Elementary Statistics Chapter 2 (Day 2) and Chapter 3 (Day 1)
Elementary Statistics Chapter 2 (Day 2) and Chapter 3 (Day 1) Psy 202
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This 4 page Class Notes was uploaded by Stephanie on Friday September 2, 2016. The Class Notes belongs to Psy 202 at University of Mississippi taught by Matthew Mervin in Fall 2016. Since its upload, it has received 19 views. For similar materials see Elementary Statistics in Psychology at University of Mississippi.
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Date Created: 09/02/16
PSY 202: Elementary Statistics *Note*: We did not have many notes to cover for Day 2 of Chapter 2, and I did not take any notes on how to use R. So, instead of charging you guys for something that didn’t qualify as complete lecture notes, I have decided to combine Day 2 of Chapter 2 and Day 1 of Chapter 3 as one upload. Chapter 2: Describing Quantitative Data with Frequency Distributions – Day 2 I. Ogives a. These are used for cumulative frequency and grouped cumulative simple frequencies b. Identifiers i. Yaxis is the cumulative frequency of the raw scores (simple or relative) ii. Highest cf(Y) is always equal to n (the total number of scores for simple frequencies) or to 1.00 (relative frequencies) iii. Points on the ogive are not necessarily connected by lines II. Stem and Leaf Displays a. This shows the shape of the distribution and individual scores i. Stems: This is the tens column from highest interval to lowest interval (or vice versa) 1. The intervals divide evenly by 10 ii. Leaves: Ones column with scores in ascending order 1. Each score in each interval is displayed III. Salient Characteristics a. 2 Key Characteristics i. Frequency polygon with infinite number of scores 1. Measure of Central Tendencies a. The central tendency is the one score that summarizes the entire distribution i. If other scores are close then the central tendency is doing a good job summarizing the scores ii. If the other scores are far away then the central tendency is not doing a good job summarizing the distribution 2. Variability a. Basically how well the central tendency summarizes the scores b. Other characteristics i. Mode, median, and mean 1. Skewness: Lets you know how symmetrical the distribution is 2. Kurtosis: This is how curved the distribution tends to be in a frequency polygon a. Most scores fall over one point b. Low kurtosis shows that scores are evenly placed on the polygon and distribution i. If the curve is really pointy then it has a high kurtosis ii. If the curve is really curvy then it has a low kurtosis Chapter 3: Describing Quantitative Data with Summary Statistics – Day 1 I. Central Tendency a. 3 Types (from least to most preferred) i. The Mode 1. This is the score that has the most relative frequency a. The mode is the score that happens most often b. It is the typical score in the distribution 2. Why we don’t like the mode a. The mode might not be in the center of the scores b. We could have more than one mode c. The mode only gives information about the score that becomes the mode i. The mode does not give information about other scores ii. The Median 1. The median gives category and rank order 2. It is the score that has 50% distribution both above and below it 3. Why we like the median a. It gives information about the rank of scores b. It matches what we want for the central tendency 4. Why we don’t like the median a. It does not tell us the distance between scores iii. The Mean 1. The mean incorporates the most information (category, rank, and distance information) 2. Notation Summation a. 3. Symbols a. Ʃ = notation summation b. μ = Population mean c. i = 1 : You start with this score d. n = upper limit : Finish with this score e. Yi = Sum of all these scores from the lower to upper limits, inclusive f. For the mean divide by the total number of scores 4. Mean as a balance point a. Deviations from the mean i. Positive: Score higher than the mean ii. Negative: Score below the mean iii. The deviation score will always sum to 0 5. Mean as a leastsquares estimate a. Square the deviations to get rid of – sign b. Look for the sum of squared deviation i. These are also known as squared errors ii. The one that gives you the smallest squared errors is the best estimate 6. Sampling stability of the 3 measures of central tendency a. The central tendency for the sample is the same as the population if you use the mean b. Median is so scattered and the mode does not tell anything about the sample or the population II. Properties of Measures of Central Tendency a. Mode i. It is used for categorical scores ii. Benefit: The mode applies to every measurement scale iii. Drawback: It gives the least amount information about the scores iv. This is the measure we like the least b. Median i. Incorporates anything that can be put into rank order ii. Benefits: The median is usable with all shapes iii. Drawbacks: 1. It does not give distance information a. We are not able to tell how far apart two scores are c. Mean i. Benefits: Uses all available information ii. Drawback: The mean is most sensitive to outlier scores III. Variability a. The range i. The range looks at the gap between the lowest and highest scores of the distribution ii. To find the range take the high and subtract the low from it iii. The range is extremely sensitive to outlier scores b. The interquartile range i. The interquartile range gets rid of the outliers and gives a better representation of how the scores are spread out
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