# understanding data distributions, correlations, z-scores-psych

 (shapes of distributions 1) Frequency tables -a frequency table shows how often each value of the variable occurs *how many people belong to a certain group (shapes of distributions 1) Frequency polygon -visual representation of info contained in a frequency table -the way score frequencies are distributed with respect to the values of the variable*it can take on different forms (shapes of distributions 1) Unimodal distributions -mode of distribution refers to the most frequently occuring score -in this distirbution, one score occurs much more frequently than others (shapes of distributions 1) Multimodal distributions -more than one mode exists (or approx. so) -2 modes exist (shapes of distributions 1) Symmetrical distribution -is balanced*if we cut it in half both sides will be equal -normal distribution resembles a bell (shapes of distributions 1) Skewed distributions - is unbalanced, has more values on one end than the rest (shapes of distributions 1)( skewed distributions) Negative Skew -it is heaveir on the larger quantity side, ending in the lighter side (shapes of distributions 1)( skewed distributions) Positive skew it is heavier on the lighter side and ending on the larger side (measures of central tendency) Central tendency most typical or common score -mode-median-mean (measures of central tendency) Mode most frequently occuring score (measures of central tendency) Median the value at which 1/2 of the ordered scores falls above and 1/2 of the scores fall below (measures of central tendency) mean balancing point of a set of scores; average score (measures of central tendency) mode=median=mean normal distribution*bell-shaped in the center (measures of central tendency) modemedian>mean negatively skewed. (standard deviation) Spread or dispersion degree to which there are variation in the scores (standard deviation) Standard deviation an index that is used as common way of quantifying dispersion -SD is an average that can be interpreted as the average amount of dispersion around the mean*larger SD= more dispersion Interpreting the SD number 2.6.. exp) peoples scores are usually less or more than 2.6 units away from mean on average . (correlation) How can we quantify the linear relationship between 2 variables? -using a common way called correlation coefficient (r) (correlation) Properties of Correlation coefficeints - they range between -1 to 1 -value of the correlation conveys information about the form of the relationship between 2 variables - (r) can be interpreted as the slope of the line that maps relationship between 2 standarized variables (correlation properties) (r) conveys information about the form of relationship between 2 variables - r>0= relationship is positive - r<0= relationship between 2 variables is negative - r=0= there is no relationship between 2 variables (correlation) magnitude of correlations- When is a correlation big vs small? -correlation between variables rarely get larger than .30* variables are influences by many things (z-scores) we must interpret mark's grade relative to the average performance of class (z-scores) z-scores -standarized scores provide a way to express how far a person is from the mean, relative to the variation of the scores (z-scores)  useful properties of z-scores 1-3 1. mean is always zero for a set of zscores 2. the SD of a set of standardized scores is alwasy 1*-2-1-0-1-2 3. distribution of a set of standardized scores has same shape as the unstandardized scores*beware of the normalizaton misinterpretation (zscores) useful properties of zscores 4-5 4. standard scores may be used to compute centile scores 5. z-scores provide way to standardize different metrics*different varaibales expressed as zscores can be used under same metric(zscore) LArger groups of people are called population *this is what we aim in our research when we conduct a study, we can only study a limited group which is called... sample Sampling error -difference we observe as a result of studying a sample of a larger population*we are only working with subsets of a large population Standard Error of the mean (SEM) it tells us how far on average we would expect our sample mean to vary from our expected population mean*quantifies amount of smapling error Meaning of SEM? ex) SEM of 5 -we can expect the participants to score about 5% from the mean (significance tests) How to deal with problem of sampling error in psych research? is by using larger sample sizes (significance tests) formal methods of discussing if an observed effect is greater than what we would expect due to sampling error alone... null hypothesis significance tests (significance tests) what criteria do we use to determine if a something is unlikely to occur by sampling error alone? -scientists agree that something is unlikely to be due to chance if it is likely to occur less than 5% of the time*does not mean it could not be due to chance, just unlikely (significance tests) IF statistic exceeds critical value.. reject null hypothesis*results support research hypothesis (significance tests) If stat does not exceed critical value... retain null*results are likely due to sampling error (sample t-test) if calculated t does not exceed critical value... we fail to reject the null hypothesis (sample t-test) Our calcualted risk should fall on the tail ends of graph -it will indicate it occurs less than 5 %.  - if it falls on the middle than the null hypothesis will be supported (inferential errors) Type I error -reject the null hypothesis when it is actually true*accept as "real" an effect that is due to chance only*error determined by choice of critical value (.5,.1.001)*worst error (inferential errors) Type II errors -accept null hypothesis when it is actually false*assume that a real effect is only due to chance*error influenced by alpha*way to prevent it, is to collect sufficient sample size 4 common ways of null hypothesis significance tests -t-tests-analysis of varience (ANOVA)-z-tests-chi-squares Authorefrain12 ID177635 Card Setunderstanding data distributions, correlations, z-scores-psych Description5 powerpoints/ 2nd half Updated2012-10-27T23:02:02Z Show Answers