Question

Please use an example to explain when we should use the test. The example should specify how will you manipulate your IVs and measure your DV, and how the participants will be tested (e.g., same group of participants or different groups) (8 points):

1) Independent sample t test

2) Paired-sample t test

3) One-way ANOVA

4) 2*2 factorial ANOVA

Answer 1

Solution :-

a) Independent Sample t test :-
The Independent Samples t Test compares the means of two independent groups in order to determine whether there is statistical evidence that the associated population means are significantly different
In this test , Your Independent variable is grouping variable

and Dependent variable is your test variable .

1. Dependent variable that is continuous (i.e., interval or ratio level)
2. Independent variable that is categorical (i.e., two or more groups)
3. Cases that have values on both the dependent and independent variables
4. Independent samples/groups (i.e., independence of observations)

example : We have to compare the average marks of two independent groups, we have a data of two highschool students, we have to compare the mean average of percentage of these two different groups.

2) Paired sample t test :

The Paired Samples t Test compares two means that are from the same individual, object, or related units. The two means typically represent two different times (e.g., pre-test and post-test with an intervention between the two time points) or two different but related conditions or units.

The Paired Samples t Test is commonly used to test the following:

• Statistical difference between two time points
• Statistical difference between two conditions
• Statistical difference between two measurements

Statistical difference between a matched pair

1. Dependent variable that is continuous (i.e., interval or ratio level)
   1. Note: The paired measurements must be recorded in two separate variables.
2. Related samples/groups (i.e., dependent observations)
   1. The subjects in each sample, or group, are the same. This means that the subjects in the first group are also in the second group.
3. Random sample of data from the population
4. Normal distribution (approximately) of the difference between the paired values
5. No outliers in the difference between the two related groups

example :-

We have to check the weight loss of sample of some peoples , we take observation before going to gym and after joining jym. checking the difference between before and after is paired t-test.

3) One way ANOVA :

The One-Way ANOVA ("analysis of variance") compares the means of two or more independent groups in order to determine whether there is statistical evidence that the associated population means are significantly different.

1. Dependent variable that is continuous (i.e., interval or ratio level)
2. Independent variable that is categorical (i.e., two or more groups)
3. Cases that have values on both the dependent and independent variables

Independent samples/groups (i.e., independence of observations.

Example: -

We have to check yield of crop (dependent variable) with respect to four fertiliser ( fertiliser1 , fertiliser2 ,fertiliser3 , fertiliser4). means our null hypothesis is that all fertilisers are equally affecting for the yield of crop.all means are equal.

4) 2*2 factorial ANOVA:

A factorial ANOVA compares means across two or more independent variables . Factorial ANOVA which not only helps us to study the effect of two or more factors but also gives information about their dependence or independence in the same experiment.

example:

Let us claim that blonde women have on average longer hair than brunette women as well as men of all hair colors. We find 100 undergraduate students and measure the length of their hair. A conservative statistician would then state that we measured the hair of 50 female (25 blondes, 25 brunettes) and 25 male students, and we conducted an analysis of variance and found that the average hair of blonde female undergraduate students was significantly longer than the hair of their fellow students. A more aggressive statistician would claim that gender and hair color have a direct influence on the length of a person’s hair.