descriptive stat hand

# descriptive stat hand - Descriptive Statistics Central...

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Descriptive Statistics Central Tendency Variability Shape PSY 2801: Summer 2010 Descriptive Statistics Jeﬀ Jones University of Minnesota Jeﬀ Jones Chs 4 and 5 Descriptive Statistics Central Tendency Variability Shape Descriptives versus Inferentials There are two major types of statistics that we will encounter in this course: 1 Descriptive Statistics e.g. mean, median, mode, range, variance, standard deviation, quartiles, midspread, skew, kurtosis, correlation The ﬁrst 10 describe distributional properties of 1 variable The last 1 describes relational properties between 2 variables 2 Inferential Statistics e.g. z, t, χ 2 , F These try to get at how representative our sample is of a hypothesized population Jeﬀ Jones Chs 4 and 5 Descriptive Statistics Central Tendency Variability Shape Descriptives versus Inferentials What do descriptive statistics . .. describe? Descriptive statistics can apply to both the sample and the population 1 Population: μ , σ 2 , ρ 2 Sample: ¯ x , s x , r xy Often, you will see a subscript “N”, indicating sample values e.g. ¯ x N This indicates that the average is only applied to the “N” people in the sample Furthermore, if a descriptive statistics will be used to test an inference, statisticians often put a hat over the parameter e.g. ˆ μ = ¯ x This indicates that ¯ x will be used to estimate the parameter value μ Jeﬀ Jones Chs 4 and 5 Notes Notes Notes

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Descriptive Statistics Central Tendency Variability Shape Sum-things Important There are two mathematical things you should know: N X i = 1 blah i That math statement says “take the N observations of blah and sum them” blah could be anything: x i or ( x i - ¯ x ) 2 or 2 + 3 x i - x 2 i 4 x 3 i Just form the particular observation, make a table, and sum. Jeﬀ Jones Chs 4 and 5 Descriptive Statistics Central Tendency Variability Shape Sum-things Important So let’s say we have observations: x = { 3 , 5 , 2 , 4 , 7 } and we want to ﬁnd: N i = 1 ( x 2 i + x i + 2 ) Jeﬀ Jones Chs 4 and 5 Descriptive Statistics Central Tendency Variability Shape Sum-things Important First: write down each piece of “blah” that you are trying to ﬁnd x i x 2 i x 2 i + x i + 2 3 5 2 4 7 Jeﬀ Jones Chs 4 and 5 Notes Notes Notes
Descriptive Statistics Central Tendency Variability Shape Sum-things Important Second: ﬁll in the remaining pieces for each observation x i x 2 i x 2 i + x i + 2 3 9 14 5 25 32 2 4 8 4 16 22 7 49 58 Jeﬀ Jones Chs 4 and 5 Descriptive Statistics Central Tendency Variability Shape Sum-things Important Third: sum down the column that contains “blah” for each observation x i x 2 i x 2 i + x i + 2 3 9 14 5 25 32 2 4 8 4 16 22 7 49 58 N X i = 1 blah i = N X i = 1 ( x 2 i + x i + 2 ) = 14 + 32 + 8 + 22 + 58 = 134 Jeﬀ Jones Chs 4 and 5 Descriptive Statistics Central Tendency Variability Shape Rules of Summation Here are some rules of summation: 1 ( x i + y i ) = x i + y i 2 ( x i - y i ) = x i - y i 3 ( cx i ) = c x i 4 ( x i + c ) = x i + Nc 5 ( x i y i ) 6 = x i y i 6 x 2 i 6 = ( x i ) 2 7 ( x i + y i ) 2 = x 2 i + y 2 i + 2 ( x i y i ) Jeﬀ Jones Chs 4 and 5

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## This note was uploaded on 10/08/2010 for the course PSY 2801 taught by Professor Guyer during the Summer '08 term at Minnesota.

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descriptive stat hand - Descriptive Statistics Central...

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