TEST OF SIGNIFICANCE.pptx ests of Significance: Process, Example and Type
- 1. TESTS OF SIGNIFICANCE GUIDED BY: DR. NEEMA SHEETY DR. ADITI MATHUR DR. ASHISH BALI DR. TRISHI PRESENTED BY: Dr. ASHWINI BHANDARE
- 2. 2 CONTENTS • Introduction • Important terminologies • Classification of hypothesis tests • Parametric tests • Non-parametric tests • Conclusion • References
- 3. 3 INTRODUCTION • A test of significance is a formal procedure for comparing observed data with a claim (also called a hypothesis), the truth of which is being assessed. • The claim is a statement about a parameter, like the population proportion p or the population mean μ. •The results of a significance test are expressed in terms of a probability that measures how well the data and the claim agree. • The test which is done for testing the research hypothesis against the null hypothesis.
- 4. 4 IMPORTANT TERMINOLOGIES • Population The entire group under study as defined by research objectives. sometimes called the “universe.” • Sample A subset of the population that should represent the entire group.
- 5. 5 • Normal distribution • when we take large number of observations of any variable such as height, blood pressure, pulse rate etc. • Then we draw a frequency distribution curve or a graph, we get normal distribution or normal curve. -
- 6. 6 SYMMETRICAL AND SKEWED DISTRIBUTIONS Mean Median Mode Mode Median Mean Symmetrical Skewed When data is normally distributed When data is not normally distributed
- 7. 7 NULL HYPOTHESIS VS ALTERNATIVE HYPOTHESIS
- 8. 8 • By using various tests of significance we either: Reject the Null Hypothesis (or) Accept the Null Hypothesis • Rejecting null hypothesis → difference is significant. • Accepting null hypothesis → difference is not significant
- 9. 9 • Standard Error (SE): • The standard deviation of sampling distribution is called as the standard error. it provides the estimate that how far from the true value the estimated value is likely to be. ERROR Even though hypothesis tests are meant to be reliable, there are two types of errors that can occur.
- 10. 10 • Level of significance and confidence • Significance means the percentage risk to reject a null hypothesis when it is true and it is denoted by . 𝛼 • Probability of Type I error should be less than 5%, i.e, less than 0.05. • (1 − 𝛼) is the confidence level in which the null hypothesis will exist when it is true or we can attribute significance with 95% confidence. TYPE I ERROR
- 11. 11 • Accepting the null hypothesis when it is false • Denoted as β and 1−β is called power of the test. • The probability of type II error shold be 10% or 20% • Power of the test : • 1−β since is usually kept at 10%-20% , power is 80%-90%. TYPE II ERROR
- 12. 12 Parametric test • Based on assumptions that data follow normal distribution or normal family of distribution. • estimate parameter of underlying normal distribution. • significanc of difference known CLASSIFICATION OF HYPOTHESIS TESTS • Non parametric test • Variable under study don’t follow normal distribution or any other distribution of normal family. • Association can be estimated.
- 13. 13 • t-Test Unpaired ‘t’ test Paired ‘t’ test • ANOVA One way ANOVA Two way ANOVA • Z test • F Test Parametric tests :
- 14. 14 ‘T’-TEST • This test was designed by W.S Gossett, whose name was student hence this test is also called student t test. • A t-test is an analysis of two populations means through the use of statistical examination at test with two samples. • It is commonly used with small sample size, testing the difference between the samples when the variances of two normal distributions are not known. • It compares two averages means and tell you they are different from each other, also tells you how significant the differences.
- 15. 15 ONE SAMPLE T-TEST • It determines whether the sample mean is statistically different from a known or hypothesized population mean. • This test is also known as: single sample t test • This test is applied to unpaired data of independent observation made on individuals of two different or separated group or samples drawn from two populations • It is applied to find the significance of difference between two propertions.
- 16. 16 PAIRED T TEST • The paired samples t test compares two means that are from the same individual, object, or related units. • The purpose of the test is to determine whether there is statistical evidence that the mean difference between paired observations on a particular outcome is significantly different from zero. • This test is also known as: dependent t test. • The paired samples t test can only compare the means for two (and only two) related (paired) units on a continuous outcome that is normally distributed
- 17. 17 UNPAIRED T TEST • The independent samples t test compares the means of two independent groups . • To determine whether there is statistical evidence that the associated population means are significantly different. • This test is also known as: Independ t-test . A z-test is a statistical test to determine whether two population means are different when the variances are known and the sample size is large. it can be used to test hypotheses in which the z-test follows a normal distribution. ‘z’-TEST
- 18. 18 ANALYSIS OF VARIANCE (ANOVA) • ANOVA is a technique used when multiple sample cases are involved. • Anova determines whether the means of more than two quantitative populations are equal. • The basic principle of Anova is to test for differences among the means of the populations by examining the amount of variation within each of these samples, relative to the amount of variation between the samples. • Anova can test hypotheses that the t-test cannot.
- 19. 19 • When performing an ANOVA procedure the following assumptions are required: The observations are independent of one another The observations in each group come from a normal distribution
- 21. 21 ADVANTAGES AND DISADVANTAGES OF ANOVA • Advantages: 1.It is an improved technique over t-test and z-test. 2.Suitable for multidimensional variables. 3.Analysis of various factors at a time. 4.Economical method of parametric testing. 5.can be used in 3 or more than 3 groups.
- 22. 22 • Disadvantages: 1.It is difficult to analyze anova under strict assumptions regarding the nature of data. 2.It is not so helpful in comparison with t-test that there is no special interpretation of the significance of two means. 3.The requirement of post-anova t-test for further testing.
- 23. 23 NON-PARAMETRIC TESTS • It is defined as the hypothesis test which is not based on the underlying assumptions i.e. It does not require population’s distribution to be denoted by the specific parameters. • The test is mainly based on the differences in the medians. • Hence its alternatively known as the distribution-free test. • The test assumes that the variables are measured on the nominal or the ordinal level.
- 24. 24 Chi square test Fisher’s exact test Kruskal–wallis test Mann-Whitney U Test Wilcoxon Signed Rank Test Friedman's Test McNemar’s Test VARIOUS NON-PARAMETRIC TESTS ARE AS FOLLOWS:-
- 25. 25 CHI SQUARE TEST • This test (as a non-parametric test) is based on frequencies and not on the parameters like mean and standard deviation. • The test is used for testing the hypothesis and is not useful for estimation • This test is an important non-parametric test as no rigid assumptions are necessary in regard to the type of population, no need of parameter values and relatively less mathematical details are involved.
- 26. 26 • Applications Of Chi Square Test:- 1) Goodness of fit of distributions 2) Test of independence of attributes 3) Test of homogenity.
- 27. 27 FISHER’S EXACT TEST • Is used in the place of chi square test in 2 by 2 tables, especially in cases of small samples. • It tests the probability of getting a table that is as strong due to the chance of sampling. The word ‘strong’ is defined as the proportion of the cases that are diagonal with the most case • It is generally used in one tailed tests. However, it can also be used as a two tailed test as well. • It also involves the finding of the probability of every possible combination which indicates more evidence of association.
- 28. 28 KRUSKAL–WALLIS TEST • It is used for comparing two or more independent samples of equal or different sample sizes. It extends the mann–whitney U test, which is used for comparing only two groups. The parametric equivalent of the kruskal–wallis test is the ANOVA.
- 29. 29 MANN-WHITNEY U TEST • It is a nonparametric test of the null hypothesis that it is equally likely that a randomly selected value from one population will be less than or greater than a randomly selected value from a second population. • It is used to compare differences between two independent groups when the dependent variable is either ordinal or continuous, but not normally distributed.
- 30. 30 • Requirements 1. Two random, independent samples. 2. The data is continuous . 3. Scale of measurement should be ordinal, interval or ratio.
- 31. 31 WILCOXON SIGNED RANK TEST • It is used to compare two related samples, matched samples, or repeated measurements on a single sample to assess whether their population mean ranks differ (i.e. It is a paired difference test). • It can be used as an alternative to the paired student's t-test when the distribution of the differences between the two samples cannot be assumed to be normally distributed.
- 32. 32 FRIEDMAN TEST • The friedman test is a non-parametric statistical test developed by milton friedman. • Similar to the parametric repeated measures anova, it is used to detect differences in treatments across multiple test attempts. • The procedure involves ranking each row (or block) together, then considering the values of ranks by columns. • The friedman test can be used on metric or ordinal variables
- 33. 33 MCNEMAR’S TEST • A statistical test used on paired nominal data. • It is applied to a dichotomous trait, with matched pairs of subjects, to determine whether the row and column marginal frequencies are equal . • An application of the test in genetics is the transmission disequilibrium test for detecting linkage disequilibrium. • The commonly used parameters to assess a diagnostic test in medical sciences are sensitivity and specificity. Sensitivity is the ability of a test to correctly identify the people with disease. Specificity is the ability of the test to correctly identify those without the disease.
- 34. 34 ADVANTAGES AND DISADVANTAGE OF NON PARAMETRIC TEST
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- 36. 36 CONCLUSION • Significance test plays a key role in experiments. • It helps in structuring the findings from different sources of data. • It helps in keeping the human bias away from the researchers conclusion with the help of proper statistical treatment.
- 37. 37 REFERENCES • Essentials Of Preventive And Community Dentistry, Soben Peter , 4th Edition • MAHAJANS METHOD IN BIO STATISTICS -10 TH EDITION