Statistics Study Notes: Definitions and Formulas for Key Statistics Concepts, Exams of Statistics

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PSY 3801/ Stats - Test Questions And Answers Four Ways in Which Statistics Help Us to Make Sense of Data - correct answer 1) ORGANIZE scores so that we can see any data patterns 2) SUMMARIZE the data to allow for faster understanding 3) COMMUNICATE the results of a study through use of symbols and techniques 4) INTERPRET what the data indicates to answer a question population - correct answer the ENTIRE group of individuals to which a law of nature applies sample - correct answer a relatively small subset OF a population participants - correct answer individuals who are measured in a sample variable - correct answer anything that can produce 2+ different scores quantitative variable - correct answer indicates the AMOUNT of the variable that is present qualitative variable - correct answer indicates a CLASSIFICATION/CATEGORIZATION of the variable, NOT measured in amounts PSY 3801/ Stats - Test Questions And Answers relationship - correct answer pattern in which, as the scores on one variable change, the scores on the other variable change in a consistent manner perfectly consistent relationship - correct answer a score on one variable is ALWAYS paired with one (and ONLY ONE) score on the other variable descriptive statistics - correct answer procedures for organizing and summarizing SAMPLE data - answers from such data are often a single number that describes important info about the scores inferential statistics - correct answer procedures for drawing inferences about the scores and relationship that would be found in a POPULATION - help us to decide whether or not our sample accurately represents the relationship statistic - correct answer number that describes an aspect of the scores in a SAMPLE parameter - correct answer a number that describes an aspect of the scores in a POPULATION - obtained when applying INFERENTIAL procedures PSY 3801/ Stats - Test Questions And Answers continuous variable - correct answer variable that CAN be measured in fractional amounts discrete varaible - correct answer variable that CANNOT be measured in fractional amounts (ex. gender) What represents the total number of scores in a data? - correct answer the letter 'N' raw scores - correct answer the scores initially measured in a study frequency (f) - correct answer the number of times each score occurs in a set of data, also called simple frequency frequency distribution - correct answer a distribution showing the number of times each score occurs in the data *frequency table* - correct answer can be made by starting with a score column and an f (frequency) column, put the highest scores at the TOP of the column PSY 3801/ Stats - Test Questions And Answers bar graph - correct answer a graph showing a vertical bar over each X score, but adjacent bars DO NOT touch; used with NOMINAL or ORDINAL scales histogram - correct answer a frequency graph similar to a bar graph, but adjacent bars DO touch; used with a small range of INTERVAL or RATIO scales frequency polygon - correct answer a frequency graph showing a data point above each score, with the adjacent points connected by straight lines ; used with many different INTERVAL or RATIO scores data point - correct answer a dot plotted on a graph to represent a pair of X and Y scores -- (X,Y) a graph of frequency distribution ALWAYS... - correct answer shows the SCORES on the x-axis and their FREQUENCY on the y-axis. grouped distribution - correct answer a distribution created by combining individual scores into small groups and then reporting the total frequency (or other description) of each group (ex. scores 1, 2, 3, and 4 are the 1-4 group) PSY 3801/ Stats - Test Questions And Answers normal curve - correct answer the symmetrical bell-shaped curve produced by graphing a normal distribution normal distribution - correct answer a set of scores in which the MIDDLE score has the highest frequency and, proceeding toward higher or lower scores, the frequencies at first decrease slightly and then decrease drastically tail of the distribution - correct answer far-left or far-right portion of a frequency polygon; lowest scores negatively skewed distribution - correct answer an asymmetrical distribution with low-frequency, extreme LOW scores, but WITHOUT corresponding low-frequency, extreme HIGH scores; its polygon has one one PRONOUNCED tail OVER THE LOW SCORES positively skewed distribution - correct answer an asymmetrical distribution with low-frequency, extreme HIGH scores, but WITHOUT corresponding low-frequency, extreme LOW scores; its polygon has one one PRONOUNCED tail OVER THE HIGH SCORES bimodal distribution - correct answer a distribution formed a symmetrical polygon with two 'humps' where there are relatively high- frequency scores, with center scores of the same, less-high frequency PSY 3801/ Stats - Test Questions And Answers line graph - correct answer typically used when graphing experimental results with 1+ independent variable; used to show how values change scatterplot - correct answer used to see the relationship between two QUANTITATIVE variables; each dot on it represents one observation from a data set box plot/ box and whisker plot - correct answer used to display patterns of QUANTITATIVE data; two horizontal lines (whiskers) extend from both the front and the back of the box stem & leaf plot - correct answer type of GRAPH used with CONTINUOUS data; allows one to see exact value of the data; each data value is split into a 'leaf' (usually the last digit) and the 'stem' (the other digits) frequency distribution (as opposed to other graphs) - correct answer comes in many different types -- simple, relative, cumulative, and cumulative percentage, etc.; table that displays the frequency of various outcomes in a sample correlation coefficient - correct answer a statistic that describes the important characteristics of a relationship PSY 3801/ Stats - Test Questions And Answers 2 types of relationships - correct answer linear: straight line; y scores only move in one direction nonlinear/curvilinear: y scores change direction as x scores increase linear relationship - correct answer a relationship in which the y scores tend to change in only ONE direction as the x scores increase linear regression line - correct answer straight line that summarizes a linear relationship by passing through the center of the scatterplot positive linear relationship - correct answer a relationship in which the y scores tend to INCREASE as the x scores increase negative linear relationship - correct answer a relationship in which the y scores tend to DECREASE as the x scores increase nonlinear/curvilinear relationship - correct answer a relationship in which the y scores CHANGE their direction of change as the x scores increase strength of a relationship - correct answer the extent to which ONE value of Y is consistently associated with one, and ONLY ONE, value of X. a relationship becomes WEAKER as the VARIABILITY among the group of each Y score paired with each X becomes larger. PSY 3801/ Stats - Test Questions And Answers 4 Ways to Interpret the Coefficient - correct answer 1) Consistency: an absolute value that is greater than -1 or less than 1 indicates that not EVERY participant who obtains a particular X obtained the same Y. this means that the relationship between X and Y is INTERMEDIATE (subject to change) 2) Variability: a coefficient greater than -1 or less than 1 indicates that there IS variability among the Y scores at each X. 3) The Scatterplot: a coefficient greater than -1 or less than 1 indicates variability in Y at each X, so the data points at an X are vertically spread out above and below the regression line. 4) Predictions: a coefficient greater than -1 or less than 1 means that there is NOT ONLY ONE Y SCORE for a particular score of X, so we can predict only AROUND what one's Y score will be. Use of CONSISTENCY in Interpreting a Coefficient - correct answer an absolute value that is greater than -1 or less than 1 indicates that not EVERY participant who obtains a particular X obtained the same Y. this means that the relationship between X and Y is INTERMEDIATE (subject to change) PSY 3801/ Stats - Test Questions And Answers this says to multiply each Zx times the paired Zy, sum the products, and divide by N (N is the number of pairs of scores) *COMPUTING* FORMULA FOR THE PEARSON r - correct answer r= (N(ΣXY)-(ΣX)(ΣY))/√((N(ΣX^2)-(ΣX)^2)(N(ΣY^2)-(ΣY^2)) proportion of variance accounted for - correct answer in a correlational design, the proportion of the differences in y scores associated with changes in X --> the FORMULA FOR THIS IS r^2. FORMULA FOR THE proportion of variance accounted for - correct answer r^2 linear regression - correct answer the procedure for predicting unknown Y scores based on known correlated X scores; to use regression, 'r' must be both computed and proven to be significant predictor variable - correct answer refers to the *X* variable in correlational research criterion variable - correct answer refers to the *Y* variable in correlational research PSY 3801/ Stats - Test Questions And Answers Y' - correct answer pronounced "Y Prime"; the predicted Y score; is the value of Y at any X *on* the regression line LINEAR REGRESSION EQUATION - correct answer Y'= bX + a (where b is the slope and a is the Y intercept) standard error of the estimate - correct answer difference between predicted and actual y scores EQUATION TO FIND *SLOPE* (b) FOR A LINEAR REGRESSION EQUATION - correct answer b= [∑XY-((∑X)(∑Y)/N)]/[∑x^2- ((∑x^2)/N)] EQUATION TO FIND THE INTERCEPT (a) FOR A LINEAR REGRESSION - correct answer a= ∑Y-(b(∑X)/N EQUATION TO FIND THE STANDARD ERROR OF THE ESTIMATE - correct answer = √[∑(Y-Y1)^2/N] Experimental vs. Correlational Design - correct answer An experiment isolates and manipulates the independent variable to observe its effect on the dependent variable, and controls the environment in order that extraneous variables may be eliminated. Experiments establish cause PSY 3801/ Stats - Test Questions And Answers and effect. A correlation identifies variables and looks for a relationship between them. negative skew (what does it LOOK like?) - correct answer positive skew (what does it LOOK like?) - correct answer mean - correct answer all numbers added up, then divided by the number of total numbers (ex. 1, 2, 3 1+2+3= 6, divide by 3, =2) median - correct answer middle number when ranked lowest to highest (ex. 7, 5, 3, 6, 1 rearrange = 1, 3, 5, 6, 7 median is 5)