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Share It. Pages Encyclopaedia Britannica. Ronald Fisher. Although it is possible to do statistical calculations on the TI, it is much more practical to use a program such as SPSS. A paired-samples t-test was run on a sample of 20 long-term smokers to determine whether there was a statistically significant mean difference in cigarette consumption before and after a hypnotherapy programme.
Participants' cigarette consumption was lower after the hypnotherapy programme To make your results easier for others to understand, you can also produce a bar chart with error bars e. Furthermore, you are increasingly expected to report an "effect size" in addition to your paired t-test results.
Effect sizes are important because whilst the paired t-test tells you whether differences between group means are "real" i. Minitab does not automatically produce effect sizes through the paired t-test procedure, but there is a separate procedure in Minitab to do so.
All such material remains the exclusive property and copyright of Minitab Inc. All rights reserved. Paired t-test using Minitab Introduction The paired t-test also known as the paired-samples t-test or dependent t-test determines whether there is a statistically significant difference in the mean of a dependent variable between two related groups.
Minitab Assumptions The paired t-test has four "assumptions". Assumptions 1 and 2 are explained below: Assumption 1: Your dependent variable should be measured at the continuous level i. Examples of such continuous variables include height measured in feet and inches , temperature measured in o C , salary measured in US dollars , revision time measured in hours , intelligence measured using IQ score , firm size measured in terms of the number of employees , age measured in years , reaction time measured in milliseconds , grip strength measured in kg , power output measured in watts , test performance measured from 0 to , sales measured in number of transactions per month , academic achievement measured in terms of GMAT score , and so forth.
If you are unsure whether your dependent variable is continuous i. Assumption 2: Your independent variable should consist of two categorical , "related groups" or "matched pairs". The reason that it is possible to have the same participants in each group is because each subject has been measured on two occasions on the same dependent variable.
For example, you might have measured participants' salary in US dollars i. Since the same participants were measured at these two time points, the groups are related. It is also common for related groups to reflect two different conditions that all participants undergo i. For example, you might have measured 50 participants' test anxiety i.
Assumptions 3 and 4 are explained below: Assumption 3: There should be no significant outliers in the differences between the two related groups. An outlier is simply a case within your data set that does not follow the usual pattern.
The mean text anxiety score was 56 and the vast majority of students scored between 42 and However, one student scores just 2 on the scale, with the second lowest test anxiety score being As such, a student scoring just 2 on the scale "could" be considered an outlier. Where a score is an outlier this is problematic because outliers can have a disproportionately negative effect on the paired t-test, distorting the differences between the two related groups whether increasing or decreasing the scores on the dependent variable , which reduces the accuracy of your results.
In addition, they can affect the statistical significance of the test. Fortunately, when using Minitab to run a paired t-test on your data, you can easily detect possible outliers.
Assumption 4: The distribution of the differences of the dependent variable between the two related groups should be approximately normally distributed. We talk about the paired t-test only requiring approximately normal data because it is quite "robust" to violations of normality, meaning that the assumption can be a little violated and still provide valid results. You can test for normality using the Shapiro-Wilk test of normality, which is easily tested for using Minitab.
If you do not have normally distributed difference scores, you might consider running a Wilcoxon signed-rank test instead. Minitab Example A researcher wants to determine whether a hypnotherapy programme can help to reduce cigarette consumption amongst long-term smokers, defined as people that have been regular smokers for more than 10 years.
You sampled 25 chips from five different manufacturers. You decide to examine all 10 comparisons between the five plants to determine specifically which means are different. Using Tukey's method, you specify that the entire set of comparisons should have a family error rate of 0. Minitab calculates that the 10 individual confidence levels need to be Understanding this context, you can then examine the confidence intervals to determine whether any do not include zero, indicating a significant difference.
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