Week 3 PSYC*1010(02) Online Quiz PDF

Week 3 PSYC*1010(02) W25 Skylar J. Laursen, MSc Online Quiz 1 Average: Mean = 84.21 Median = 84.38 Mode = 90.63 What type of distribution is this? Standard Deviation: 7.92 Range: 40.62 2 Online Quiz 1 – Type...

Week 3 PSYC*1010(02) W25 Skylar J. Laursen, MSc Online Quiz 1 Average: Mean = 84.21 Median = 84.38 Mode = 90.63 What type of distribution is this? Standard Deviation: 7.92 Range: 40.62 2 Online Quiz 1 – Types of Scales Determining a person’s reaction time (in milliseconds would involve measurement of a(n) ______ scale of measurement? RATIO The participants in a research study are classified as high, medium, or low in self-esteem. This classification involves measurement on a nominal scale. FALSE 3 Online Quiz 1 – Types of Studies In a correlational study, _____. TWO VARIABLES ARE MEASURED AND THERE IS ONLY ONE GROUP OF PARTICIPANTS 4 Correlational Study Examines the relationship between 2 variables Example: Number of classes attended and final grade 100 90 Final Grade 80 70 60 50 10 20 30 Number of classes attended 5 Online Quiz 1 – Types of Studies In a correlational study, _____. TWO VARIABLES ARE MEASURED AND THERE IS ONLY ONE GROUP OF PARTICIPANTS In the simplest experimental study, _____. ONE VARIABLE IS MEASURED AND TWO GROUPS ARE COMPARED 6 Experimental Study The goal of an experimental study is to demonstrate a cause-and-effect relationship between two variables Example: Note taking and quiz performance 100 Quiz Performance 75 50 25 0 type write 7 Group Online Quiz 1 In a research study comparing attitude scores for males and females, participant gender is an example of what kind of variable? A QUASI-INDEPENDENT VARIABLE 8 Central Tendency - Recap A statistical measure to determine a single score that defines the centre of a distribution Goal: to find the single score that is most typical or most representative of the entire group 9 Central Tendency - Recap Mean: A “balance point” – the distances above the mean have the same total as the distances below the mean Population: Sample: Σ$ Σ$ != &= % ' Example: The final grades for a fourth year Example: Professor X wants to examine psychology course at U of G are listed below. Psyc*1010 final grades at the U of G over the Find the Mean. last 4 years. They ask 5 students from each year (1st year, 2nd year, 3rd year, 4th year) to provide Scores: their final grade. Find the Mean. 83, 99, 81, 92, 93, 74, 89, 81, 82, 88, 84, 88, 69, 90, 68, 87, 87, 80, 85, 83 Scores: 75, 100, 52, 58, 82, 91, 73, 72, 60, 87, 74, 65, 80, 59, 90, 46, 60, 86, 85, 50 10 Central Tendency - Recap Mean: A “balance point” – the distances above the mean have the same total as the distances below the mean Median: The middle of the distribution (in terms of scores) X values: 61, 98, 75, 77, 66, 75, 70, 83, 52, 53 11 Central Tendency - Recap Mean: A “balance point” – the distances above the mean have the same total as the distances below the mean Median: The middle of the distribution (in terms of scores) Mode: The score/value that occurs most often X values: 7, 2, 4, 5, 10, 15, 19, 12, 5, 13 12 When to Use Measures of Central Tendency Median: When the data contains extreme scores When the distribution is skewed When there are undetermined or unknown values within the data set When you have an open-ended distribution When you are using an ordinal scale Mode: When you are using a nominal scale Mean: Most common Used in all other instances 13  Central Tendency and the Shape of the Distribution Symmetrical Positively Negatively Distribution: Skewed: Skewed: Mean = Median = Mode Mode < Median < Mean Mean < Median < Mode Mean Median Mode 14 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 15 Variability: The Range Range: the distance covered by the scores in a distribution, from the smallest score to the largest score Common Definition: measures the difference between the largest score (Xmax) and the smallest score (Xmin) ()'*+ = $!"# − $!$% 16 The Range: Example Example 1: A researcher samples 15 students and has them complete an IQ test. Each student’s score is listed below. Calculate the Range of IQ scores IQ Scores: 75, 95, 65, 82, 73, 90, 121, 107, 116, 76, 65, 98, 110, 121, 107 &'()* = ,!"# − ,!$% 17 The Range: Example Example 2: Professor X wants to know how much each student’s exam score changed from Midterm 1 to Midterm 2. He calculates the amount of change for 15 students from his class. Calculate the Range of the change scores. Change Scores: -4, 16, 20, 17, 8, 3, 18, -1, 7, 12, 9, 8, 5, 5, 8 &'()* = ,!"# − ,!$% 18 Standard Deviation and Variance Deviation: the distance from the mean.*/0'102( 342&* = , − 5 Variance: equals the mean of the squared deviations 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 19  The Calculation of Variance and Standard Deviation Example: A researcher wants to investigate how much the number of drinks consumed by her lab members varies. She has each of her five lab members report the number of drinks they consume each week. Number of drinks: 6, 3, 0, 8, 6 Find the deviation (distance from the mean) for each score Add the deviations and compute the average 20  The Calculation of Variance and Standard Deviation Example: A researcher wants to investigate how much the number of drinks consumed by her lab members varies. She has each of her five lab members report the number of drinks they consume each week. Number of drinks: 6, 3, 0, 8, 6 Find the deviation Square each deviation Take the square root of (distance from the mean) the variance for each score Find the average of the Add the deviations and squared deviations The standard deviation compute the average (“variance”) (standard distance from the mean) 21 Measuring Variance and Standard Deviation for a Population Variance: the mean of the squared deviations Find the sum, and then divide by the number of scores -)(.)'/+ = 0+)' 123)(+4 4+5.)6.7' 130 78 123)(+4 4+5.)6.7'1 = '309+( 78 1/7(+1 22 Measuring Variance and Standard Deviation for a Population Variance: the mean of the squared deviations Find the sum, and then divide by the number of scores -)(.)'/+ = 0+)' 123)(+4 4+5.)6.7' 130 78 123)(+4 4+5.)6.7'1 = '309+( 78 1/7(+1 Sum of Squares (SS): sum of the squared deviations 23 Measuring Variance and Standard Deviation for a Population Definitional formula: 66 = Σ(, − 5): 1. Find each deviation score: $ − ! 2. Square each deviation score: ($ − !): 3. Add the squared deviations 24 Measuring Variance and Standard Deviation for a Population Population Variance: represented by the symbol ; : and equals the mean squared distance from the mean Population variance is obtained by dividing the sum of squares (SS) by N Population standard deviation: represented by the symbol ; and equals the square root of the population variance 25 Population Variance and Standard Deviation: Example Example: Nancy works at an ice cream store. She is interested in knowing whether her co-workers eat more or less ice cream than Canadians on average (~4.5 liters/year). She asks each of her co-workers to estimate how many liters of ice cream they consume. Calculate the variance and standard deviation Ice Cream Consumption: 3, 6.5, 9, 7, 8, 7, 6, 5, 5.5, 5 2. Calculate SS (sum of squares) - 4. Calculate = (standard deviation) - = = = : 26 Measuring Variance and Standard Deviation for a Sample The goal of inferential statistics is to use the limited information from samples to draw general conclusions about populations The basic assumption of this process is that samples should be representative of the populations from which they are drawn This assumption poses a special problem for variability because samples consistently tend to be lass variable than their populations Fortunately, the bias in sample variability is consistent and predictable, which means it can be corrected 27 Population Variability 28 Formulas for Sample Variation and Standard Deviation Definitional Formula: 66 = Σ(, − @): Calculating SS for a sample is exactly the same as for a population, except for minor changes in notation After you compute SS, however, it becomes critical to differentiate between samples and populations 29 Formulas for Sample Variation and Standard Deviation Sample Variance: represented by the symbol 3 : and equals the mean squared distance from the mean Sample variance is obtained by dividing the sum of squares (SS) by (' − 1) Sample Standard Deviation: represented by the symbol s and equals the square root of the sample variance 30 Sample Variance and Standard Deviation: Example Example: After Nancy investigate how much ice cream her co-workers consume, she is interested in whether the amount consumed by the customers at the ice cream store is more or less than the Canadian population. Nancy randomly selects the next 10 customers in the ice cream store and has them estimate how many liters of ice cream they consume each year. Calculate the variance and standard deviation Ice cream consumption: 9, 0.5, 4.5, 7.5, 2, 12, 5, 7, 6.5, 5