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# stat 205 notes and homework aid STAT 205 001

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This 10 page Class Notes was uploaded by Janay Notetaker on Friday September 2, 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 90 views.

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Date Created: 09/02/16

Week 2 notes Elementary Statistics for the Biological and Life Sciences Lecture and HW (homework) More R commands that are useful and can help in homework/assignments data<-read.table("width.txt") Will put your data into R (if you have the working directory set to be the folder where your file is in) > hist(width, freq=FALSE) The TRUE and FALSE here tell R whether to make a density vertical axis or a frequency vertical axis > hist(width, freq=TRUE) *and yes capitalization matters If you want to know more about the Histogram difference: Density = (observation/total # of observations) giving probabilities Frequency = # of times that observation occurred (without the regard of dividing by the full sample) > hist(width, breaks=8,freq=TRUE) Breaks change the “bins” on the x axis > hist(width, breaks=16,freq=TRUE) Bins = what values the bars are in between on the x axis Note if your data has no observations in that bin range then there will be an empty spot Week 2 notes Elementary Statistics for the Biological and Life Sciences Lecture and HW (homework) Week 2 notes Elementary Statistics for the Biological and Life Sciences Lecture and HW (homework) More commands that help on week 2 gives “5 number summary” ------------------------------------------------------------------------------------------------------------------------------------- Gives first quartile *note: all you have to do to get the third quartile is change 0.25 to 0.75 --------------------------------------------------------------------------------------------------------------------------------------- Write this command all on one line and it will give you… This bar plot (aka bar chart) xlab … what you want to title the x axis ylab … what you want to title the y axis main … what you want to title your graph names.arg=c(“ “)… what you want to title the categories for the x axis, you must type them in the order you want them to show up, and place commas in between each title height=c( ) … place your data set in between the ( ) you must separate each Reminder… Graphs R can make are: observation with a comma Boxplots Histograms Bar charts Scatterplots IMPORTANT: don’t forget that xlab (what you want to title the x axis) and ylab (what you want to title the y axis) are for naming the axis in other graphs too, not just the burrito spice levels bar chart. For example, xlab and ylab can name axis in scatterplots too. (can help in homework) Week 2 notes Elementary Statistics for the Biological and Life Sciences Lecture and HW (homework) Problem 1. If asked something like, input the data from table 1 and make a scatterplot of the data with proper labeling of x and y axis… Problem 2. If asked to use a probability tree… The probabilities are basically at this point… (probability of what happened the first time) x (probability of what happened the second time) … and so on. Then you use these to answer other questions where you may have to add and subtract *see problem 3 below. So for the example below, probabilities are 0.04, 0.16, and 0.64 =0.04 =0.16 =0.16 =0.64 Week 2 notes Elementary Statistics for the Biological and Life Sciences Lecture and HW (homework) (1) If both chosen events need to be true: Use the pathway where the outcome is the (it occurred twice) (2) If at least one of the events need to be true: Use the pathways where the event occurred at least once **so yes! Don’t forget to count probability where it occurred twice too… aka part (1)** Problem 3. If you’re given that 5% of a population has a flu. And if a person has that flu then there is a 92% chance of seeing the flu in a test. But if they actually don’t have that flu then there is a 94% chance of the test seeing that they are not sick. Approach these medicine problems Step 1) Find and start a tree with the or problems where a certain phrase about the percent of people in number of people have blank and the population that have it. “5% of a half show blank and another do not like this… population has a flu” Step 2) Next, start making the branches. To branch off of the 5% that really actually have the flu use the phrase about who has the flu/disease. In this case its a 92% chance, Here the other branch would be 8% because 1 - 0.92=0.08 Step 3) To branch off of the 95% do like you did in Step 2. One branch saying: 94% have test showing they are not sick The other branch saying: 6% have test showing they are sick Week 2 notes Elementary Statistics for the Biological and Life Sciences Lecture and HW (homework) Your final tree should look something like this (but with final probabilities actually calculated) step (1) If you have to answer the probability that a random person will have a positive flu test, Add them: (probability #1) + (probability #3) step (2) If you have to answer the probability that a random person will have the flu given the flu test was positive: Take the probability #1 (have a positive test and have the disease) then Divide by the total probability of positive tests that you found above in step (1) … (test was positive) Problem 4. Weights For any similar problem that asks something around the lines of: if one is chosen at random from the group… Week 2 notes Elementary Statistics for the Biological and Life Sciences Lecture and HW (homework) (a) What is the probability that the one chosen has no schedule? **Look at the two starred boxes** And divide (total that have no schedule) / (total number in the sample) (b) What is the probability that the one chosen will have low weight? **Look at these two starred boxes** And divide (total that have low weight) / (total number in the sample) (c) Given that the one chose does have a true schedule, what is the probability of low weight. Look at the box with the total of the given statement: (has a schedule) …then look at the number who have a low weight and are in the group that has a schedule (like intersection) Now Divide… (amount that have low weight and a schedule) / (total amount that have a schedule) Where to find topics in more detail in the book for Weeks 1 and 2 Important topic summary: 2.1: Numeric (continuous & discrete) vs. categorical (ordinal & nominal) variables; observational unit. 2.2 frequency distributions for categorical and continuous data: tables, bar charts, and histograms; shape: skewed vs. symmetric, modality (could be bimodal). 2.3 Measures of center: sample mean y¯ and sample median y˜; when to use which; what happens with skewed data. (remember the study where you have to wait until patients have an event occur like moving to stage 2 of a disease and that can take a long time to happen … this is where you may have to use the median instead of the mean) and (with skew, check to see if there were any outliers, then read on) 2.4 Five number summary and boxplots; IQR; outliers. Week 2 notes Elementary Statistics for the Biological and Life Sciences Lecture and HW (homework) 2.5 Looking for association: categorical-categorical, categorical-numeric, numeric-numeric. 2.6 Measures of spread/dispersion: range, IQR, and s; empirical rule for y¯ & s. 2.8 Inference: parameter vs. statistic. And this intense looking formula is just using something called a limit (which is explored a little more in calculus) but at a basic sense a limit is saying as the number of something continues until infinity (getting bigger and bigger). The main point should be that you take the number of times something occurs and divide it by the total amount of times that something occurs to get the sample probability. More notes/addendum: (my handwriting is not the best, so I have typed out what is included but thought I would include this anyways) A contingency table Standard deviation tells about the distance from the mean. It is the square root of the variance. Empirical rule: 68% one standard deviation each way 95% two standard deviations each way 99% three standard deviations each way Week 2 notes Elementary Statistics for the Biological and Life Sciences Lecture and HW (homework) Week 2 notes Elementary Statistics for the Biological and Life Sciences Lecture and HW (homework)

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