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12 Cards in this Set
- Front
- Back
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t distribution--describe distribution
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1. It does not have a normal distribution. It has a t distribution that is similar 2. The t distributions have more probability in the tails and less in the center than does the standard Normal. This is true because substituting the estimate s for the fixed parameter (standard deviation) introduces more variation into the statistic 3. As the degrees of freedom k increase, the t(k) density curve approaches the N(0,1) curve ever more closely. THis happens because s estimates standard deviation more accurates as the sample sixe increases
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t statistic
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says how far x bar is from its mean mu in standard deviation units. There is a different t distribution for each sample size as noted by the degrees of freedom
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matched pairs, what is t procedure?
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the mean difference in the response to the two treatments within matched pairs of subjects in the entire population. It is incorrect to ignore the pairs and analyze the data as if we had two samples, one from subjects who wore unscented masks and a second from subjects who wore scented masks
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what is a robust confidence interval or significance test?
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the confidence level or P value does not change very much when the conditions for use of the procedure are violated
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discuss robustness of t procuedure
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t procedures are not robuts against outliers because x bar and s are not resistant to outliers. The condition that the population be Normal rules out outliers so the presence of outliers shows that this conditions is not fulfilled 2. T procedures are fairly robust against non-Normality of hte population except when outliers or strong skewness are present . As the sample size increases, the central limit theorem ensures tha the distribution of the sample mean x bar becomes more nearly Normal and that hte t distribution becomes more accurate for critical values
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when to use the t procedures
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1. Sample size <15 only if data appears close to normal 2. Sample size at least 15 except in the presence of outliers or strong skewness 3. Large samples( roughly greater than or equal to 40): even for clearly skewed
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two sample problem goal
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1. Compare the responses to two treatments or to compare the characteristics of two populations 2. We have separate samples from each treatment or population
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matched or 2 sample? a medical researcher is interested in the effect on blood pressure of added calcium in our diet. She conducts a randomized comparative experiment in which one group of subjects receives a calcium supplement and a control group gets a placebo
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2 sample
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conditions for comparing 2 means
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1. We have 2 SRS that are independent 2. Both populations are normally distributed. The means and standard deviations of the populations are unknwon.
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what is the basic distributon of the two sample t statistic?
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it has approximately a t distribution. It doesn't have exactly a t distribution even if the populations are both exactly Normal.
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robustness of 2 sample t procedures
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more robust than the one sample t methods when the distributions are not symmetric. When the sizes of the two samples are equal and the two poulations being compared have distributions with similar shapes, probability values from the t table are quite accurate for a broad range of distributions. When the two population distributions have different shapes, larger samples are needed
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What is the probability of rejecting Hnought when it is false?
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1-B or power
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