Cheat sheet 1 - Population A set of items (experimental...

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Population A set of items (experimental units) under study Parameter (Variable) A descriptive measure of the population that is of interest e.g. the mean (Typically Unknown -- Use Greek letters) (Random) Sample A (random) subset chosen from the population Statistic A descriptive measure that is calculated from the sample, e.g. the sample mean (Use regular (Roman) letter) Purpose of Inferential Statistics Making inferences about a parameter (Symbol – μ ) of a population based on information obtained from a statistic of the sample. The confidence level is the proportion of times that an estimation procedure will be correct. = U The significance level measures how frequently the conclusion will be wrong in the long run. = 1-u Interval Values are real numbers. All calculations are valid. Data may be treated as ordinal or nominal. Ordinal Values must represent the ranked order of the data. Calculations based on an ordering process are valid. Data may be treated as nominal but not as interval. Nominal Values are the arbitrary numbers that represent categories. Only calculations based on the frequencies of occurrence are valid. Data may not be treated as ordinal or interval. We can summarize the data in a table that presents the categories and their counts called a frequency distribution. Number. Bar Chart. A relative frequency distribution lists the categories and the proportion with which each occurs. Percentage. Pie chart. The most important graphical method is the histogram . The histogram is not only a powerful graphical technique used to summarize interval data, but it is also used to help explain probabilities. Skewness A skewed histogram is one with a long tail extending to either the right or the left: Modality A unimodal histogram is one with a single peak , while a bimodal histogram is one with two peaks : How two interval variables are related - scatter diagram , which plots two variables against one another. The independent variable is labeled X and is usually placed on the horizontal axis, while the other, dependent variable, Y, is mapped to the vertical axis. The following are typical measures of central tendency for a population Mean - the average Median - the middle observation after the data has been ordered Mode - the observation that occurs most often If a distribution is symmetrical , the mean, median and mode coincide If a distribution is non symmetrical, and skewed to the left or to the right, the three measures differ. Negative – skewed to the left. Measures of Variability Population Variance σ 2 ; Standard Deviation σ Sample Range Variance s 2 ; Standard Deviation s When we are talking about a sample, the range is the difference between the highest and lowest observation POPULATION VARIANCE (σ 2 ) Averages the squares of the differences
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Cheat sheet 1 - Population A set of items (experimental...

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