Methods of testing for statistical significance

Overview

Software systems like SPSS provide us the ability to quickly conduct statistical analysis. For each assignment, you will utilize the SPSS software to complete each scenario presented to you. Each Write-Up Assignment will cover a different method of testing for statistical significance. You may even use some of these methods when you are conducting your dissertation.

Instructions

Review each assignment tutorial and template. See the chart below for the specific documents you should be reviewing and downloading. The tutorial will provide information on how to use the SPSS software for each assignment. Use the techniques that you gained from the tutorial to complete the template.

Statistics are the arrangement of statistical tests which analysts use to make inference from the data given. These tests enables us to make decisions on the basis of observed pattern from data. There is a wide rangeof statistical tests. The choice of which statistical test to utilize relies upon the structure of data, the distribution of the data, and variable type.There are many different types of tests in statistics like t-test,Z-test,chi-square test, anova test ,binomial test, one sample median test etc.

**Choosing a Statistical test-**

Parametric tests are used if the data is normally distributed .A **parametric statistical test** makes an assumption about the population parameters and the distributions that the data came from. These types of test includes** t-tests,z-tests** and **anova tests**, which assume data is from normal distribution.

**Z-test-** A z-test is a statistical test used to determine whether two population means are different when the variances are known and the sample size is large. In z-test mean of the population is compared.The parameters used are population mean and population standard deviation. Z-test is used to validate a hypothesis that the sample drawn belongs to the same population.

Ho: Sample mean is same as the population mean(Null hypothesis)

Ha: Sample mean is not same as the population mean(Alternate hypothesis)

**z = (x — μ) / (σ / √n),**

where , x=sample mean, u=population mean, σ / √n = population standard deviation.

If z value is less than critical value accept null hypothesis else reject null hypothesis.

**T-test-**In t-test the mean of the two given samples are compared. A t-test is used when the population parameters (mean and standard deviation) are not known.

**Paired T-Test**-Tests for the difference between two variables from the same population( pre- and post test score). For example- In a training program performance score of the trainee before and after completion of the program.

**Independent T-test-** The independent t-test which is also called the two sample t-test or student’s t-test, is a statistical test that determines whether there is a statistically significant difference between the means in two unrelated groups.For example -comparing boys and girls in a population.

**One sample t-test**– The mean of a single group is compared with a given mean. For example-to check the increase and decrease in sales if the average sales is given.

**t = (x1 — x2) / (σ / √n1 + σ / √n2),**

where x1 and x2 are mean of sample 1 and sample 2 respectively.