Week 4 PSYC*1010(02) PDF

Week 4 PSYC*1010(02) W25 Skylar J. Laursen, MSc Online Quiz 2 Average: Mean = 74.04 Median = 72.22 Mode = 72.22 What type of distribution is this? Standard Deviation: 9.05 Range: 52.78 2 Grouped Frequency Di...

Week 4 PSYC*1010(02) W25 Skylar J. Laursen, MSc Online Quiz 2 Average: Mean = 74.04 Median = 72.22 Mode = 72.22 What type of distribution is this? Standard Deviation: 9.05 Range: 52.78 2 Grouped Frequency Distributions For the following distribution, what is the width of each class interval? X f 20-24 2 15-19 5 10-14 4 5-9 1 15, 16, 17, 18, 19 5 3  Frequency Histograms For the distribution in the accompanying graph, Figure 2.1, what is the value of 𝚺𝑿? Σ𝑋 = Σ𝑓𝑋 4 = 1×1 + 2×2 + 4×3 + 2×4 + (1×5) 3 f = 1 + 4 + 12 + 8 + 5 2 = 30 1 X 1 2 3 4 5 4 The Shape of a Distribution What is the shape of the distribution for the following set of data? Scores: 1, 2, 3, 3, 4, 4, 4, 5, 5, 5, 5, 6 4 NEGATIVELY 3 SKEWED 2 1 1 2 3 4 5 6 5 The Mode It is possible to have a distribution of scores where no individual has a score exactly equal to the mode. FALSE The Mode: The only measure of central tendency that corresponds to an actual score in the data The mean and median are both calculated value and often produce an answer that does not equal any score in the distribution 6 Midterm 1 Review 7  Measurement Scales Nominal: Ordinal: Interval: Ratio: Label & categorize A set of categories Ordered categories Ordered categories observations that is organized in that have intervals that have intervals Do not make any an ordered of exactly the same of exactly the same quantitative sequence size size distinctions Ranks observations The zero point is The zero point between categories in terms of arbitrary indicates zero size/magnitude Example: Example: Sex: Temperature (C or F): 1.Male 2.Female -4° -3° -2° -1° 0° 1° 2° 3° 4° Animals: 1.Dog 2.Cat Example: Example: Satisfaction: Time: 1.Very Unsatisfied 2.Unsatisfied 3.Satisfied 4.Very Satisfied 0sec 1sec 2sec 3sec 4sec 5sec Happiness: 8 1.Very Unhappy 2.Unhappy 3.Happy 4.Very Happy  Measurement Scales & Graphs Nominal: Ordinal: Interval: Ratio: Bar Graph 8 Bar Graph Histogram Histogram 7 8 8 8 6 7 Frequency 5 6 7 7 Frequency 4 5 6 6 3 4 Frequency 5 Frequency 2 3 5 1 2 4 4 0 1 3 3 0 g t rd r Ca ste 2 Do 2 Bi m py y y py Ha pp pp 1 ap 1 ap ha Ha nh H Un ry 0 U 0 Ve ry Ve -4 -3 -2 -2 -1 0 1 2 3 4 0 1 2 3 4 5 Bar represent distinct categories Separate bars are used because Histograms or polygons are used you cannot assume that the because the intervals between categories are all the same size scores are the same size 9 Frequency Distribution Tables X f An organized tabulation showing exactly how many individuals are located in each category on the scale of measurement X values: 5, 3, 4, 8, 5, 2, 8, 4, 2, 6, 8, 10 Total 10 Frequency Distribution Tables X f Σ𝑋 = Σ𝑓𝑋 10 1 9 0 8 3 𝑁 𝑜𝑟 𝑛 = Σ𝑓 7 0 6 1 Σ𝑋 𝑀= 5 2 𝑛 4 2 3 1 2 2 1 0 Total N = 12 11 The Weighted Mean Often it is necessary to combine two sets of scores and then find the overall mean for the combined group (Σ𝑋! + Σ𝑋" ) 𝑊𝑒𝑖𝑔ℎ𝑡𝑒𝑑 𝑀𝑒𝑎𝑛 = (𝑛! + 𝑛" ) To calculate the overall mean, we need 2 values: 1. The overall sum of the scores for the combined group (Σ𝑋), and 2. The total number of scores in the combined group (n) 12 The Weighted Mean Unless there are the same number of scores for each group, the overall mean will not be halfway between the original two sample means When the samples are not the same size, one makes a larger contribution to the total group and therefore carries more weight in determining the overall mean 13 The Weighted Mean Samples with the same n Samples with different n’s Professor L wants to examine the weighted mean of Professor L wants to examine the weighted mean of exam scores across sections 01 and 02 of Psyc*1010 exam scores across sections 01 and 03 of Psyc*1010 at at U of G. She collects a sample of 10 students from U of G. She collects a sample of 15 students from each section and has them report their exam grade. section 01 and 5 students from section 03, and has Calculate the weighted mean for the two samples. them report their exam grade. Calculate the weighted mean for the two samples. Section 01: Section 01: 87, 49, 78, 59, 66, 42, 59, 52, 69, 44 60, 63, 47, 72, 80, 59, 80, 65, 67, 62, 72, 62, 73, 54, 59 Σ𝑋! = 605 Σ𝑋! = 975 𝑀! = 60.50 𝑀! = 65.00 Section 02: Section 03: 61, 54, 43, 48, 67, 84, 48, 70, 89, 65 48, 39, 72, 38, 77 Σ𝑋" = 629 Σ𝑋" = 274 𝑀" = 62.90 𝑀" = 54.8 Weighted Mean (MW) = 61.70 Weighted Mean (MW) = 62.45 14 Skewed Distributions and Central Tendency Measures Positively Skewed Negatively Skewed 15 Skewed Distributions and Central Tendency Measures What is the shape of the following distribution? Scores: 69, 70,70,70,70,71,71,71, 72,72, 73, 75 POSITIVELY 4 SKEWED 3 2 1 69 70 71 72 73 74 75 16 Variability Variability: provides a quantitative measure of the differences between scores in a distribution and describes the degree to which the scores are spread out or clustered together Describes the distribution Measures how well an individual score (or group of scores) represents the entire distribution 17 Variability Deviation: the distance from the mean 𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 𝑠𝑐𝑜𝑟𝑒 = 𝑋 − 𝑚𝑒𝑎𝑛 Sum of Squares: the sum of the squared deviation scores 𝑆𝑆 = Σ(𝑋 − 𝑚𝑒𝑎𝑛)" Variance: provides a measure of the average squared distance from the mean 18 Population Variability vs. Sample Variability Population: Sample: Variance: sum of the squared deviations Variance: sum of the squared deviations (SS) divided by N (SS) divided by (n-1) 𝑆𝑆 𝑆𝑆 𝜎" = 𝑠" = 𝑁 (𝑛 − 1) 19 Population Variability vs. Sample Variability 20 Variability Deviation: the distance from the mean 𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 𝑠𝑐𝑜𝑟𝑒 = 𝑋 − 𝑚𝑒𝑎𝑛 Sum of Squares: the sum of the squared deviation scores 𝑆𝑆 = Σ(𝑋 − 𝑚𝑒𝑎𝑛)" Variance: provides a measure of the average squared distance from the mean Standard Deviation: the square root of the variance Provides a measure of the standard, or average distance from the mean 21 Population Variability vs. Sample Variability Population: Sample Standard Deviation: square root of the Standard Deviation: square root of the variance variance 𝜎= 𝜎" 𝑠= 𝑠" 22 Example: Jenna is a first-year master’s student and wants to know how many papers her supervisor will require her to read per week. She asks each person in her lab how many research papers they read per week on average. Calculate the mean and standard deviation and indicate these on Jenna’s histogram 3 1. Calculate the Mean 2 2. Calculate the Sum of Squares 3. Calculate the Variance 1 4. Calculate the Standard Deviation 5. Indicate the Mean and Standard Deviation on the histogram 1 2 3 4 5 23  Mean Mean: Σ𝑋 = Σ𝑓𝑋 3 2 𝑁 = Σ𝑓 1 Σ𝑋 𝜇= 1 2 3 4 5 𝑁 24  Sum of Squares, Variance & Standard Deviation Sum of Squares: 𝑆𝑆 = Σ(𝑋 − 𝜇)" 3 2 Variance: 1 " 𝑆𝑆 𝜎 = 1 2 3 4 5 𝑁 Standard Deviation: 𝜎= 𝜎" 25 Adding Mean and Standard Deviation to the Histogram 𝜇 = 3.38 3 𝜎 = 1.50 𝜎 = 1.50 2 1 1 2 3 4 5 26