Download Methods of Knowing & Statistical Analysis: Rationalism, Intuition, Scientific Method and more Exams Psychology in PDF only on Docsity!
psych stats midterm 1
4 methods of knowing -
- authority
- rationalism
- intuition
- scientific method 4 methods of knowing--authority - we consider something to be true because of tradition/someone important telling us it is true can cause error 4 methods of knowing--rationalism - use reasoning alone to arrive at knowledge-assumption that sound reasoning and logic will lead to the truth ex: all stats professors are cool because my stats professor is cool 4 methods of knowing--intuition - sudden insight/clarifying idea that suddenly springs into consciousness 4 methods of knowing--scientific method - use both reasoning and intuition but relies on objective assessment of a scientific measurement: -hypothesis -conduct experiment -statistically analyze data -conclusion Populations (definition) -
the complete set of individuals, objects, or scores that the investigator is interested in studying Sample (definition) - a subset of the population ex: alcoholics in denver (take small number of population) Random sampling (definition) - data are collected on a sample of subjects rather than the entire population -statistically analyze data found Variable (definition) - any property or characteristic of same event, object, or person that may have different values at different times depending on the conditions ex: height, weight, etc Independent variables - is systematically manipulated by investigator Dependent variables - is measured by the investigator to determine the effect of the other variable ex: drug dosage (first variable) on reaction time (second variable) Constant (control) - variable that stays the same throughout an experiment on purpose ex: temp of room Data - measurements that are made on subjects of an experiment
-averages, variability, shape of distribution Inferential statistics - involves techniques that use the obtained sample data to make assumptions about the population -not just concerned with the obtained data Characteristics/process of descriptive stats - -collection -organization -summary -presentation of data Characteristics/process of inferential stats - -generalizing -conclusion -prediction from sample data Mathematical Notation: multiple variables - use subscripts to distinguish Mathematical Notation: N - total number of participants in a study Mathematical Notation: single score in the x distribution - Xi (subscript i) i (Xi/subscript i) - can take on any value from 1 to N1 (subcript 1)
Mathematical notation: Summation - more frequent operations performed in stats is to sum all parts (or part) of scores in the distribution... we use Σ (greek letter sigma) Algebraic expression for summation - Σ "N" goes on top of Σ and symbolizes total number of values...i=1 is written below Σ and symbolizes the first number that the sequence includes.... Xi= X1+ X2+ X3 etc is to the right of Σ and symbolizes all of the values in the sequence if we want the sum of some of the values, but not others (ex: starts at third number in sequence), we replace the i=1 below Σ with i=3 to indicate the starting point) Σ^2 - the sum of all the squared x scores (square each score separately, then add them together for sum) (Σ)^2 - sum of x scores, quantity squared -sum of all scores, then square the result of the sum Measurement scale (use) - the type of scale used will determine what statistical analysis is used Measurement scale: nominal scale - -lowest level of measurement -typically used w/ qualitative variables ex: types of running shoe, type of music, type of fruit
ex: if we weigh in at 180, then our upper limit=180.5 and lower=179. Discrete variables - no possible values between adjacent units on the scale ex: number of students in a class, children in a family (we have 40 students in the class, not 39.5) Frequency distributions - presents score values and their frequency of occurrence lowercase itallicized f=frequency Frequency distribution: grouping scores - can group scores to make frequency distribution more manageable Frequency distribution: width - how many scores are in each interval most work well between 10-20 (intervals) ex: 100, 110, 120 relative f - proportion of total # of scores in each interval Relative f= f/N (N= number of scores) cumulative f - number of scores that fall below the upper real limit of each interval calculate: add frequency from the bottom interval and go up....tells us how many scores are below a specific interval
cumulative %: percentage of scores that fall below the upper real limit of each interval cum%=(cum f)/N x where cum f=cumulative frequency and N=total number of scores Percentile rank - the percentage of scores w/ values lower than the score in question (if I score a 95% on an exam, I scored better than 95% of other test takers) Graphing frequency distribution - can be displayed as graphs rather than tables -easier to see important feed of data on graph independent variable on x axis; dependent variable on y axis intersection of x and y axis is 0 Bar graph - utilized as easiest way to display nominal or ordinal data Histogram - utilized for interval and ratio data -bar is drawn for each class interval -plot midpoint of each class interval Frequency Polygon - utilized when using interval or ratio data -point plotted for each interval, line used to connect the points -plot the midpoint of each class interval
if repeatedly take random samples from population, the mean will vary from sample to sample Overall mean - When want to know mean of several groups of scores.... x̅=(N1(subscript1)x̅1(subscript1))+(N2(subscript1)x̅2(subscript1))+......+(Nk(subscript k)x̅2k(subscript k))/N1(subscript 1) + N2(subcript 2) +.....+Nk(subscript k) k=#of groups Median - middle # of a set of scores -if number of scores are even, take average of both -less average than the mean to extreme scores -more subject to sampling variability than mean -less stable than the mean from sample to sample Mode - most frequent score in a distribution Variability - shows extent of how far the different scores are from each other -measures of central tendency are a quantification of averages of distributions, while [this term] quantifies the extent of the dispersion Standard deviation - deviation score tells us how far away the raw score is from the mean of the distribution X - x̅ is the deviation score for sample data
X - μ is the deviation score for population -if the X scores are 2, 4, 6, 8, and 10... Σ= -there are 5 scores in the sample so... x̅ = 30/5 = 6 -so...X - x̅ (the deviation score) is the values of the scores subtract 6: (2-6, 4-6, etc) -values of (X - x̅) column ass up to 40 -standard deviation equation: (X - x̅)^ (X - x̅)^2 --> value found in the deviation score (ex: 2-6=-4), squared... (2-6=(-4^2)) -standard deviation= Equation for standard deviation for sample data: S= square root of (Σ (X - x̅)^2/N-1) Equation for standard deviation for population data: σ (sigma)= square root of (Σ (X -μ)^2 / N) so... if the (X - x̅) column adds up to 40 (Σsubscript1=40), and the number of scores is 5, then the standard deviation of sample data is: square root of 40/(5-1)=square root of 10 square root of 10=3.16 and the
Variance of population equation - S^2+ SS/N Range - difference between highest score and lowest score in the distribution Normal Curve - theoretical distribution of population scores -bell-shaped curve in which many variables measured in the behavioral science closely relate ex: height, weight, intelligence -special relationship between mean and standard deviation in these distributions -further away you get from the mean, lower the score is What is all the same in the normal curve? - Mean, median, and mode Standard scores (z scores) - transformed score that designates how many standard deviation units the corresponding raw scores above or below the mean z score for sample data equation - z= (X - x̅)/S z score for population data equation - z= (X-μ)/σ
Z score problem example - population of 10,000 IQ scores μ= σ= score= percentile rank: z= (X-μ)/σ z=125-100/ =25/ =1. z score=1. area between mean and z score (1.67)=.4525 9can find this on z score chart) add .5 to area under the curve .5 + .4525=. 95% percentile Z score facts - -have same shape as set of raw scores transforming raw scores into z scores does not change the shape of the distribution -mean of the score is always 0 -standard deviation of score is always 1
Imperfect relationships - -positive or negative relationship exists but all of the points do NOT fall on the same line (line of best fit) Correlation coefficient - looks for exact magnitude and direction of correlation -pearson r -spearman rho Pearson R - for interval or ratio data measures extent to which paired scores occupy the same positions within distributions -if we have diff values for diff distributions, how do we know if they are related? (USES Z SCORES!) z scores are standard scores (can transform GPA to z score) Pearson R equation - r= n (Σsubscript1 xy) - (Σx)(Σy)/ square root of [nΣx^2 - (Σx)^2][nΣy^2 - (Σy)^2] Pearson R r^2 and variability - once r is found, square the result and .... gives us correlation of determination What doe r^2 tell us? - -coefficient of determination proportion of total variability of y that can be accounted for by x
ex: r^2 = 0. if the relationship is causal, then 30% of the variability can be accounted for -->leaves us w 70% of variability that is caused by other factors Spearman Rho - used when one of both of the variables are of ordinal or nominal scaling What can change the magnitude of a correlation coefficient? - an outlier 4 Reasons for Correlation -
- x was the cause of y
- y was the cause of x
- a third variable caused the correlation
- correlation was fake (does not cause causation!) Linear regression - focuses less on magnitude and direction of relationship an more on prediction -if relationship is perfect, so is prediction regression line - best fitting line used for prediction Problem we face w prediction - how to determine a single straight line that best describes the data Least Squares Regression Line -
ex: predict GPA using variables IQ an study time
