**What is an independent sample t test?**

Through Independent Samples t Test the means of two independent groups are compared. This is done to determine whether there is any presence of statistically significant difference between the two groups studied. It is a parametric test.

**This test is also known as:**

- Independent
*t*Test - Independent Measures
*t*Test - Independent Two-sample
*t*Test - Student
*t*Test - Two-Sample
*t*Test - Uncorrelated Scores
*t*Test - Unpaired
*t*Test - Unrelated
*t*Test

**The variables used in this test are known as:**

- Dependent variable, or test variable
- Independent variable, or grouping variable

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

- If there is any Statistical differences between the means of two groups
- If there is a presence of Statistical differences between the means of two interventions
- If there is any Statistical differences between the means of two change scores

Note: The Independent Samples *t* Test can be used to compare the means for only two groups. It cannot be used for comparing more than two groups. If one wants to compare more than two groups, then ANOVA must be used.

**What is the difference between a dependent and independent samples t-test?**

Dependent samples are paired measurements for one set of items. Independent samples are measurements made on two different sets of items. If the values in one sample reveal no information about those of the other sample, then the samples are independent.

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**What is an example of an independent sample?**

For example, to compare heights of males and females, we could take a random sample of 100 females and another random sample of 100 males. The result would be two samples which are independent of each other.

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**Data Requirements:**

Your data must meet the following requirements:

- Dependent variable that is continuous (i.e., interval or ratio level)
- Independent variable that is categorical (i.e., two or more groups)
- Cases that have values on both the dependent and independent variables
- Independent samples/groups (i.e., independence of observations)
- There is no relationship between the subjects in each sample. This means that:
- Subjects in the first group cannot also be in the second group
- No subject in either group can influence subjects in the other group
- No group can influence the other group

- Violation of this assumption will yield an inaccurate
*p*value

- There is no relationship between the subjects in each sample. This means that:
- Random sample of data from the population
- Normal distribution (approximately) of the dependent variable for each group
- Non-normal population distributions, especially those that are thick-tailed or heavily skewed, considerably reduce the power of the test
- Among moderate or large samples, a violation of normality may still yield accurate
*p*values

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**Hypotheses:**

The null hypothesis (*H*0) and alternative hypothesis (*H*1) of the Independent Samples *t* Test can be expressed in two different but equivalent ways:

*H*0: µ1 = µ2 (“the two-population means are equal”)

*H*1: µ1 ≠ µ2 (“the two-population means are not equal”)

where µ1 and µ2 are the population means for group 1 and group 2, respectively.

**Test Statistic**

When the two independent samples are assumed to be drawn from populations with unequal variances (i.e., σ12 ≠ σ22), the test statistic *t* is computed as:

Where,

x¯1 = Mean of first sample

x¯2= Mean of second sample

n1= Sample size (i.e., number of observations) of first sample

n2= Sample size (i.e., number of observations) of second sample

s1= Standard deviation of first sample

s2= Standard deviation of second sample

The calculated *t* value is then compared to the critical *t* value from the *t* distribution table with degrees of freedom

and chosen confidence level. If the calculated *t* value > critical *t* value, then we reject the null hypothesis.

Reference: https://libguides.library.kent.edu/spss/independentttest