PSYC 2019H Lecture 2 Handout PDF

PSYC 2019H – Lecture 2 Central Tendency and Variability Visual Displays of Data Central Tendency Variability  Visual Displays of Data Sca;erplot  Visual Displays of Data Line Graph Wood et al. 1992 Nightmares about earthquakes following large 1989 San Francisc...

PSYC 2019H – Lecture 2 Central Tendency and Variability Visual Displays of Data Central Tendency Variability  Visual Displays of Data Sca;erplot  Visual Displays of Data Line Graph Wood et al. 1992 Nightmares about earthquakes following large 1989 San Francisco earthquake  Visual Displays of Data Bar Graph Figure 3-6  Visual Displays of Data Country Years of Education Country Years of Education Argentina 10 Grenada 9 Azerbaijan 11 Guyana 8 Belarus 12 Honduras 7 Belgium 12 Ireland 13 Belize 11 Micronesia 8 Botswana 10 Palau 12 Bulgaria 12 Panama 10 Canada 13 Papua New Guinea 5 Chad 2 Samoa 10 Congo 7 Sao Tome and Principe 6 Cuba 12 Sudan 4 Czechia 13 Switzerland 13 El Salvador 7 United States 13 Finland 12 Yemen 3  Visual Displays of Data Dot Plot Figure 3-9 Visual Displays of Data  Central Tendency Mean – “… the arithmeGc average of a group of scores” (Nolan & Goedert, 2024, p. 93). 2, 4, 6, 9, 2, 4 1 2 3 4 5 6 7 8 9  Central Tendency Mean – “… the arithmeGc average of a group of scores” (Nolan & Goedert, 2024, p. 94). Number Used for … Symbol Pronounced Table 4-1 Statistic Sample M or X bar “M” or “X bar” Parameter Population μ “Mew” Figure 4-3  Central Tendency Median – “… the middle score of all the scores in a sample when all the scores are arranged in ascending order. If there is no single middle score, the median is the mean of the two middle scores” (Nolan & Goedert, 2024, p. 95).  Central Tendency Median – What is the median of these scores? 1, 5, 7, 9, 7  Central Tendency Median – What is the median of these scores? 1, 5, 8, 9, 6, 8, 9, 3  Central Tendency Mode – “The most common score in a sample” (Nolan & Goedert, 2024, p. 97). 1, 2, 3, 5, 6, 6, 6, 6, 8, 9 1, 2, 2, 4, 5, 5, 7, 8, 9, 10 1, 1, 2, 3, 4, 4, 6, 7, 9, 9, 10  Central Tendency Aron, Coups, and Aron (2013)  Wilcox (2009): An investment [rm is trying to recruit you. They tell you the average salary of the 12 people at their [rm is $84,583. $25,000 $28,000 Here are the data: $29,000 $30,000 $30,000 What is the median? $31,000 $32,000 If we change the last number to $800,000? $35,000 What is the median? $36,000 $39,000 $200,000 What is the mean? $500,000 13  Central Tendency Trimmed Means Discard a porGon of the data from each end  12 values x.10 = 12 va lu es Original Data x. 10% Trimmed Data 20 20 % $25,000 $25,000 $25,000 $25,000 = Tr im $28,000 $28,000 $28,000 m $28,000 ed $29,000 $29,000 $29,000 Da $29,000 ta $30,000 $30,000 $30,000 $30,000 $30,000 $30,000 $30,000 $30,000 $31,000 $31,000 $31,000 $31,000 $32,000 $32,000 $32,000 $32,000 $35,000 $35,000 $35,000 $35,000 $36,000 $36,000 $36,000 $36,000 $39,000 $39,000 $39,000 $39,000 $200,000 $200,000 $200,000 $200,000 $500,000 $500,000 $500,000 $500,000  Measures of Variability Variability “… is a numerical way of describing how much spread there is in a distribuGon” (Nolan & Goedert, 2024, p. 103). Why is Variability Important? Measures of central tendency do not tell the whole story  38 35 30 30 26 23 Frequency Frequency 18 15 15 15 9 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 Age Age 35 35 26 26 Frequency 18 Frequency 18 9 9 2 3 4 3 2 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 Age Age Which Lecturer would you prefer?  Measures of Variability Range “… is a measure of variability calculated by subtracGng the lowest score (the minimum) from the highest score (the maximum)” (Nolan & Goedert, 2024, p. 103).  Variability InterquarTle Range (IQR) “… is a measure of the distance between the [rst and third quarGles” (Nolan & Goedert, 2024, p. 104). First QuarTle (Q1) “… marks the 25th percenGle of a data set” (Nolan & Goedert, 2024, p. 104). Third QuarTle (Q3) “… marks the 75th percenGle of a data set” (Nolan & Goedert, 2024, p. 105). An example with more numbers… 1 2 3 4 5 5 7 9 9 11 13 53 1 2 3 4 5 5 7 9 9 11 13 53  Measures of Variability Variance – “…the average of the squared deviaGons from the mean” (Nolan & Goedert, 2024, p. 106). – DeviaTon from the mean (deviaTon): “… is the amount that a score in a sample diaers from the mean of the sample” (Nolan & Goedert, 2024, p. 107).  Measures of Variability Variance (SD2): Steps 1) Calculate mean 2) Compute ‘deviaGon scores’: Subtract mean from each observaGon 3) Square the deviaGon scores 4) Compute the ‘sum of squares (SS)’: Sum the squared deviaGon scores 5) Divide the SS by N  Measures of Variability Standard DeviaTon – “…the square root of the average of the squared deviaGons form the mean; it is the typical amount that each score varies, or deviates, from the mean” (Nolan & Goedert, 2024, p. 109). Square root of the variance  Measures of Variability The variance or standard deviation of a sample is an example of a statistic, whereas the variance or standard deviation of a population is an example of a parameter. The symbols we use depend on whether we are referring to the spread of a sample or of a population. Standard Deviation Number Used for... Pronounced Variance Symbol Pronounced Symbol Statistic Sample SD or s As written SD2, s2, or MS Letters as written; if there is a superscript 2, the term is followed by “squared” (e.g., “ess squared”) Parameter Population σ “Sigma” σ2 “Sigma squared” Table 4-2  2.4 1.4 Variance -0.6 -1.6 -1.6 Standard DeviaGon