Statistics notes A standard deviation shows the average distance each score is from the mean In this way it provides information on how spread out the scores are in a set of data From your example it appears that scores are not too spread out from the mean of 4 2278 such that the average difference between each score and the mean is less than 1 0 i e 87709 In contrast if the standard deviation was larger say 3 0 or 4 0 with a mean of 4 2278 the scores would have a huge range such that the mean would not be very informative at all in describing the set of scores In this way the standard deviation in relation to the mean helps us know if the mean is a reliable measurement or not Variance always non negative a small variance indicates that the data points tend to be very close to the mean expected value and hence to each other while a high variance indicates that the data points are very spread out around the mean and from each other Standard deviation is the square root of the variance The variance is the arithmetic mean of the squared difference between each value and the mean value Cronbach s alpha measures internal consistency between questions in a survey that are similar It also allows us to see if a question is removed how the consistency would change The closer cronbach s alpha is to 1 the better the consistency in answers This is definitely used in questionnaire s taken for job prospects It allows us to remove questions that hinder the consistency https www youtube com watch v B0ABvLa u88 Types of variables Independent one thing you change variable that is varied or manipulated limit to only one in an experiment ie time spent studying Dependent the change that happens the result of the independent variable that is measured because of the independent variable ie test score dependent variables are measured and it produces scales of measurement Controlled everything you want to remain constant and unchanging Ie type of plant used pot size amount of liquid soil type Both are variables that are being evaluated defined and analyzed but then categorized into independent or dependent both are their own axis in a program In an equation d 4c where c is the independent variable and d is the dependent variable Example d represents the cost of the cookies c represents number of boxes you buy You are holding a fundraiser for cancer research A certain charity organization has agreed to contribute 10 10more than the amount of money you raise to cancer research In the graph and table below ff is the amount of money that you raise during your fundraiser and cc is the amount of money that the charity organization donates Which of the following statements are true Select all that apply The dependent variable is the amount of money that you raise The dependent variable is the amount of money the charity organization donates The independent variable is the amount of money that you raise The independent variable is the amount of money the charity organization donates y x 10 dependent independent Standard deviation measures how the variables deviate from the mean It also measures the distribution of your data Closer to 0 the less variance there is But if the SD is too high then the mean would not describe the data A high standard deviation shows that the data is widely spread less reliable and a low standard deviation shows that the data are clustered closely around the mean more reliable Inferential the branch of statistics that involves drawing conclusions about a population based on info contained in a sample taken from that pop Measurements on data include qualitative and quantitative Qualitative labels categories Quantitative numerical measurements that arise from natural numerical code Relationship between population of interest and a sample drawn from that pop Is perhaps the most important concept x1 and x2 represent each data of the sample A parameter is a number that summarizes some aspect of the population as a whole A statistic is a number computed from the sample data The distinction between a population together with its parameters and a sample together with its statistics is a fundamental concept in inferential statistics the sample was drawn Information in a sample is used to make inferences about the population from which 1 The genders of the first 40 newborns in a hospital one year qualitative 2 The natural hair color of 20 randomly selected fashion models qualitative 3 The ages of 20 randomly selected fashion models quantitative 4 The fuel economy in miles per gallon of 20 new cars purchased last month quantitative 5 The political affiliation of 500 randomly selected voters qualitative 1 A researcher wishes to estimate the average weight of newborns in South America in the last five years He takes a random sample of 235 newborns and obtains an average of 3 27 kilograms 1 What is the population of interest Newborns in South America in the last 5 yrs 2 What is the parameter of interest Newborns avg weight in the last 5 yrs 3 Based on this sample do we know the average weight of newborns in South America Explain fully No not exactly but we know the approximate value of the average Pearson correlation If the relationship is not linear then the correlation coefficient does not adequately represent the strength of the relationship between variables Denoted by R product moment correlation draws a line of best fit Indicates how far away the data points are to the line of best fit Does not matter which variable is on what axis Still will show if there is a linear correlation or not Does not represent the slope of the line Variables must be interval or ratio Assumptions pearson correlation makes Two variables must be normally distributed Linear relationship Outliers are kept to a minimum or removed There is homoscedasticity of the data Test normality in SPSS use Explore degrees of freedom number of data points 2 included when you test the significance of the relationship By rejecting the null hypothesis you accept the alternative hypothesis that states that there is a relationship but with no information about the strength of the relationship or its importance Coefficient of determination is found by squaring r Measures the proportion of the variance that is shared by both variables Ie r 0 6 r 2 0 36 or 36 which is the amount that the variance is shared by both http www psych utah edu aoce web text Correlation cherry picking notes example if marketing campaign stopped at a certain point