Stat 371 1nd EditionExam # 1 Study Guide Lectures: 1 - 12Lecture 1 (Wed, 9/3)Why do we have to take this class? -Stats are in all medical articles-Stats prove/disprove all hypothesesWhat stats does:- Stats takes a random sample from a population in order to make an inference about a particular problem- Population: all subjects of interest- Sample: subset of population; some of subjects of interest- Inference: info from sample to draw conclusions about a population- Random sample: where every member of the population has the same chance of being chosen independently of each otherLecture 2 (Fri, 9/5) - Statistics: numerical measurement derived from sample data; numerical letters: s, s^2, x^2- Parameter: numerical measure derived from the population; greek leters: -, -^2, μo We use statistics to infer something about parameter- Descriptive statistics: describe a set of data (sample)- Variable: characteristic of a subject that can be assigned # or categoryo Categorical: “in categories” Ordinal: “order;” rank matters Nominal: order doesn’t mattero Numeric: “numbers” Continuous: can take the form of any real number on number line Discrete: only can take specific values (1,2,3,4..)- Observational Unit: item on which a variable measure is taken; what is the thing that you measure variable on- Frequency Distribution: a graphical representation of the number of times a particular unit occurs; similar to a bar chart; aka histogramo Shows us: where the middle is, where most of the data lies, spread of the data- How to make a frequency distribution:o X-axis Bins: either the categories of the data/intervals of #’s that the data takeo Y-axis: Frequency: # of times a # from that bin occurs OR Relative Frequency: % of times a # from that bin occurs (Frequency/n)- Shapes of frequency distribution (6)o Unimodal: has one mode Mode: a central peak; bin where the greatest # of data occurso Symmetric: same on both sideso Biomodal: has two modeso Exponential: an extremely right skewed distribution; left most pt is the highest and it decreases as it moves righto Right skewed: there is a longer right tail; mean is higher than the mediano Left skewed: there is a longer left tail; mean is lower than the medianLecture 3 (Mon, 9/8) - Median: the value that lies in the center of the data; split data into 2 equal parts- Mean: average; denoted by x and μo X bar is a statistic (sample); μ is a parameter (population)- Quartiles: median not included in q1 and q2o Q1: median of the lower half of data seto Q2: median of entire data seto Q3: median of the upper half of data set- Interquartile range (IQR): the difference between Q3 and Q1; 50% of data- Boxplot: visual representation of a data set using the Q1, Q2, and Q3, min, and max- Modified boxplots: account for outliers: data pts that don’t fit w/the other data ptso Lower fence (left whisker): whichever is bigger: min of data or Q1-(1.5*IQR)o Upper fence (Right whisker): whichever is smaller: max of data or Q3+(1.5*IQR)o If a number in data set falls outside of fences, the it is denoted by an *.Lecture 4 (Wed, 9/10) - Range: the difference between the max and min numbers in a data set- Deviation: the difference between a data point and the mean, squaredo(xi-x)2- variance: average of the squared deviations, denoted as s2 (statistic) or σ2 (parameter)oΣ(xi-x)2 / (n-1)- Standard deviation: (√(s2)) a unit of measurement in statistics, denoted by s or μ- Empirical rule: about 68% of observations fall within 1 SD of the x ± soAbout 95% of observations fall within 2 SD of the x ± 2soAbout 99% of observations fall within 3 SD of the x ± 3s- Coefficient of variation: the standard deviation expressed as a percentage of the meano(s/x) * 100% Interpretation: the standard deviation is --- as large as the meanLecture 5: Probability (Fri, 9/12) - Probability: a numerical quantity that expresses the likelihood of an event- Experiment: a process or study which results in the collection of data- Outcome: a possible result of an experiment- Event: any set of outcomes in an experiment- Sample Space: the set of all possible outcomes in an experiment- To find Probabilityo (#outcomes in the event)/(#outcomes in the sample space)o Notation: P(A)- Complement: probability of an event NOT occurringo Notation: (A)o P(A)= 1- P(A)- Either A or B happens: A U B- A and B happens: A Ω B- Mutually Exclusive: two events have no interaction probability of A intersect B = 0- Conditional Probability: probability can change when we condition it on another event occurring. Notation: P(A⁄B)o ⁄=giveno The probability of event A happening given event B has occurred- Identifying mathematical expressions in word problems:o Label events with letters that represent themo Try to figure out what type of probability it is (union, intersection, conditional)o “And” =interactionso “IF” and “GIVEN” typically represent conditional probabilitieso “OR” represents union- For events to be independent, the outcome of one event doesn’t affect the outcome of the other eventso 2 events are considered independent of one
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