Class Notes 5 - A parameter (μ) is a measurable characteristic of the population, such as the PDF

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A parameter (μ) is a measurable characteristic of the population, such as the mean or the standard deviation and a statistic () is a characteristic of a sample. ...

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1. Parameters, statistics - A parameter (μ) is a measurable characteristic of the population, such as the mean or the standard deviation. The parameter is usually the unknown and what we calculate are ´ ) is a estimates of the parameter, which we call statistics. In contrast, a statistic ( X characteristic of a sample, such as the sample mean (estimate of the real population mean), or sample deviation. 2. Descriptive statistics, inferential statistics - Descriptive statistic describes or summarizes a large amount of data (mean, median, interquartile range, standard deviation). Inferential statistics deals with how we can draw the best possible conclusion about a population, from the study of a carefully designed sample, that is drawn from that population (asks how do we use a sample to say something about a population? There are also two schools of thought in terms of inferential statistics  Frequentist statistics V Bayesian statistics  Frequentist statistics is based on thought experiments; we will flip a coin to see how many time we get heads or tails, but we cannot launch a rocket 100 times to see its success rate, so Bayesians will say there is a limited usefulness to frequentist statistics. Instead, they ask what do we know? They take data (prior estimates) and use actual observations instead of theoretical thought experiments. Descriptive statistics for all variables Frequency tables, Mode Median, Percentile Descriptive statistics for ordinal, interval, and ratio scales Mean, Variance, Standard deviation, Descriptive statistics for interval and ratio scales Coefficient of variation Descriptive statistics for nominal scales Cross tabulation Graphs to describe data Bar, Box plot, Histogram, Pie

3. Mean, mode, median, standard deviation, variance, percentile - The mean is the sum of all observations divided by the number of observations. The ΣN X (N is the population size). The calculation of the Population Mean (μ) ¿ i=1 i N calculation of the sample mean is the sum of all the elements in the sample divided by the Σn X sample size (n)  Sample Mean ´x = i=1 i . The mode is the most common value in the n variable and can be used for both categorical and continuous variables. The mode is sometimes called a Measure of central tendency, but it could be at the low or high end of the distribution of a variable (3 measures of central tendency are the mode, median, and range). The median is the observation that falls in the middle when the variables are ranked from low to high. Measures of dispersion include the range (difference between greatest/ smallest value), variance, and standard deviation. The variance is a measure of how spread out the values of one variable are from their mean.

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