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# UNDERSTANDING RESEARCH INF 397C

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This 18 page Class Notes was uploaded by Maryse Herman on Monday September 7, 2015. The Class Notes belongs to INF 397C at University of Texas at Austin taught by Randolph Bias in Fall. Since its upload, it has received 44 views. For similar materials see /class/181904/inf-397c-university-of-texas-at-austin in Information Studies at University of Texas at Austin.

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Date Created: 09/07/15

NF397C Introduction to Research in Information Studies Fa 2007 Day 9 R G Bias School oflnformation SZB 5628 Phone 512 4717046 rbiasischoolutexasedu Where we ve been Descriptive statistics Frequency distributions Graphs Types of scales Probability Measures of central tendency and spread z scores Experimental design The scientific method Operational definitions IV DV controls counterbalancing confounds Validity reliability Within and betweensubject designs Qualitative research Gracy Rice Lively R G Bias School oflnformation SZB 5628 Phone 512 4717046 rbiasischoolutexasedu Context cont d Where we re going More descriptive statistics Correlation Inferential statistics Confidence intervals Hypothesis testing Type and II errors significance level ttests Anova Which method when Cumulative final R G Bias School oflnformation SZB 5628 Phone 512 4717046 rbiasischoolutexasedu First correcting a lie Parameters Statistics for for samples populations Mean p ZXN M or X bar ZXN Standard 0 SQRT of s SQRT of deviation 2X2ZX2N ZXZ ZX2N N N1 R G Bias School otlntormatlon 845 bBZB Phone b12 41 046 rblaslscnoolutexasedu Degrees of Freedom Demo R G Bias School oflnformation SZB 5628 Phone 512 4717046 rbiasischoolutexasedu Standard Error of the Mean So far we ve computed a sample mean M X bar and used it to estimate the population mean u One thing we ve gotten convinced of I hope is larger sample sizes are better Think about it what if I asked ONE of you what School are you a student in Versus asking 10 of you R G Bias School oflnformation SZB 5628 Phone 512 4717046 rbiasischoolutexasedu Standard Error cont d Well instead of picking ONE sample and using that mean to estimate the population mean what if we sampled a BUNCH of samples If we sampled ALL possible samples the mean of the means would equal the population mean pM Here are some other things we know As we get more samples the mean of the sample means gets closer to the population mean Distribution of sample means tends to be normal We can use the 2 table to find the probability of a mean of a certain value And most importantly R G Bias School oflnformation SZB 5628 Phone 512 4717046 rbiasischoolutexasedu Standard Error cont d We can easily work out the standard deviation of the distribution of sample means SE SM SSQRTN So the standard error of the mean is the standard distance that a sample mean is from the population mean Thus the SE tells us how good an estimate our sample mean is of the population mean Note as N gets larger the SE gets smaller and the better the sample mean estimates the population mean Hold on we ll use SE later R G Bias School oflnformation SZB 5628 Phone 512 4717046 rbiasischoolutexasedu A research question 1 Does an iSchool lTprovided online tutorial lead to better learning than a faceto face class R G Bias School oflnformation SZB 5628 Phone 512 4717046 rbiasischoolutexasedu Two methods of making statistical inferences I Null hypothesis testing Assume IV has no effect on DV differences we obtain are just by chance error variance If the difference is unlikely enough to happen by chance and enough tends to be p lt 05 then we say there s a true difference Confidence intervals We compute a confidence interval for the true population mean from sample data 95 level usually If two groups confidence intervals don t overlap we say we INFER there s a true difference R G Bias School oflnformation SZB 5628 Phone 512 4717046 rbiasischoolutexasedu 1o Remember Earlier I said that there are two ways for us to be confident that something is true Statistical inference Replicability Now I m saying there are two avenues of statistical inference Hypothesis testing Confidence intervals R G Bias School oflnformation SZB 5628 Phone 512 4717046 rbiasischoolutexasedu 11 ttests Remember the z scores z X po It is often the case that we want to know What percentage of the scores are above or below a certain other score Asked another way What is the area under the curve beyond a certain point THIS is why we calculate a z score and the way we do it is with the 2 table on p 362 of Hinton Problem We RARELY truly know u or o R G Bias School oflnformation SZB 5628 Phone 512 4717046 rbiasischoolutexasedu 12 ttests cont d I So typically what we do is use M to estimate p and s to estimate 0 Duh Note When we estimate 0 with s we divide by N1 which is degrees of freedom Then instead of z we calculate t Hinton s example on p 66 is for a ttest when you have a null hypothesis population mean p0 That is you want to test if your observed sample mean is different from some value Hinton then offers examples in Chapter 8 of related dependent withinsubjects and independent unrelated betweensubjects ttests S Z amp Z s example on p 447 is for a ttest to compare independent means R G Bias School oflnformation SZB 5628 Phone 512 4717046 rbiasischoolutexasedu 13 Formulae For a single meancompared with uo t M usSQRTn For related withinsubjects groups 39 tM1 M23 M1 M2 Where 3 NH M2 sX1 X2SQRTn See Hinton p 86 For independent groups From 8 Z amp Z p 447 and Hinton p 90 39 tM1 M23 M1 M2 Where 3 M1M2 SQRT 812n1 822n2 See Hinton p 90 R G Bias School oflnformation SZB 5628 Phone 512 4717046 rbiasischoolutexasedu 14 Steps For a t test for a single sample Restate the question as a research hypothesis and a null hypothesis about the populations Determine the characteristics of the comparison distribution The mean is the known population mean Compute the standard deviation by Calculate the estimated population variance S2 SSdf Calculate the variance ofthe distribution of means SZIn Take the square root to get SE Note we re calculating t with N l df Determine the cutoff sample score on the comparison distribution at which the null hypothesis should be rejected Decide on an alpha and onetailed vs twotailed Look up the critical value in the table Determine your sample s t score t m u SE Decide whether to reject or not reject the null hypothesis If the observed value oft exceeds the table value reject R G Bias School oflnformation SZB 5628 Phone 512 4717046 rbiasischoolutexasedu 15 Steps For a t test for dependent means Restate the question as a research hypothesis and a null hypothesis about the populations Determine the characteristics of the comparison distribution Make each person s score into a difference score From here on out use difference scores Compute the mean ofthe difference scores Assume a population mean of 0 u 0 Compute the standard deviation ofthe difference scores Calculate the estimated population variance 82 SSdf Calculate the variance ofthe distribution of means 8 Take the square root to get SE Note we re calculating t with N1 df Determine the cutoff sample score on the comparison distribution at which the null hypothesis should be rejec e Decide on an alpha and onetailed vs twotailed Look up the critical value in the table Determine your sample s t score t m p SE Decide whether to reject or not reject the null hypothesis If the observed value of t exceeds the table value reject R G Bias School oflnformation SZB 5628 Phone 512 4717046 rbiasischoolutexasedu 16 Steps For a t test for independent means Same as for dependent means except the value for SE is that squirrer formula on Hinton p 90 Basically here s the point When you re comparing DEPENDENT withinsubject related means you can assume both sets of scores come from the same distribution thus have the same standard deviation But when you re comparing independent between subject unrelated means you gotta basically average the variability of each of the two distributions R G Bias School oflnformation SZB 5628 Phone 512 4717046 rbiasischoolutexasedu 17 Three points df Four people take your choice of candy One df used up calculating the mean One or two tails Must be VERY careful choosing to do a onetailed test Comparing the z and ttables Check out the 05 t table values for infinity df 196 for twotailed test 1645 for onetailed Now find the commensurate values in the 2 table R G Bias School oflnformation SZB 5628 Phone 512 4717046 rbiasischoolutexasedu 18

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