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Description : T-tests - Parametric Testing

Tags : T tests, Parametric Testing, Students T tests, parametric statistic

Published on : Apr 25, 2021 | Views : 4538 | Downloads : 24

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Statistical Tests Research Methodology Shukur Smail Lecture 6
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Testing the assumptions Data collection & study design Histogram & Q-Q plot Levene’s test Independence Normality of distribution Similar variance across groups
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T-TESTS
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T-tests The t test is one type of inferential, parametric statistic Determine whether there is a significant difference between the means of two groups / conditions There are three main types
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Student's T-test How can we determine, to a reasonable degree of scientific certainty, if one variety of barley yields more than another? William Sealy Gosset 1908
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Student's T-test Determines whether there is a statistically significant difference between the means in two unrelated groups. It is also known as independent samples t-test, two sample t-tests, between samples t-test and unpaired samples t-test.
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Independent groups Independent measurements One independent, categorical variable that has two levels/groups One continuous dependent variable Student's T-test
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FORMULA The difference betweent the meand divided by the pooled standard error of the mean.
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One-tailed and two-tailed tests P= ≤ 0.05
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Which intervention is more effective in lowering cholesterol levels in overweight males: Exercise or weight loss? This study found that overweight, physically inactive male participants had statistically significantly lower cholesterol concentrations (5.80 ± 0.38 mmol/L) at the end of an exercise-training programme compared to after a calorie-controlled diet (6.15 ± 0.52 mmol/L), t(38) = 2.428, p = 0.020.
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Paired T-test Estimate whether the means of two related measurements are significantly different from one another Used when two continuous variables are related Same participant at different times Different sites on the same person Cases and their matched controls. Also known as within-subjects, repeated-measures and dependent-samples.
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Paired T-test The outcome variable has a continuous scale The differences between the pairs of measurements are normally distributed The interest is on the difference in the outcome measurements between each pair
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One sample T-test There is only one group which is to be compared to a set value or a known population mean.
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ANOVA One-way ANOVA Two-way ANOVA
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Analysis of Variance - ANOVA 2 Groups 1 Parameter ➔ ? 3+ groups 2+ parameters ➔ t-test ANOVA
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One-way ANOVA Comparing means between 3+ groups Does height differ significantly according to origin ? Height X1 X3 X2
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The model Software output looks like this: The mathematical model: General mean Effect of group Individual variance
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Calculating F F is the between group variance divided by the within group variance : We want to check if the between group variance is significantly larger than the within group variance
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Factorial ANOVA Comparing means of groups defined by 2+ parameters Does height differ significantly according to origin and gender ?
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The model Software output looks like this: The mathematical model: Xijk=µ+αi+βj+αβij+εijk General mean Effect of variable 1 Effect of variable 2 Effect of interaction between 1 & 2 Individual variation
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Post-Hoc tests If the test proves significant, we can expect an effect, but which one ? Several tests can be run after the ANOVA : Conservative tests include Bonferroni correction Liberal tests include Student-Newman-Keuls test They tell us which groups are significantly different, and how they are different.
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What one-way ANOVAs can tell us What can we conclude from a one-way ANOVA ? The mean value of group #1 is significantly higher than that of population #2 & 3 In a paper: There was a statistically significant difference between groups as determined by one-way ANOVA (F(2,27) = 4.467, p = .021). A Tukey post hoc test revealed that the time to complete the problem was statistically significantly lower after taking the intermediate (23.6 ± 3.3 min, p = .046) and advanced (23.4 ± 3.2 min, p = .034) course compared to the beginners course (27.2 ± 3.0 min). There was no statistically significant difference between the intermediate and advanced groups (p = .989). The short way:
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What factorial ANOVAs can tell us There is an effect of the interaction between variables #2&3 on the mean value of the continuous variable. The short way: In a paper: A two-way ANOVA was conducted that examined the effect of gender and education level on interest in politics. There was a statistically significant interaction between the effects of gender and education level on interest in politics, F (2, 54) = 4.643, p = .014. Simple main effects analysis showed that males were significantly more interested in politics than females when educated to university level (p = .002), but there were no differences between gender when educated to school (p = .465) or college level (p = .793).
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Quick recap If we want to compare … Mean of 1 continuous variable between 2 levels of a categorical variable Mean of 1 continuous variable between 3+ levels of a categorical variable Mean of 1 continuous variable between 3+ levels of 2+ categorical variables ➔ T-TEST ➔ One-Way ANOVA ➔ Factorial ANOVA
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Short summary
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Questions?
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References Bozeman Science. (2016). Student's t test. [Video]. Available at: https://www.youtube.com/watch?v=pTmLQvMM-1M. (Accessed: 25 October 2018) Peat, J., & Barton, B.(2005). Medical Statistics. A Guide to Data Analysis and Critical Appraisal. Sydney: Blackwell Publishing. University of Wisconsin. (2017) T test. Available at: https://researchbasics.education.uconn.edu/t-test/. (Accessed: 22 October 2018) https://statistics.laerd.com/