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# HPHY 212 Week 6 Lecture Notes HPHY 212

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This 5 page Class Notes was uploaded by Scott Morrison on Friday May 8, 2015. The Class Notes belongs to HPHY 212 at University of Oregon taught by Dr. Andrew Karduna in Spring2015. Since its upload, it has received 127 views. For similar materials see Evidence, Inference and Biostatistics in Human Development at University of Oregon.

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Date Created: 05/08/15

HPHY 212 Lecture Notes Week 6 Distribution and sampling Central Tendency Scores ways of measuring the general area around which a set of numbers tend to lie Mean Median Mode Variability Scores ways of measuring how much a set of numbers varies Standard Deviation STDEV Range Confidence Intervals CI A Normal Distribution of Data V K SAMflL 322 Because there is variability in a population a median can be a better way to represent a population Sampling Taking a small portion of a population a sample and using data from that portion to extrapolate the properties of a population In order for a study to be valid the sample needs to accurately represent the population Standard Error of the Mean SEN 4quot SW J Jfg We 57v rmL a4 5 pk In The standard error of the mean attempts to estimate the uncertainty in the estimated population mean obtained from the sample The reported mean is the sample mean not the population mean the sample mean is an estimation of the population mean How can you know how well the sample mean represents the population mean You can t but there are factors that make one sample mean better than another like a larger sample size Confidence Intervals Confidence intervals tell you the odds of your data being a correct representation of the population The three levels of confidence intervals are 68 confidence 95 confidence and 99 confidence Each of these intervals mean that X of the population falls within that interval if you were for instance measuring height a confidence interval of 95 would have a maximum measurement and a minimum measurement 95 of the population would fall somewhere between those two measurements Confidence intervals correspond to standard deviations a 68 confidence interval has an interval of 1 standard deviation A 95 confidence interval has an interval of 2 standard deviations A 99 confidence interval has an interval of 3 standard deviations mtistical Hypothesis Testing A way of applying the scientific method to analyzing data while accounting for random fluctuations Are these fluctuations in the data statistically significant or are theyjust a result of chance Research Hypothesis The hypothesis that the researchers expect to be supported by the experiment Eg hypothesize that tall people weigh MORE than short people This hypothesis is the difference between two means that the researchers are expecting Alternative Hypothesis The opposite of what the researchers expect to happen in terms of the relationship of the two variables eg tall people weigh LESS than short people The alternative hypothesis means that the difference between two means is the opposite of what researchers expected to happen Null Hypothesis The hypothesis that there are no relationships between the two variables eg tall people weigh THE SAME AS short people The null hypothesis means that there is no statistically significant difference between two means a Level The alphalevel is the level of probability that is defined as statistically significant The alphalevel is set before statistics tests are done The alphalevel is the amount of likelihood that the differences between data sets are statistically significant and not due to chance alone In order to test this researchers will perform a Student Ttest The result of this test is called a pvalue probability value An accepted p value will be less than 005 A pvalue of 005 means that there is a 5 chance that the differences in data were a result of chance Researchers want low pvalues 005 is the accepted threshold in the scientific community A pvalue is the measurement of the probability that the null hypothesis is correct If plt005 your data supports your research hypothesis f pgt 005 you fail to reject the null hypothesis We say quotfail to reject instead of accept because we only know that the data doesn t support the null hypothesis it could be that the sample size is too small or there could be other errors Nothing in research is definitive You can t solidly prove you can only support Ttests In order for a ttest to be valid you need two things a normal distribution of data a decent sample size that wellrepresents the population Independent unpaired ttests Unpaired ttests are done when two different groups of subjects are being compared Dependent paired ttests Paired ttests are done when the same group is being tested before and after an experimental treatment Shown below is the formula for an unpaired ttest 6 NtkMLZ a Was k 39 J SbeV Sm 6 quot L V I V L v J W 39 L o f X l 5 EM T l 3 aquot A Using a Table to Find PValues 1 Go to the pvalue chart and find your degree of freedom see df formula below 2 Find your threshold tvalue for plt005 3 Your tvalue must be higher than the critical tvalue listed if not then p is not less than 005 and you fail to reject the null hypothesis Excel can also calculate pvalues Degree Of Freedom V I 2 m I L l L YA SM A El rrc fcw P114 TwoTailed ttest Done when the difference in the groups could follow two quottailsquot the researchers don t know which direction the difference will fall but they expect a difference eg tall people may weigh more or less than short people OneTailed ttest Done when the difference in the groups is expected to follow one quottailquot the researchers know there will be a difference and they expect the difference to follow one direction eg tall people will weigh more than short people Analysis of Variance ANOVA An ANOVA is an extension of a ttest ANOVAs are done when researchers need to compare more than three groups Simply doing multiple ttests would oversimplify the statistical analysis doing more comparisons leaves more room for error ANOVAS are also done when there is more than one independent variable This is called a twoway ANOVA

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