Test comparing two population means

Test comparing two population means - Two-Sample t-test...

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Two-Sample t-test procedures Two-sample t-test procedures enable inference about the difference of means for two populations, ± ² ³ ± ´ µ Samples from the two populations denoted 1 and 2 are stored in vectors called x and y for convenience. The procedures make use of the sample statistics indicate in the orange part of the table below. Population Mean ± ² ± ´ Samples Sample 1 Sample 2 Sample size m n Mean ¶· ¸ ¹ Variance º » ¼ º ¼ ¼ The two-sample t confidence interval for ± ² ³ ± ´ with confidence level 100 (1- α)% is given by ¶· ¸ ¹ ½ ¾ ¿ ¼ À ÁÂ Ã Ä Å Æ Ç È Ä Æ Æ É
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The formula for computing the degrees of freedom, ν, for confidence intervals and hypothesis tests is ± ² ³ ´ µ · ³ µ µ ¸ ¹ µ ³ ´ µ º » µ ¶ ¼ ½ · ³ µ µ ¸ º » µ ¸ ¼ ½ Two sample t Test ¾ ¿ ÀÁ à ¼ Â Ä ±ÁÅ ¿ Often the constant Å ¿ ± Æ so the null hypothesis can be written a ¾ ¿ À  à ± Â Ä Test statistics: t = Ç ÈÉÊ ÈÉÅ ¿ Ë Ì Ã Ä Í Î Ì Ä Ä Ï Alternative Hypothesis Rejection Region Ð Ñ ÀÁÒ ´ ¼ Ò µ ÓÁÅ Ô Õ Ö Õ ×ØÙ Ð Ñ ÀÁÒ ´ ¼ Ò µ ÚÁÅ Ô Õ Û Õ ×ØÙ Ð Ñ ÀÁÒ ´ ¼ Ò µ ÜÁÅ Ô Õ Û ¼ÁÕ × µ º ØÙ ÁÝÞÁÕ Ö Õ × µ º ØÙ For small sample inferences to be valid, the two populations must have approximately normal distributions. Normal qqplots plots can suggest if the assumptions are plausible or not. This is illustrated at the end.
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Using the R t.test function for two samples The t.test arguments start with two vectors containing the sample
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Test comparing two population means - Two-Sample t-test...

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