t-test Parametric test Biostatics and Research Methodology

t-test Parametric test Biostatics and Research Methodology

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  Parametric Test: t-test/Studentt-test Ms. Nigar K.Mujawar Assistant Professor, Shri.Balasaheb Mane Shikshan Prasarak Mandal Ambap Womens College of Pharmacy, Peth-Vadgaon, Kolhapur, MH, INDIA. 1
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  Parametric Test: A parametrictest is a statistical method used to analyze data that assumes specific characteristics about the population distribution, typically that it follows a normal distribution. Used when sample size is small (i.e. less than 30) and when population standard deviation is not available. These tests often involve making inferences about population parameters, such as means or variances. Examples of parametric tests include: 1. t-tests 2. Z-test 3. F-test 4. Analysis of variance (ANOVA), and 5. Linear regression 6. Correlation Analysis 7. Parametric Survival Analysis 8. Parametric Bayesian Methods 9. Parametric Classification and Regression Trees (CART) They are commonly used when certain assumptions about the data can be met, such as when the data is continuous and normally distributed. If the assumptions are not met, non-parametric tests, which make fewer assumptions about the population distribution, may be more appropriate. 2
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  T-test: A T-test isa statistical hypothesis test used to determine if there is a significant difference between the means of two groups. It's commonly used when you have two sets of data and want to compare their means to see if they are significantly different from each other. There are several types of T-tests: 1. Independent samples T-test: Used when you want to compare the means of two independent groups to determine if they are significantly different from each other. 2. Paired samples T-test: Used when you want to compare the means of two related groups, such as before and after measurements from the same individuals. 3. One-sample T-test: Used when you want to compare the mean of a sample to a known value or hypothesized population mean. 3
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  • The T-testcalculates a T-value based on the means and standard deviations of the samples, as well as their sample sizes. • This T-value is then compared to a critical value (A critical value is the threshold used to determine whether to reject the null hypothesis in hypothesis testing, based on the chosen significance level and the distribution of the test statistic.) from the T-distribution to determine if the difference between the means is statistically significant. • If the T-value exceeds the critical value, then there is evidence to reject the null hypothesis and conclude that there is a significant difference between the 4
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  1. Sample T-test: •This term generally refers to any T-test that involves comparing the means of two groups, but it doesn't specify whether the groups are independent or related (paired). • It's a broad term encompassing both independent samples T-tests and paired samples T-tests. 2. Pooled T-test: • In the context of independent samples T-tests, a pooled T-test assumes that the variances of the two groups being compared are equal. • The pooled variance is calculated by combining the variances of the two groups, weighting each variance by its degrees of freedom. • This approach can increase the precision of the estimated standard error and thus the power of the test. 5
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  3. Unpaired T-test: •This is another term for an independent samples T-test. • It's called "unpaired" because the observations in one group are not paired or matched with the observations in the other group. • Each observation in one group is considered independent of the observations in the other group. 6
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  7 Purpose: Compares meansof two independent groups to see if they're significantly different. Steps: 1. Define null (no difference) and alternative (difference exists) hypotheses. 2. Collect data from two separate groups. 3. Check if data in each group follows a normal distribution and if variances are similar. 4. Calculate t-statistic using group means, pooled standard deviation, and sample sizes. 5. Determine degrees of freedom(the maximum number of logically independent values, which may vary in a data sample) 6. Compare calculated t-statistic to critical value or calculate p-value. 7. Interpret results: Reject null hypothesis if p-value is less than significance level. Outcome: - If p-value is low (less than significance level), there's evidence to suggest a significant difference between group means. - If p-value is high, there's no significant difference detected.
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  4. Paired T-test: •This refers to a T-test where each data point in one group is paired or matched with a data point in the other group. • This pairing is usually based on some natural pairing, such as before- and-after measurements on the same individuals, or matched pairs in a study. • The paired T-test is used to compare the means of these paired observations to determine if there is a significant difference between them. In summary, "Sample T-test" is a broad term referring to any T-test comparing the means of two groups, while "Pooled, Unpaired, and Paired" describe specific variations or conditions within the context of independent samples T-tests or paired samples T-tests. 8
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  9 Applications of t-test: 1.Comparing Means: Assess if there's a significant difference between two groups' averages. 2. Before and After Studies: Evaluate changes in a variable before and after an intervention. 3. Quality Control: Ensure products meet standards by comparing measurements to set values. 4. Market Research: Determine differences in responses between different consumer groups. 5. Psychological Studies: Compare mean scores of different experimental groups. 6. Biological Studies: Analyze differences in measurements between groups of organisms. 7. Economic Analysis: Compare economic indicators between populations or assess policy impacts.
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  10 Assumptions of t-test A.IndependentSamples t-test: 1. Independent Observations: The observations in each group are independent of each other. This means that the score of one individual does not affect or influence the score of another individual. 2. Normal Distribution: The data in each group should follow a normal distribution. However, the t-test is robust to violations of normality when sample sizes are large (typically considered as n > 30). If sample sizes are small, a violation of normality can affect the validity of the t-test. 3. Homogeneity of Variance: The variances of the two groups should be equal (homogeneity of variances). This means that the spread of scores within each group should be similar. 4. Population standard deviation is not known. 5. Samples are random and independent.
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  11 B.Paired Samples t-test: 1.Independence of Differences: The differences between paired observations should be independent of each other. For example, if you're comparing pre- test and post-test scores of the same individuals, the change in one individual's score should not be influenced by the change in another individual's score. 2. Normal Distribution of Differences: The differences between paired observations should be approximately normally distributed. 3. Homogeneity of Differences (Optional): While not always necessary, if the sample size is small, it's advisable for the differences between paired observations to have a similar spread (homogeneity of differences).
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  12 Formula in ttest:
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  14 One sample t-testformula
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  15 Two sample t-testformula
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