Statistical Workshop Series 2023 SPSS T-Test PDF

StatisticalWorkshop Series 2023 Workshop 2: SPSS, the t-test statistical analysis Dr. Arass J. Noori  Analysis Normality Statistics Report Goals Parametric vs Distributions Test selection Test result Non parametric...

StatisticalWorkshop Series 2023 Workshop 2: SPSS, the t-test statistical analysis Dr. Arass J. Noori  Analysis Normality Statistics Report Goals Parametric vs Distributions Test selection Test result Non parametric t-test Sample size calculation G*Power Scale of measures What is the t-distribution? The t-distribution describes the standardized distances of sample means to the population mean when the population standard deviation is not known, and the observations come from a normally distributed population. Is the t-distribution the same as the Student’s t-distribution? Yes. What’s the key difference between the t- and z-distributions? The standard normal or z-distribution assumes that you know the population standard deviation. The t-distribution is based on the sample standard deviation. What is a t-test? A t-test (also known as Student's t-test) is a tool for evaluating the means of one or two populations using hypothesis testing. A t-test may be used to evaluate whether a single group differs from a known value (a one- William Sealy Gosset sample t-test), whether two groups differ from each other (an independent two-sample t- (1876 – 1937) test), or whether there is a significant difference in paired measurements (a paired, or dependent samples t-test). ▪ It is a parametric test which tells you how significant the differences between groups are; In other words, it lets you know if those differences (measured in means/averages) could have happened by chance. ▪ T-tests are called so, because the test results are all based on t-values. ▪ A t-test looks at the t-statistic, the t-distribution values, and the degrees of freedom to determine the probability of difference between two sets of data. t-Test Formula How are t-tests used? First, you define the hypothesis you are going to test and specify an acceptable risk of drawing a faulty conclusion. For example, when comparing two populations, you might hypothesize that their means are the same, and you decide on an acceptable probability of concluding that a difference exists when that is not true. Next, you calculate a test statistic from your data and compare it to a theoretical value from a t- distribution. Depending on the outcome, you either reject or fail to reject your null hypothesis. What if I have more than two groups? You cannot use a t-test. Use a multiple comparison method. Examples are analysis of variance (ANOVA), Tukey- Kramer pairwise comparison, Dunnett's comparison to a control, and analysis of means (ANOM). t-Test assumptions While t-tests are relatively robust to deviations from assumptions, t-tests do assume that: The data are continuous. The sample data have been randomly sampled from a population. There is homogeneity of variance (i.e., the variability of the data in each group is similar). The distribution is approximately normal. For two-sample t-tests, we must have independent samples. If the samples are not independent, then a paired t-test may be appropriate. µ Types of t-tests  Types of t-tests One-sample t-test Two-sample t-test Paired t-test Independent groups t-test Independent samples t-test Paired groups t-test Synonyms Student’s t-test Equal variances t-test Dependent samples t-test Pooled t-test Unequal variances t-test Number of variables One Two Two Continuous measurement Continuous measurement Type of variable Continuous measurement Categorical or Nominal to define pairing within Categorical or Nominal to define groups group Decide if the difference between paired Decide if the population mean is equal to a Decide if the population means for two Purpose of test measurements for a population is zero or specific value or not different groups are equal or not not Mean difference in heart rate for a group of Mean heart rate of a group of people is equal to Mean heart rates for two groups of people Example: test if... people before and after exercise is zero or 65 or not are the same or not not Sample average of the differences in paired Estimate of population mean Sample average Sample average for each group measurements Unknown, use sample standard deviations Unknown, use sample standard deviation of Population standard deviation Unknown, use sample standard deviation for each group differences in paired measurements Sum of observations in each sample minus Number of paired observations in sample Number of observations in sample minus 1, or: Degrees of freedom 2, or: minus 1, or: n–1 n1 + n 2 – 2 n–1 One-tailed vs. two-tailed tests Two-tailed test example One-tailed test example How to perform a t-test For all of the t-tests involving means, you perform the same steps in analysis: 1) Define your null (Ho) and alternative (Ha) hypotheses before collecting your data. 2) Decide on the alpha value (or α value). This involves determining the risk you are willing to take of drawing the wrong conclusion. For example, suppose you set α=0.05 when comparing two independent groups. Here, you have decided on a 5% risk of concluding the unknown population means are different when they are not. 3) Check the data for errors. 4) Check the assumptions for the test. 5) Perform the test and draw your conclusion. All t-tests for means involve calculating a test statistic. You compare the test statistic to a theoretical value from the t-distribution. ID G1 G2 G3 1 240.32 225.2 72 2 279.32 215.65 78.7 3 237.14 171.89 80.1 4 229.98 229.98 77 5 276.93 230.77 76.39 6 223.61 224.41 74 7 222.82 202.13 69.7 8 289 215.65 67 9 175.07 163.93 73 10 290 248.28 73.45 Groups: 3 Variable: 1 (Tensile strength, Glucose level, temperature, push out strength,…etc ) Equal/Unequal sample size: for what ever reason! Report the result of a t-test:  G*Power Sample size estimation for t-test Q&A