# Hypothesis Testing — 2 Sample t Test — Create your quick working guide

Hypothesis testing is a very important element in many areas of work which includes studies and education also. Many think that there is a statistical software needed to perform hypothesis testing — but the good news is that it can be done very easily using MS Excel formula . In this article I will explain how we can perform 2 Sample t Test using MS Excel. Before we proceed, if you have not read my article Hypothesis Testing — One Sample z Test — How to create your quick workbook using MS Excel , request you to spend 5 min to read this. You can also visit my Facebook Page https://www.facebook.com/FBTrainBrain for such interesting articles.

The 2 Sample t Test is used to test whether the unknown population means of two separate groups are equal or not.

In this article we will learn on how to perform the t test in the *Equal Sample Size Equal Variance* scenario.

We will learn about both the following ways of performing the test:

**p-value approach****Critical Value approach**

Let us form the problem statement and see the datasets:

**Mean of Population 1 (not known) :** m1

**Mean of Population 2 (not known):** m2

**Null Hypothesis (Ho) :** m1 **=** m2

**Alternate Hypothesis(Ha) :** m1 **Not Equal To** m2

*Based on the Null and Alternate Hypothesis , this is a **Two Tail Test*

**Confidence Level:** 0.05

Now let us see the datasets:

For each of the sample data above, let us first calculate : **Mean, Standard Deviation, Variance and Sample Size** using simple excel formulae as below:

**p-value approach:**

First we have to calculate **t** **Statistic** value. Mathematically **t** **Statistic** is defined as :

**(**Sample1 Mean** — **Sample2 Mean**) / [SquareRoot((**Sample1 Standard Deviation² + Sample2 Standard Deviation²**) / **Sample Size**)]**

Using the above formula, let us calculate the **t Statistic** in our case. *Keep referring to Image1*

**t Statistic** = (G4-G12) / **SQRT**(((G5 ^ 2 )+(G13 ^ 2))/G7) = -**0.66183 [ assume that the t Statistic value of -0.66183 is kept in cell G16]**

Since this is a Two Tail Test, hence formula for calculating **p-value** is:

TDIST( absolute value of <t statistic value>,<degrees of freedom>,<tail>)

**p-value**=**TDIST**(**ABS**(G16),G7+G15–2,2)=**0.5174**

**TDIST** is an excel function for t Distribution

**ABS** is an excel function for finding the absolute value

**Conclusion based on p-value** : *Since the p-value (0.5174) is more than the Significance Level(0.05) , we fail to reject Null Hypothesis*

**NOTE**:

**For Left Tail Test:**

- If
**t Statistic**>0 then p-value = 1 —**TDIST**(<t statistic value>,<degrees of freedom>,<tail>) - If
**t Statistic**<0 then p-value = 1-(1 —**TDIST**(absolute value of <t statistic value>,<degrees of freedom>,<tail>))

**For Right Tail Test:**

- If
**t Statistic**>0 then p-value =**TDIST**(<t statistic value>,<degrees of freedom>,<tail>) - If
**t Statistic**<0 then p-value = 1 —**TDIST**(absolute value of <t statistic value>,<degrees of freedom>,<tail>)

**Critical Value Approach**

We already know the **t Statistic** Value which is -**0.66183**( *and this value is kept at G16 cell of the excel sheet*)

For critical value approach, we first need to calculate the Upper Critical Value and Lower Critical Value:

**Upper Critical Value** = **TINV**( 2*<Significance Level>,<degrees of freedom>) = **TINV**(2*0.05,G7+G15–2)= **1.7458**

**Lower Critical Value** = -**TINV**( 2*<Significance Level>,<degrees of freedom>) = -**TINV**(2*0.05,G7+G15–2)= -**1.7458**

**Conclusion based on Critical Value** : *Since the t Statistic (-0.66183) is within the Critical Value Intervals [-1.7458, 1.7458] , we fail to reject Null Hypothesis*

**IMPORTANT NOTE:**

- For Left Tail Test
**t****Critical value**is calculated as -**TINV**( 2*<Significance Level>,<degrees of freedom>) - For Right Tail Test
**t****Critical value**is calculated as**TINV**( 2*<Significance Level>,<degrees of freedom>)

Thanks for your interest in reading through this article. Watch this space for many more such handy techniques .