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Testing Differences between Means

This guide explores the concept of the null hypothesis in statistics, particularly in testing the difference between means using 2-tailed t-tests. The null hypothesis assumes no difference between the sample means drawn from equivalent populations. It details how to calculate sample means, variances, and the standard error, ultimately guiding you to determine whether to reject or retain the null hypothesis based on the t-score in comparison to critical values. Gain clarity on how to statistically assess mean differences and understand the significance of your findings.

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Testing Differences between Means

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  1. Testing Differences between Means Null Hypothesis Levels of Significance 2-tailed t - tests

  2. Null Hypothesis • There is no difference, hence “null” • Assumption: mean of sample 1 = mean of sample 2. • The 2 samples have been drawn from equivalent populations, and the differences between them could result from chance alone.

  3. Null Hypothesis • If the results we actually get are very unlikely (less than 5 in 100), we reject the null hypothesis, and confirm that there is a statistically significant difference between the populations from which these 2 samples are drawn.

  4. Null Hypothesis • We often carry out experiments, where our “research hypothesis” is that there is a difference between the means. It is what we “want” to find. • But the statistical hypothesis is still whether or not the differences are large enough to say they are unlikely to be due to chance.

  5. Sample mean differences • Mean differences among samples from a population are themselves normally distributed • So, if we know the population variance, we calculate a z-score

  6. Test of Difference Between Means • H0: m1 = m2 • 1. Find the sample means. • 2. Find the sample variances. • 3. Compute the standard error of the difference between means. • 4. Compute t. • 5. Compare to critical value of t from the table. (df = N1+ N2 - 2 )

  7. Test of Difference Between Means • Compare your calculated t to the table t. If calculated t is greater than table t, reject the null hypothesis. • If calculated t is smaller, retain the null hypothesis.

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