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# Exam 1 Study Guide Stat 239

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This 18 page Study Guide was uploaded by an elite notetaker on Thursday September 17, 2015. The Study Guide belongs to Stat 239 at St. Cloud State University taught by Diane Lovett in Summer 2015. Since its upload, it has received 54 views. For similar materials see Statistics for the Biological and Physical Sciences in Statistics at St. Cloud State University.

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Date Created: 09/17/15

Statistics for Biology Exam 1 Study Guide Compiled by Brook Hoffman Chapter 1 0 Section 1 0 Data Set of measurements taken in a set of individual units 0 Each Case row in dataset 0 Each Variable Column in data set 0 Explanatory variable x predicts the response variable y 0 Section 2 0 Population all individuals or objects of interest 0 Sampl all the cases that data was collected on A subset of the population 0 Statistical inference using data from a sample to gain information about the population 0 Sampling Bias Occurs when the method of selecting a sample causes the sample to differ from the population in some relevant way 0 Random Sampling Avoid sampling bias only thing trusted when making population generalizations Simple Random Sample Each unit has the same chance of being selected regardless of other units chosen for the sample 0 Realities of Sampling Random is ideal but often unfeasible Generalizations are limited to the population that was sampled from o NonRandom Samples Targeting a specific group 0 Bad sampling methods Sampling based on a related variable Volunteer Bias Poor Question wording Context Inaccurate Responses 0 Section 3 Experiments and Observations 0 Associated values of one variable tend to be related to values of the other variable 0 Causally associated changing the value of the explanatory variable influences the value of the response variable 0 Confounding Variable 2 variables that are not actually related they just follow each other closely Section 4 Study Design 0 Control Group No variables to find base line results 0 Placebo Effect the thought that something causes a change even though you didn t actually receive it 0 Double Blind Neither the researchers administering the test nor the patients are aware of which treatment the patient is actually getting placebo or real Chapter 2 0 Section 1 Categorical Variables 0 Usually have a fixed number of potential categories that individuals will fall into Example The color of a marble eg red green blue 1 variable can be displayed with a Frequency Table or a Bar Chart 0 Proportion Number in CategoryTotal Sample Size Proportion for sample 5 phat 0 Measures of Center typical values m 0 Population mean u 0 Sample mean sensitive to extreme outliers Median the 50th Percentile Specify population or sample m o resistant to influence of outliers 0 Measures of Spread Standard Deviation Population SD 6 0 Sample SD s 0 Measurement of the average distance of a point to the mean 0 Range Max Min Interquartile Range IQR 0 Based on percentiles 50th percentile median o Percentile percentage that lies below a value 0 Five Number Summary Minimum 3901 25th percentile Median QB 75th percentile Maximum 0 Section 2 Quantitative Variables 0 Shape Riqht Skewed Data meangt median Left Skewed Data meanltmedian Mean is pulled in direction of skew o Symmetric Data mean zmedian o Boxplot Picture of the 5 number summary often with possible outliers separated out l l Section 3 95 Rule 0 95 Rule If the distribution of the data set is approximately normal then 95 of the observations will fall within 2 STD Dev from the mean Only works for large samples Gives central 95 and 25 on each side to exclude any extreme outliers Section 4 Zscores 0 2 Scores The zscore for an observation is the number of STD Dev that observation lies from the mean 2 xm 0 Z Zscore o Xobservation o M mean SSTD Dev If a distribution is normal it will have 0 Zscore of 2 in 975th percentile o Zscore of 2 in 25th percentile 0 Section 5 Correlation 0 Correlation Measures the strength of the linear relationship between 2 quantitative variables How closely a scatterplot follows a straight line 1 perfect negative line 0 no linear relationship E1 perfect positive line sample correlation r population correlation p Greek ro Any set of pairs of numeric variables can be measured for correlation X and y cannot explain each other Cannot conclude causation NO MATTER WHAT o r correlation coefficient 11 0 Find r2 value take square root 0 r2 coefficient of determination 01 0 The proportion of the variability in y that can be explained by the fit to a line with x o 1 00 percentage of variance due to regression Least Squares Linear Regression 0 Line of best fit 0 Ypredicted slope x y intercept Q Residuals For a linear fit this is the yobserved ypredicted for a given x yslopex intercept An average residual of 0 means the points and line match up fairly close Usually presented in a scatterplot next to the data plot Don t want to see 0 Signs of poor fit 0 Trend in residuals may indicate nonlinear 0 Large residuals outliers pulls line to compensate for residuals 0 General Form of describing a slope As x increases by one unit then y changes by the slope in units Interpretation of the linear relationship should not go beyond the observed range because the linear relationship cannot be assumed to continue 0 Features of all linear regression o The mean point is always a point of the predicted line 0 Regression to the mean ZScore ZyrZX 0 Extreme values in one variable tend to get less extreme in the other variable Chapter Only Vocab will be included on Test 0 Section 1 Sampling Distributions 9 Sampling Distribution set of the sample drawn from a population 0 Population All the subjects you might be interested in studying 0 Sample Subjects drawn from the population Also called a subset of a population Symbol Term M Population Mean Population Parameter 57C Sample Mean Sample Statistic 0 Parameter value belonging to the entire population of interest It is often unknown 0 CorrespondingSample Statistic point estimate Q Estimation of parameter Statistics for Biology Exam 1 Study Guide Compiled by Brook Hoffman Chapter 1 0 Section 1 0 Data Set of measurements taken in a set of individual units 0 Each Case row in dataset 0 Each Variable Column in data set 0 Explanatory variable x predicts the response variable y 0 Section 2 0 Population all individuals or objects of interest 0 Sampl all the cases that data was collected on A subset of the population 0 Statistical inference using data from a sample to gain information about the population 0 Sampling Bias Occurs when the method of selecting a sample causes the sample to differ from the population in some relevant way 0 Random Sampling Avoid sampling bias only thing trusted when making population generalizations Simple Random Sample Each unit has the same chance of being selected regardless of other units chosen for the sample 0 Realities of Sampling Random is ideal but often unfeasible Generalizations are limited to the population that was sampled from o NonRandom Samples Targeting a specific group 0 Bad sampling methods Sampling based on a related variable Volunteer Bias Poor Question wording Context Inaccurate Responses 0 Section 3 Experiments and Observations 0 Associated values of one variable tend to be related to values of the other variable 0 Causally associated changing the value of the explanatory variable influences the value of the response variable 0 Confounding Variable 2 variables that are not actually related they just follow each other closely Section 4 Study Design 0 Control Group No variables to find base line results 0 Placebo Effect the thought that something causes a change even though you didn t actually receive it 0 Double Blind Neither the researchers administering the test nor the patients are aware of which treatment the patient is actually getting placebo or real Chapter 2 0 Section 1 Categorical Variables 0 Usually have a fixed number of potential categories that individuals will fall into Example The color of a marble eg red green blue 1 variable can be displayed with a Frequency Table or a Bar Chart 0 Proportion Number in CategoryTotal Sample Size Proportion for sample 5 phat 0 Measures of Center typical values m 0 Population mean u 0 Sample mean sensitive to extreme outliers Median the 50th Percentile Specify population or sample m o resistant to influence of outliers 0 Measures of Spread Standard Deviation Population SD 6 0 Sample SD s 0 Measurement of the average distance of a point to the mean 0 Range Max Min Interquartile Range IQR 0 Based on percentiles 50th percentile median o Percentile percentage that lies below a value 0 Five Number Summary Minimum 3901 25th percentile Median QB 75th percentile Maximum 0 Section 2 Quantitative Variables 0 Shape Riqht Skewed Data meangt median Left Skewed Data meanltmedian Mean is pulled in direction of skew o Symmetric Data mean zmedian o Boxplot Picture of the 5 number summary often with possible outliers separated out l l Section 3 95 Rule 0 95 Rule If the distribution of the data set is approximately normal then 95 of the observations will fall within 2 STD Dev from the mean Only works for large samples Gives central 95 and 25 on each side to exclude any extreme outliers Section 4 Zscores 0 2 Scores The zscore for an observation is the number of STD Dev that observation lies from the mean 2 xm 0 Z Zscore o Xobservation o M mean SSTD Dev If a distribution is normal it will have 0 Zscore of 2 in 975th percentile o Zscore of 2 in 25th percentile 0 Section 5 Correlation 0 Correlation Measures the strength of the linear relationship between 2 quantitative variables How closely a scatterplot follows a straight line 1 perfect negative line 0 no linear relationship E1 perfect positive line sample correlation r population correlation p Greek ro Any set of pairs of numeric variables can be measured for correlation X and y cannot explain each other Cannot conclude causation NO MATTER WHAT o r correlation coefficient 11 0 Find r2 value take square root 0 r2 coefficient of determination 01 0 The proportion of the variability in y that can be explained by the fit to a line with x o 1 00 percentage of variance due to regression Least Squares Linear Regression 0 Line of best fit 0 Ypredicted slope x y intercept Q Residuals For a linear fit this is the yobserved ypredicted for a given x yslopex intercept An average residual of 0 means the points and line match up fairly close Usually presented in a scatterplot next to the data plot Don t want to see 0 Signs of poor fit 0 Trend in residuals may indicate nonlinear 0 Large residuals outliers pulls line to compensate for residuals 0 General Form of describing a slope As x increases by one unit then y changes by the slope in units Interpretation of the linear relationship should not go beyond the observed range because the linear relationship cannot be assumed to continue 0 Features of all linear regression o The mean point is always a point of the predicted line 0 Regression to the mean ZScore ZyrZX 0 Extreme values in one variable tend to get less extreme in the other variable Chapter Only Vocab will be included on Test 0 Section 1 Sampling Distributions 9 Sampling Distribution set of the sample drawn from a population 0 Population All the subjects you might be interested in studying 0 Sample Subjects drawn from the population Also called a subset of a population Symbol Term M Population Mean Population Parameter 57C Sample Mean Sample Statistic 0 Parameter value belonging to the entire population of interest It is often unknown 0 CorrespondingSample Statistic point estimate Q Estimation of parameter

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