University:
College
Course:
College Statistics
Academic year:

2021
Views:

487

Pages:

52
Author:

anjaranaye8

Correlation When one trait or behavior accompanies another, we say the two correlate. Correlation Coefficient (r) Correlation Coefficient is a statistical measure of relationship between two variables. • +/- 1 Indicates strength of relationship (0.00 to 1.00) r = + 0.37 Indicates direction of relationship (positive or negative) A. Which correlation coefficient is the strongest? Example 1 a. +.95 b. +.75 Example 2 a.-.45 b.-.15 B. Match the correct scatterplots 1. Which ones are positively correlated? 2. Which ones are negatively correlated? 3. Which one has strong negative correlation? 4. Which one has moderately positive correlation? 5. Which one has no correlation? A B D E C WHS AP Psychology Unit 1: Science of Psychology Essential Task 1-8: Apply basic statistical concepts to explain research findings: - Descriptive Statistics: Central Tendency (mean, median, mode, skewed distributions) Variance ( range, standard deviation, and normal distributions) - Inferential Statistics: Statistical significance (ttest and p-value) Approaches Growth of Psych to Psych Careers The Science of Psychology Ethics Research Statistics Methods Sampling Descriptive Correlation Naturalistic Observation Case Study Survey Experiment Descriptive Central Tendency Inferential We are here Variance Essential Task 1-: Outline • Descriptive Statistics: – Central Tendency • Mean, median, and mode • skewed distributions – Variance • Range • standard deviation • normal distributions • Inferential Statistics: – Statistical significance • t-test and the p-value – Confidence intervals Statistical Reasoning Statistical procedures analyze and interpret data and let us see what the unaided eye misses. Composition of ethnicity in urban locales Descriptive Statistics • Summarizes numbers so they became more meaningful and easier to communicate to others – Describes data – Measures central tendency Central Tendency • Tendency of scores to congregate around some middle variable • A measure of central tendency identifies what is average or typical in a data set Measures of Central Tendency Mode: The most frequently occurring score in a distribution. - Easy to obtain, but often reliable Mean: The arithmetic average of scores in a distribution obtained by adding the scores and then dividing by their number. - sensitive to extremely high and low numbers (skews the data) Median: The middle score in a rankordered distribution. C. Find the central tendencies 1, 2, 3, 3,3, 4, 5, 6, 7 Mean: Median: Mode: But the mean doesn’t work in a skewed distribution The Median is a much better measure of the center Measures of Variation •Statistical dispersion (how distributed the data points are) is a key concept in statistics. •Two key ways of measuring statistical dispersion »Range »Standard Deviation 1. Range •The range simply gives the lowest and highest values of a data set. D. Sample Questions • What is the range between 4 to 25? • What is the range between 5, 7, 8, 10? 2. Standard Deviation •Standard deviation gives a measure of dispersion. •Essentially, they are measures of the average difference between the values. •Low deviation means scores are compressed •High deviation means scores are spread out •Standard deviation gives a value that is directly comparable to your mean values. Standard Deviation: 15 +15 +15 +15 E. Sample Questions The mean in an IQ test is 100 . the Standard Deviation is 15. 1.What is Jake’s IQ if he is 2 Standard Deviation above the mean? 2.What is Finn’s IQ if he is 1 Standard Deviation below the mean? 3. If John Cena’s IQ score is 85 and the mean is 100 and the S.D. is 5, which Standard deviation does he fall under? E. Sample Questions Example: If Johnny Uppercut’s IQ score is 85 and the mean is 100 and the S.D. is 10, which Standard deviation does he fall under? 3. If John Cena’s IQ score is 85 and the mean is 100 and the S.D. is 5, which Standard deviation does he fall under? Z score Z score measure distance of a score from the mean in units of standard deviation. Example 1 Clarence scored a 72 on a test with a mean of 80 and SD of 8. What would Clarence’s Z score be? Z score Example 2 Sumo scored a 84 on a test with a mean of 80 and SD of 8. What would Sumo’s Z score be? Normal Distribution (Bell Curve) • If it is a Normal Distribution/Curve, always assume the Mean/Median/Mode is 100. • IQ score will always have a normal distribution • Standard Deviation is 15 IQ follows a Normal Distribution Mean = 100 SD = 15 Normal Distribution (Bell Curve) What percentage score below 100? Mean = 100 SD = 15 What percentage score above 100? Mean = 100 SD = 15 34.1% + 13.6% + 2.1% What percentage score below 100? Mean = 100 SD = 15 F. Sample Question If the Mean is at 100 and SD is 15 1.What is the percentage of people scored between 85 and 100? 2.What percentage of people scored between 85 and 115? 3.What percentage of people scored between 70 and 130? 4.What percentage score below 70 and above 130? Normal Distribution 1. What percentage score between 85 and 100? 34.1% Mean = 100 SD = 15 What percentage score between 85 and 115? Mean = 100 SD = 15 34.1% + 34.1% = 68.2% What percentage score between 70 and 130? Mean = 100 SD = 15 13.6% + 34.1% + 34.1% + 13.6% = 95.4% What percentage score below 70 and above 130? Mean = 100 SD = 15 4% F. Sample Questions 5. What percentage of people that will score 1 SD above the mean? 6. What percentage of people will score below 2 SD below the mean? Curve Ball! Read carefully!! 1. Approximately what percentage of people will fall within one standard deviation of the mean? a) 34% b) 68% c) 95% d) 99% Approximately what percentage of people will fall within one standard deviation of the mean? 68 Mean = 100 SD = 15 34.1% + 34.1% = 68.2% Read carefully!! 2. Approximately what percentage of people will fall within two standard deviation of the mean? a) 34% b) 68% c) 95% d) 99% Approximately what percentage of people will fall within two standard deviation of the mean? 95 Mean = 100 SD = 15 13.6% + 34.1% + 34.1% + 13.6% = 95.4% Read carefully!! 3. Approximately what percentage of people will fall within three standard deviation of the mean? a) 34% b) 68% c) 95% d) 99% Approximately what percentage of people will fall within three standard deviation of the mean? 99 Mean = 100 SD = 15 2.1%+ 13.6% + 34.1% + 34.1% + 13.6% + 2.1% Normal Distribution What percentage of people will score 1 SD above the mean? Mean = 100 SD = 15 Inferential Statistics • Infer (draw-out / conclusion) • You are trying to reach conclusions that extend beyond just describing the data. • These are used to test hypothesis about samples. Outline T-test yields a p-value •Generally, the t test gives a P value that allows us a measure of confidence in the observed difference. •It allows us to say that the difference is real and not just by chance. •A p value of less than 0.05 is a common criteria for significance. • 5% chance it was due to chance •We call this statistically significant – results of the experiment did NOT happen by chance. Frequency distribution