testing of hypothesis - Statistics for Data Science & Analytics

To whom is the researcher similar in hypothesis testing: the defense attorney or the prosecuting attorney? Why?

The researcher is similar to the prosecuting attorney in the sense that the researcher brings the null hypothesis “to trial” when she believes there is a probability of strong evidence against the null.

Just as the prosecutor usually believes that the person on trial is not innocent, the researcher usually believes that the null hypothesis is not true.
In the court system, the jury must assume (by law) that the person is innocent until the evidence calls this assumption into question; analogously, in hypothesis testing the researcher must assume (to use hypothesis testing) that the null hypothesis is true until the evidence calls this assumption into question.

The world aournd us is complex enough and full of uncertainty. Onlyobserving the data can not tell us if a pattern or relationship exists, or if it is just due to random chance. Therefore, we need hypthesis testing procedure that provides us a systematic method to analyze the sample data and draw conclusions (or make wise decisions) about a larger population, with a clear understanding of the likelihood of being wrong.

In conclusion, like statistical estimation, the statistical hypothesis testing is a cornerstone of statistical analysis. It provides a way to move beyond simply observing data and allows us to draw meaningful inferences about populations, evaluate claims, and make informed decisions in the face of uncertainty.

Testing of Hypothesis in R Programming Language

Introduction (Independent Samples t test using SPSS)

Independent Samples t test is a test for independent groups and is useful when the same variable has been measured in two independent groups and the researcher wants to know whether the difference between group means is statistically significant. “Independent groups” means that the groups have different people in them and that the people in the different groups have not been matched or paired in any way.

Objectives of Independent Samples t test

The independent t-test compares the means of two unrelated/independent groups measured on the Interval or ratio scale. The SPSS t-test procedure allows the testing of the hypothesis when variances are assumed to be equal or when are not equal and also provides the t-value for both assumptions. This test also provides the relevant descriptive statistics for both of the groups.

Assumptions (Independent Samples t test)

Variable can be classified into two groups independent of each other.
The variable is Measured on an interval or ratio scale.
The measured variable is approximately normally distributed
Both groups have similar variances (variances are homogeneity)

Data Required for (Independent Samples t test)

Suppose a researcher wants to discover whether left and right-handed telephone operators differed in the time it took them to answer calls. The data for reaction time were obtained (RT’s measured in seconds):

Data Telephone: Independent Samples t test

The mean reaction times suggest that the left-handers were slower but does a t-test confirm this?

Independent Samples t Test using SPSS

Perform the following steps to perform the Independent Samples t-test by using the SPSS and entering the data set in the SPSS data view

1) Click Analyze > Compare Means > Independent-Samples T Test… on the top menu as shown below.

2) Select continuous variables that you want to test from the list.

3) Click on the arrow to send the variable in the “Test Variable(s)” box. You can also double-click the variable to send it in the “Test Variable” Box.

4) Select the categorical/grouping variable so that group comparison can be made and send it to the “Grouping Variable” box.

5) Click on the “Define Groups” button. A small dialog box will appear asking about the name/code used in the variable view for the groups. We used 1 for males and 2 for females. Click the Continue button when you’re done. Then click OK when you’re ready to get the output. See the Pictures for a Visual view.

independent samples t test - Define groups 3

Independent Samples t-test SPSS Output

The first Table in the output is about descriptive statistics concerning your variables. The number of observations, mean, variance, and standard error are available for both of the groups (male and female)

The second Table in the output is an important one concerning the testing of the hypothesis. You will see that there are two t-tests. You have to know which one to use. When comparing groups having approximately similar variances use the first t-test. Levene’s test checks for this. If the significance for Levene’s test is 0.05 or below, then it means that the “Equal Variances Not Assumed” test should be used (the second one), Otherwise use the “Equal Variances Assumed” test (first one). Here the significance is 0.287, so we’ll be using the “Equal Variances” first row in the second table.

In the output table “t” is the calculated t-value from test statistics, for example, the t-value is 1.401

df stands for degrees of freedom, in the example, we have 18 degrees of freedom

Sig (two-tailed) means two-tailed significance value (P-Value), for example, the sig value is greater than 0.05 (significance level).

Decision

As the P-value of 0.178 is greater than our 0.05 significance level we fail to reject the null hypothesis. (two-tailed case)

As the P-value of 0.089 is greater than our 0.05 significance level we fail to reject the null hypothesis. (one tail case with 0.05 significance level)

As the P-value of 0.089 is smaller than our 0.10 significance level we reject the null hypothesis and accept the alternative hypothesis. (one tail case with 0.10 significance level). In this case, it means that the left handler has a slower reaction time as compared to the right handler on average.

Testing of Hypothesis or Hypothesis Testing

To whom is the researcher similar in hypothesis testing: the defense attorney or the prosecuting attorney? Why?

Independent Samples t test in SPSS