All about the t-Test
All about the t-Test
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The concept
The concept
Inferential statistics are used in research to construct inferences and prediction about a population by means of data drawn from that population called a sample. In other word, researchers try to get data from the sample, then make generalizations about the population. T-test is one of those inferential statistics used to test hypothesis. Specifically, testing the null hypothesis that means of the two groups are equal. t-test is designed to determine if there is a significant difference between the means of two groups. this test is appropriate when investigating the difference between two population averages (for example in gender differences in success rate).
Types of t-Test
Types of t-Test
Statisticians distinguish three types of t-tests distinguished :
- One-sample t-test: using only one group, to test sample mean against a hypothetical one (a known figure- e.g against a required standard or a passing score).
- Two-sample t-test -known as independent t-test: using two groups, to compare the two means
- Paired t-test -known as dependent t-test: using two groups with paired observations – it is like comparing values of one sample in two occasions (e.g. husbands & wives)
How to interpret a t-score
How to interpret a t-score
In general, The t-score indicates the ratio between the difference between two groups and the difference within the groups. When conducting a t-test, the bigger the t-value, the more likely it is that the results are repeatable. In other words: The larger the t score, the more difference there is between groups. The smaller the t score, the more similarity there is between groups. For example if we have a t score of 4, this translates to the fact that the groups are times times as different from each other as they are within each other.
Bottom line: A large t-score tells you that the groups are different. & a small t-score tells you that the groups are similar.
The One-sample t-Test:
The One-sample t-Test:
The one sample t-test, is also known as student's t-test. This inferential statistical test is used with only one group, to test sample mean against a hypothetical one (a known figure- e.g against a required standard or a passing score).
The formula for one sample t-Test
The formula for one sample t-Test
Statisticians use this formula to compute the one sample t-test
To calculate the t-statistic for one sample t- test you need to have the following
- Population mean (μ)
- Sample mean (x̄ )
- Sample standard Deviation (s)
- Sample size (n)
- Degrees of Freedom (df)
- Alpha (𝝰 )
See the example below, step by step how how to run the t-test from the research question to the interpretation of the results...
Independent t-test for two samples
Independent t-test for two samples
The independent t-test, has several appellations: the two sample t-test, the independent-samples t-test, and also known as student's t-test. This inferential statistical test is used to decides if the two means in an related groups are equal or have a statistically significant difference.
The Null hypothesis is set as both sample means are equal --> H0: u1 = u2
The Alternative hypothesis is set as the two sample means are not equal--> Ha: u1 ≠ u2
It is common that the researcher is looking to demonstrate if he/she can reject the null hypothesis and accept the alternative one, which is demonstrating that the means from the two sample are not equal
Assumptions in the independent t-Test:
Assumptions in the independent t-Test:
- The normality of the dependent variable
- The homogeneity of variance
- The data (scores) are independent of each other
The formula for the independent t-test
The formula for the independent t-test
- Let A and B represent the two groups to compare.
- Let mA and mB represent the means of groups A and B, respectively.
- Let nA and nB represent the sizes of group A and B, respectively.
The t test statistic value to test whether the means are different can be calculated as follow :
S2 (S square) is an estimator of the common variance of the two samples. It can be calculated as follow :
Once t-test statistic value is determined, you have to read in t-test table the critical value of Student’s t distribution corresponding to the significance level alpha of your choice (5%). The degrees of freedom (df) used in this test are : df = nA+nB −2
Interpreting results
Interpreting results
If the absolute value of the t-test statistics (|t|) is greater than the critical value, then the difference is significant. Otherwise it isn’t. The level of significance or (p-value) corresponds to the risk indicated by the t-test table for the calculated |t| value.
The format of reporting t-score
The format of reporting t-score
When conducting a t-test, researchers / statisticians uses the following format, where df is degree of freedom , and P-value is significance value :
t(df) = t-statistic, p = significance value
Explanation & Examples T-test
Using SPSS to Calculate t-test
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