Hypothesis Tests In a directional hypothesis test, or a one-tailed test, the statistical hypothesis (h0 and H1) specify either an increase or a decrease in the population mean score. That is, they make a statement about the direction of the effect.This halves the critical region since it is only taking into account the one tail.
27Effect SizeDemonstrating a significant treatment effect does not necessarily indicate a substantial treatment effect.This is because we are looking at the relative magnitude of the difference in the sample and the population mean with respect to the S.E.What if n is very large, or sigma is very small?Then a small difference in the means may in fact be significant.
28Cohen’s dOne of the simplest and most direct methods for measuring effect size is Cohen’s dCohen’s d = (mean difference) / (standard deviation)
30PowerThe power of a statistical test is the probability that the test will correctly reject a false null hypothesis. That is, power is the probability that the test will identify a treatment effect if one really existsWhat is the relation between power and error?1 - ß
31What Affects Power? Effect size Sample size Alpha level Number of tails in the test