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Testing Differences between Means

Testing Differences between Means. Null Hypothesis Levels of Significance 2-tailed t - tests. Null Hypothesis . There is no difference, hence “null” Assumption: mean of sample 1 = mean of sample 2.

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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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