The Science of Proof: Understanding the Process of Hypothesis Testing

As we heard, a lot of that. For Data Analysis you have to good understanding of hypothesis testing. Many people facing difficulties to understand hypothesis testing. In this blog we are discussing about hypothesis testing and all the important tests, that a data analyst should have to know.

What is Hypothesis Testing??

A statistical hypothesis test is a technique for determining if the available data are sufficient to support a specific hypothesis. We can make probabilistic claims regarding population parameters through hypothesis testing.

For instance, a pharmacist thinks that the new medication is causing diabetic patients’ RBC counts to increase. The RBC Count of the sample patients (patients under inquiry) must be measured before and after the consumption of the new medication for approximately a specific period, say one month, in order to test this hypothesis. They gather all the information and run a hypothesis test. A test determines whether a drug is effective.

Steps To Perform hypothesis testing

Null Hypothesis (H0): The average RBC Count is the same after and before the consumption of the medicine, i.e., μafter = μbefore

Alternative Hypothesis (Ha): The average RBC Count after the consumption of the medicine is less than the average RBC Count before the consumption of the medicine, i.e., μafter < μbefore

If the p-value of the hypothesis test is less than the significance value (say?.o5), the null hypothesis is rejected, i.e., it can be concluded that the new drug is responsible for the rise in the RBC Count of diabetic patients.

Type of Hypothesis Test Experiment

Parametric Test?: A branch of statistics known as parametric statistics makes the assumption that the population from which the sample data is drawn may be adequately represented by a probability distribution with a given set of parameters.

1. Z Test?: Any statistical test for which the test statistic’s distribution under the null hypothesis may be roughly represented by a normal distribution is known as a Z-test. Z-tests examine a distribution’s mean. The Z-test is more practical than the Student’s t-test because it has a single critical value for each significance level in the confidence interval (for example, 1.96 for 5% two tailed). The Student’s t-critical test’s values are determined by the sample size (through the corresponding degrees of freedom). In that they both assist in determining the significance of a collection of data, the Z test and Student’s t-test are comparable to one another. The population deviation is challenging to ascertain, hence the z-test is infrequently utilized in real-world settings.
2. Students T test?: Any statistical hypothesis test called a t-test has a test statistic that, under the null hypothesis, follows a Student’s t-distribution. It is most frequently used when the test statistic would have a normal distribution if the test statistic’s scaling term’s value were known (typically, the scaling term is unknown and therefore a nuisance parameter). Under specific circumstances, the test statistic follows a Student’s t distribution when the scaling term is computed using the data. The most typical use of the t-test is to determine whether the means of two populations differ.
3. Anova Test?: Analysis of variance (ANOVA) is a statistical method for examining differences in means. It consists of a number of statistical models and the accompanying estimating techniques (such as the “variation” within and between groups). Ronald Fisher, a statistician, created ANOVA. The rule of total variance, on which the ANOVA is based, divides the observed variance in a given variable into components owing to various causes of variation. ANOVA generalizes the t-test beyond two means by offering a statistical test to determine if two or more population means are equal. In other words, the ANOVA is employed to determine whether two or more means differ from one another.

4. F Test?: Any statistical test with an F-distribution for the test statistic under the null hypothesis is known as an F-test. In order to determine which statistical model better represents the population from which the data were sampled, it is most frequently applied when contrasting models that have been fitted to data sets. Exact “F-tests” are typically required after least squares fitting of the models to the data. In honor of Ronald Fisher, George W. Snedecor came up with the name. In the 1920s, Fisher created the statistic as the variance ratio.

Non Parametric Test?: The area of statistics known as nonparametric statistics does not only rely on families of parametrized probability distributions. Nonparametric statistics is predicated on either having no distribution or having a distribution with known parameters.

1. Chi Square Test?: Chi Square Test is a statistical analysis technique that is used to determine whether the null hypothesis, that there is no relationship between two categorical variables, is statistically valid. The null hypothesis is that there is no relationship between the two categorical variables. The test is used to determine whether the sample size is large enough to detect a statistically significant relationship between the two categorical variables.
2. To conduct a chi square test:

• 1. Obtain the sample size.
• 2. Determine the degrees of freedom.
• 3. Calculate the chi square statistic.
• 4. Compare the chi square statistic to the chi-square distribution.

1. Mann–Whitney U test?: Mann-Whitney test To assess the relative frequencies of two categorical variables, the U test is a frequently used statistical test. The statistician W.S. Mann and the biologist A. Whitney are honored in the test’s names.
2. To compare the relative frequencies of two categorical variables, the Mann-Whitney U test is employed. The statistician W.S. Mann and the biologist A. Whitney are honored in the test’s names. Two categorical variables’ relative frequencies are compared using the test.
3. Two categorical variables’ relative frequencies are compared using the test. The test compares the proportional frequencies of two sets of data.
4. Wilcoxon signed-rank test?: A non-parametric statistical hypothesis test called the Wilcoxon signed-rank test is used to compare the locations of two populations by utilizing two matched samples, or to assess the location of a population based on a sample of data. Similar to the one-sample Student’s t-test, the one-sample version has the same objective. It is a paired difference test, similar to the paired Student’s t-test, for two matched samples (also known as the “t-test for matched pairs” or “t-test for dependent samples”). When population means are not of relevance, such as when determining if a population’s median is nonzero or whether there is a higher than 50% likelihood that a sample from one population represents that population, the Wilcoxon test can be an useful substitute for the t-test.

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