PSYC 241 Week 5 Fall 2024 PDF

Statistics in Psychology PSYC 241 Week 5 Shapes of distribution & the standard units in statistics: z score Fall, 2024 Demet Kara, PhD So far,… Areas under a Visualizing...

Statistics in Psychology PSYC 241 Week 5 Shapes of distribution & the standard units in statistics: z score Fall, 2024 Demet Kara, PhD So far,… Areas under a Visualizing the Measures of Variability of normal data central tendency dataset distribution Range, variance, Pie chart, bar Mean, median, 1SD-68%,2SD- standard chart, histogram mode 95%, 3SD-99% deviation We considered the distribution as normal. So far,… Ways of analyzing the distribution of the shape Skewness: the extent to which the frequency Kurtosis: the curve is lopsided steepness of the bell- rather than shaped curve symmetrical Non-normality in distributions Negative skew: more scores are to the left of the mode than to the right the mean and median are smaller than the mode. Critical value: +/- 1 Non-normality in distributions Positive skew: more scores are to the right of the mode than to the left the mean and median are bigger than the mode. Critical value: +/- 1 Non-normality in distributions Kurtosis Critical value: +/- 3 From Samples to Population Why increasing sample size affects the distribution? Population Sample 2 distribution Sample 1 Sample 3 Sample 4 Population mean Sampling Distributions Imagine you sampled a number of people from a population. You could obtain sample statistics e.g., You could obtain the sample mean for IQ Sampling Distributions Now imagine that you collected this mean from a number of different samples from the same population You obtained mean IQ scores from different samples and plotted them. Sampling Distributions You collected data from more than one sample from the same population You obtained means and you plotted those means Now, you have a “sampling distribution of the means” Sampling Distributions You collected data from more than one sample from the same population You obtained means and you plotted those means Now, you have a “sampling distribution of the means” The more samples you obtained, the closer the mean of these sample means would be to the population mean If you collected so many samples that you covered all people in the population, the mean of these samples would be the same as the population Standard Error of the mean Standard Sample mean deviation It is the average deviation of sample means from the mean of the sample means It is the deviation in sampling distributions Sampling of means distribution of the Standard error means The greater the standard error, the less precision of a sample statistic (i.e., how accurately any one sample represents the population) Let’s think! You took a Research Methods exam. Your professor told you only people who scored 2 SD above the mean will get an A☺ People who scored 2 SD below the mean will get an F  You know the average = 75 You know the standard deviation = 8 You know your exam score = 93 Can you calculate your letter grade? Let’s think! You took a Research Methods exam. Your professor told you only people who scored 2 SD above the mean will get an A☺ People who scored 2 SD below the mean will get an F  You know the average = 75 You know the standard deviation = 8 You know your exam score = 93 Can you calculate your letter grade = 75 + 8 + 8 = 91 93 > 91, so you get an A ☺ Let’s think! You took a Research Methods exam. Your professor told you only people who scored 2 SD above the mean will get an A☺ People who scored 2 SD below the mean will get an F  You know the average = 75 You know the standard deviation = 8 What is the cut off score for F? Let’s think! You took a Research Methods exam. Your professor told you only people who scored 2 SD above the mean will get an A☺ People who scored 2 SD below the mean will get an F  You know the average = 75 You know the standard deviation = 8 What is the cut off score for F : 75 – (8 + 8) = 59 Let’s think! You took a Research Methods exam. Your professor told you only people who scored 2 SD above the mean will get an A☺ People who scored 2 SD below the mean will get an F  You know the average = 75 You know your score = 84 You know the standard deviation = 8 How many SD are you away from the mean? Let’s think! You took a Research Methods exam. Your professor told you only people who scored 2 SD above the mean will get an A☺ People who scored 2 SD below the mean will get an F  You know the average = 75 You know your score = 84 You know the standard deviation = 8 How many SD are you away from the mean: (84 – 75)/8 = 1.125 Normal Distribution & Std Deviation Assume a normal distribution with a mean of 70 and a standard deviation of 12. What limits would include the middle 68% of the cases? Z-scores An indication of how many standard deviations any one value in a sample is away from the mean Z score of 0 = the mean Z score of 1 = 1 SD above the mean Z score of -1 = 1 SD below the mean Z-scores An indication of how many standard deviations any one value in a sample is away from the mean It is equally applicable to anything: time, anxiety, depression, height or any other variable. The number of standard deviations is a universal scale of measurement Normal Distribution & Z-scores Normal Distribution & Z-scores 32 40  Z-score table Second decimal First decimal Exercise Ahmet’s family earns 5.230 TL per month. The average income in Turkey is 2.500 TL with a SD of 1000 TL. What is the percentage of people who earn more than Ahmet’s family? Exercise Ahmet’s family earns 5.230 TL per month. The average income in Turkey is 2.500 TL with a SD of 1000 TL. What is the percentage of people who earn more than Ahmet’s family? 5230-2500 / 1000 = 2.73 So it is:  Z-score table Second decimal 2.73 First decimal