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# PSY 313 Week 6 Notes PSY 313

Syracuse

GPA 3.4

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## Popular in Intro. to Research Methodology

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This 12 page Class Notes was uploaded by Bria Harris on Friday October 9, 2015. The Class Notes belongs to PSY 313 at Syracuse University taught by Amy Criss in Summer 2015. Since its upload, it has received 42 views. For similar materials see Intro. to Research Methodology in Psychlogy at Syracuse University.

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Date Created: 10/09/15

PSY 313 Introduction to Research Methods Week 6 Lecture Notes October 5th amp 7th Measures of Central Tendency Mean M ZXN Sum observations Divide sum by total of observations Median Order observations by magnitude Find middle value Mode Most common observation What Measure Should We Use Mean Best in most situations very common Median Best if there are extreme values eg housing prices income Mode Best when decimals don t make sense amp for categorical response scales eg of kids can t have 23 kids How Do I Know If the Extreme Scores are Extreme Enough to use the Median Mean Median F s39 i 39 r l nuluunuius Mode Median Mean Frequencies I l l l l l l l I Mean Median Mode Positively skewed tail towards positive end median lt mean Negatively skewed tail towards negative end mean gt median Measures of Stability Dispersion Standard Deviation S xEX M2 N 1 To calculate Compute mean Subtract mean from each value Square each of these Add them all together Divide by of observations minus 1 Take the square root P S rPSNNtquot Variance v 52 v Via 2 N 1 To calculate 1 Repeat steps 1 5 2 Standard deviation squared Standard Deviation is on the same scale as the response and the mean Eg How many cups of coffee do you drink per week Mean 5 Standard Deviation 2 68 of people drink between 3 7 cups entire left half of normal distribution curve Converting to Standardized Scored Standard Score where you fall in standard deviation terms Eg a standardized score of 1 means the value is 1 standard deviation above the mean Standardized score Score X M S Primary benefit of standardized score to directly compare scores on different scales Correlation Correlational Research Purpose to examine the relationship between two variables X and Y Relationship does NOT imply causation Correlation allows us to say X and Y are related but Does X cause Y Does Y cause X Does Z cause both X amp Y 3rd variable problem How Do We Evaluate if a Relationship Exists Scatterplot graphing relationship between variables Pearson s R calculating a correlation statistic Scatterplot Each point equals 1 observation 1 participant What is the Nature of the Relationship Form pattern in the data Usually linear not a curve 0 Can you draw a line through the data amp the individual scores will cluster around it Direction positive or negative Strength numerical value close to 1 or 1 Form Correlation coefficients assume linear relation Either positive or negative If you can t draw a straight line through it you probable shouldn t use a correlation coefficient to compute Direction Positive As X increases Y increases X and Y vary in the same direction Pearson s R is greater than 0 16 14 i 12 Q 2 1 r P v 08 I 5 o 6 19 9 04 02 f 0 0 02 04 06 08 1 12 14 16 Axis Title Negative 39 As X increases Y decreases 39 X amp Y vary in the opposite direction 39 Pearson s R is less than 0 35 3 a 25 2 d 2 P L 3 15 1 05 0 0 05 1 15 2 25 Axis Title Strength Strength of the relationship Magnitude of correlation coefficient Fuzziness of the cloud on the scatterplot No relationship X amp Y are not related R is near 0 correlation coefficient Cloud is maximally fuzzy Strength is Distance from Zero R 10 perfectly positive R 0 no relationship R 10 perfectly negative Pearson s R X and Y are continuous variables Question Are X an Y correlated can you predict one given the other stdscorex gtlt stdscorey N 1 E X M S Example Dining hall food ratin X dining hall food rating Y of meals parents cookedmonth X M Mquot2 2 4 xEX M2 N 1 1164 2 Zx Zy 221 221 12 05 12 05 12 05 32 15 32 15 12 05 12 05 12 05 Compute Correlation multiply Zx and Zy 1 X 1 1 05 X 05 025 15 x 05 075 15 x 05 075 05 X 05 025 Add together total is 3 divide by N1 34 075 Notes on R Standard scores allows is to compare variables on different scales Positive or negative Ranges form 1 to 1 Allows prediction predict X given Y and vice versa prediction DOES NOT EQUAL CAUSATION Strength of Correlation Coefficients No relationship correlation 0 to 009 SmallWeak relationship 010 to 029 Medium relationship 030 to 049 Large strong relationship 050 to 10 tells you the strength amp direction of the correlation PSY 313 Introduction to Research Methods Week 6 Lecture Notes October 5th amp 7th Measures of Central Tendency Mean M ZXN Sum observations Divide sum by total of observations Median Order observations by magnitude Find middle value Mode Most common observation What Measure Should We Use Mean Best in most situations very common Median Best if there are extreme values eg housing prices income Mode Best when decimals don t make sense amp for categorical response scales eg of kids can t have 23 kids How Do I Know If the Extreme Scores are Extreme Enough to use the Median Mean Median F s39 i 39 r l nuluunuius Mode Median Mean Frequencies I l l l l l l l I Mean Median Mode Positively skewed tail towards positive end median lt mean Negatively skewed tail towards negative end mean gt median Measures of Stability Dispersion Standard Deviation S xEX M2 N 1 To calculate Compute mean Subtract mean from each value Square each of these Add them all together Divide by of observations minus 1 Take the square root P S rPSNNtquot Variance v 52 v Via 2 N 1 To calculate 1 Repeat steps 1 5 2 Standard deviation squared Standard Deviation is on the same scale as the response and the mean Eg How many cups of coffee do you drink per week Mean 5 Standard Deviation 2 68 of people drink between 3 7 cups entire left half of normal distribution curve Converting to Standardized Scored Standard Score where you fall in standard deviation terms Eg a standardized score of 1 means the value is 1 standard deviation above the mean Standardized score Score X M S Primary benefit of standardized score to directly compare scores on different scales Correlation Correlational Research Purpose to examine the relationship between two variables X and Y Relationship does NOT imply causation Correlation allows us to say X and Y are related but Does X cause Y Does Y cause X Does Z cause both X amp Y 3rd variable problem How Do We Evaluate if a Relationship Exists Scatterplot graphing relationship between variables Pearson s R calculating a correlation statistic Scatterplot Each point equals 1 observation 1 participant What is the Nature of the Relationship Form pattern in the data Usually linear not a curve 0 Can you draw a line through the data amp the individual scores will cluster around it Direction positive or negative Strength numerical value close to 1 or 1 Form Correlation coefficients assume linear relation Either positive or negative If you can t draw a straight line through it you probable shouldn t use a correlation coefficient to compute Direction Positive As X increases Y increases X and Y vary in the same direction Pearson s R is greater than 0 16 14 i 12 Q 2 1 r P v 08 I 5 o 6 19 9 04 02 f 0 0 02 04 06 08 1 12 14 16 Axis Title Negative 39 As X increases Y decreases 39 X amp Y vary in the opposite direction 39 Pearson s R is less than 0 35 3 a 25 2 d 2 P L 3 15 1 05 0 0 05 1 15 2 25 Axis Title Strength Strength of the relationship Magnitude of correlation coefficient Fuzziness of the cloud on the scatterplot No relationship X amp Y are not related R is near 0 correlation coefficient Cloud is maximally fuzzy Strength is Distance from Zero R 10 perfectly positive R 0 no relationship R 10 perfectly negative Pearson s R X and Y are continuous variables Question Are X an Y correlated can you predict one given the other stdscorex gtlt stdscorey N 1 E X M S Example Dining hall food ratin X dining hall food rating Y of meals parents cookedmonth X M Mquot2 2 4 xEX M2 N 1 1164 2 Zx Zy 221 221 12 05 12 05 12 05 32 15 32 15 12 05 12 05 12 05 Compute Correlation multiply Zx and Zy 1 X 1 1 05 X 05 025 15 x 05 075 15 x 05 075 05 X 05 025 Add together total is 3 divide by N1 34 075 Notes on R Standard scores allows is to compare variables on different scales Positive or negative Ranges form 1 to 1 Allows prediction predict X given Y and vice versa prediction DOES NOT EQUAL CAUSATION Strength of Correlation Coefficients No relationship correlation 0 to 009 SmallWeak relationship 010 to 029 Medium relationship 030 to 049 Large strong relationship 050 to 10 tells you the strength amp direction of the correlation

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