Week 6 Stats Summary - starting inferential statistics
Week 6 Stats Summary - starting inferential statistics STAT 205 001
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This 2 page Class Notes was uploaded by Janay Notetaker on Monday October 3, 2016. The Class Notes belongs to STAT 205 001 at University of South Carolina taught by in Fall 2016. Since its upload, it has received 4 views.
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Date Created: 10/03/16
Stat Sept 25 – Oct 1 Notes Summary Inferential Statistics - We were doing descriptive statistics (to describe/tell about the sample) - Now we are moving to inferential statistics (to infer/make predictions from the data) Example. Six diabetic mice were injected with insulin at 10mg/kg and their blood glucose levels were measured to be: 37, 39, 32, 34, 28, 35 step (1) Make qq plot to verify normality because the sample size is less than 30 a. If the sample size is more than 30 this step can be skipped To calculate standard error= standard deviation/sqrt(sample size) - Rcode: sd(data)/sqrt(6) To construct a 95% confidence interval - Rcode: t.test(data) To find the critical value (the value at which we decide to reject the null hypothesis or not) - Rcode: qt(0.025,df) - For example, if higher than the critical value you will reject the null, if lower than the critical value you accept the null - df = degrees of freedom USE THIS SENTENCE WHEN ASKED TO INTERPRET or explain the confidence interval We are 95% confident that the mean (insert what mean you were trying to find such as mean of 4 year old heights) is between _____ and _____ (the two blanks will be the values you get from running the t test. (change the percentage to what ever confidence level you are looking for) Example for one sample: We are 90% confident that the mean insulin concentration in 2-year-old mice after 2 hours is between 30.5 and 32.3. Two Sample tests Example for two sample difference: We are 99% confident that the mean difference is between -0.23 and 4.5 cm. - Rcode: t.test(sample1,sample2) - (Example) t.test(heights, weights) - Standard error for difference between two means aka the square root of ((s squared/n) + (s squared/n)) If you’re curious where some of these are coming from in detail - There is a Z-table on the front page of your book, called area under the normal curve - Degrees of freedom (df) for a difference between means uses as its formula (remember for one sample df=n-1… this is derived from that but just takes into account two samples) - Why we don’t have to check normality (with qq plots for example) on sample sizes larger than 30? o ANS: The Central Limit theorem says if sample size is large, the sampling distribution is normal
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