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## Student’s t test and Nonparametric Statistics

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**Hypothesis testing defined**A method for deciding if an observed effect or result occurs by chance alone OR if we can argue the results actually happened as a result of an intervention.**The Null Hypothesis**In order to decide if the results of an experiment occur by chance or if the effects seen are the result of a treatment, researchers declare a null hypothesis (Ho) and an alternative or research hypothesis (Ha).**To test a hypothesis, researchers talk about “rejecting**the null” in order to demonstrate the treatment has an effectOR“accepting the null” if the treatment does not have an effect.**When you reject the null, you say that there IS a**significant difference between the groups, indicating the likelihood the treatment was effective.**When you accept the null, you say the hypothesis that says**there is no difference (which is the null hypothesis) is correct.**Decisions to reject or accept the null….**• Based on whether the calculated value of the statistic performed is equal to or smaller than the critical value of the alpha level (the probability that a certain outcome will be achieved) • By tradition, .05 is the most common alpha level used to make this decision**The research question asked by the t test “Is there a**difference on X between the two groups?”**What is the t test?**• A parametric statistical test which analyzes the difference between the means of scores between two groups.**Which levels of measurement allow you to calculate a mean?**Interval and ratio**Assumptions**• There are assumptions about the data that need to be considered when using the t-test. These are • the data is normally distributed • the variances are homogenous or similar • the groups are of equal size**Two kinds of t tests**• t test for paired samples - when the subjects are measured on a variable, receive the treatment, then measured again. The pre and post-test means of the measures are compared. Also used with matched pairs and in twin studies. • t test for independent samples - comparison of pre and post treatment means between 2 different groups**Calculating an independent samples t test**The difference between the group means divided by the difference between the variability within the groups**The difference between the group means gives you the effect**size (the magnitude of the difference between the two groups) The variance gives you the degree of variability within each group**Between group differences and within group differences are**important factors to remember - they are used to calculate ANOVA as well as t tests.**Calculating a paired t test**mean of the difference scores___ standard error of the difference scores**The number that results from a t test is called the**“calculated value” of the test. This number is then compared in a table to the “critical value” using the alpha level set for the study.**Both point and interval estimates (confidence intervals) can**be calculated for t tests.**There are different formulas to calculate the t statistic**when variances between groups are equal and when they are unequal**Multiple t tests**• When you read a study where several t tests are used to test the same data, BEWARE… • For example, when there are repeated measures taken (3 phases) and you see t tests used to assess the differences between the first and second phase, then between the second and third. This means the risk of committing a Type I error (rejecting a true null or finding a difference when there isn’t one) is increased.**Solutions for the problem**• Perform an ANOVA • Adjust the alpha level using a Bon Ferroni correction - to do this you half (.025) or lower (.01) the alpha level**Parametric Tests vs. Nonparametric Tests**• Parametric tests are based on assumptions made using the normal curve – normal distribution of data and homogenous or similar variances • Nonparametric tests are used when the data is not normally distributed or variances are dissimilar.**Criterion for Using Nonparametric Tests**• Assumptions of normal distribution and homogeneity of variances cannot be made • Data is ordinal or nominal • Sample size is small (10 or fewer per group)**Independent samples t test**Paired t tests One way ANOVA Factorial ANOVA Mann-Whitney U test Wilcoxon Signed-Ranks Test Sign Test Kruskal-Wallis one way analysis of variance by ranks Friedman Two Way Comparable Parametric and Nonparametric Tests**Hypothesis testing with nonparametric tests is the same**procedure as with parametric tests.**Test Power**• Parametric tests are seen as more powerful • Are often used with inappropriate data because of this • Need to assess the nature of the data carefully to decide if the appropriate test is being used**Statistical Power**• Statistical power is the probability that a test will lead to rejecting the null (saying there IS a difference). • The more powerful a test, the less likely you are to make a Type II error.**Chi Square**• Is a nonparametric test • Is used to indicate whether the counts of observed events match theoretical expectations • Used with nominal or interval level data • Data is arranged in “cells” made up of rows and columns – each cell must contain at least 5 counts • The data used must consist of variables that are NOT correlated.**What if proportions are different?**• The differences between observed and expected counts are tested to see whether they are large enough to be significant • The differences themselves can be standardized and then cited as standard deviation units**Fisher’s Exact Test**• Chi square columns and rows must have 3 or more variables • If only two variables exist, then a test called Fisher’s Exact Test is done • The process is the same as for a chi-square procedure**McNemar’s Test**• When nominal and ordinal variables are related, then a test like chi-square can be carried out. • This is called McNemar’s Test.