{smcl}
{com}{sf}{ul off}{txt}{.-}
      name:  {res}<unnamed>
       {txt}log:  {res}/Users/eric/Work/MB/ATCR/200/Labs/lab 4.smcl
  {txt}log type:  {res}smcl
 {txt}opened on:  {res}20 Sep 2018, 11:29:51
{txt}
{com}. 
. /* In this lab, we first show how to use various "immediate" commands in Stata,
> which are useful for running hypothesis tests using summary data (e.g., sample 
> sizes, means, standard deviations, counts or proportions).  Then we will show 
> how to run these tests using baseline data from the 2763 participants in the 
> HERS RCT of hormone therapy as secondary prevention for coronary heart disease. 
> 
> ********************************************************************************
> Tests using immediate commands
> 
> For the population of middle-aged men who later develop diabetes, baseline BMI 
> has unknown mean and standard deviation(SD). In a sample of 58 men selected 
> from this population, mean BMI is 25.0 kg/m2, with SD 2.7.
> 
> First, calculate a 95% confidence interval for the mean. Begin by checking the 
> help for the cii command. */
. 
. help cii
{txt}
{com}. 
. /* We have to specify the means option.  The arguments, in order, are the sample 
> size, the mean, and the SD. */
. 
. cii means 58 25 2.7

{txt}    Variable {c |}        Obs        Mean    Std. Err.       [95% Conf. Interval]
{hline 13}{c +}{hline 63}
             {c |}{col 16}{res}        58{col 29}       25{col 41} .3545274{col 57} 24.29007{col 69} 25.70993{txt}

{com}. 
. /* Now test the null hypothesis that the mean in this population is 24.0 kg/m2, 
> the known mean of the population of men who do not develop diabetes.  The 
> immediate commands are restricted to parametric tests, so we are implicitly 
> assuming the BMI is reasonably normal, which is of course impossible to check 
> from the summary data. */
. 
. help ttesti
{txt}
{com}. 
. /* We need the 1-sample t-test, comparing the observed sample mean to a known value.  The last argument for the command is the null value of the mean. */
. 
. ttesti 58 25 2.7 24

{txt}One-sample t test
{hline 9}{c TT}{hline 68}
{col 10}{c |}{col 16}Obs{col 27}Mean{col 35}Std. Err.{col 47}Std. Dev.{col 59}[95% Conf. Interval]
{hline 9}{c +}{hline 68}
       x {c |}{res}{col 12}     58{col 22}       25{col 34} .3545274{col 46}      2.7{col 58} 24.29007{col 70} 25.70993
{txt}{hline 9}{c BT}{hline 68}
    mean = mean({res}x{txt})                                                t = {res}  2.8207
{txt}Ho: mean = {res}24                                    {txt}degrees of freedom = {res}      57

    {txt}Ha: mean < {res}24               {txt}Ha: mean != {res}24                 {txt}Ha: mean > {res}24
 {txt}Pr(T < t) = {res}0.9967         {txt}Pr(|T| > |t|) = {res}0.0066          {txt}Pr(T > t) = {res}0.0033
{txt}
{com}. 
. /* So reasonably strong evidence that mean BMI among men who go on to develop 
> diabetes is higher than the population mean among men who do not.
> 
> **********
> 
> In a study investigating the effect of seatbelt use on morbidity and mortality 
> among pediatric victims of motor vehicles accidents, two random samples were 
> selected, one of children wearing seat belts at the time of the accident 
> (N=123), and the other of children who were not (N=290). In the first sample, 
> 3 children died, while in the second, 13 did. Is there evidence that these 
> two proportions are different?  
> 
> We can do this using the prtesti command. */
. 
. help prtesti
{txt}
{com}. 
. /* We need the immediate two-sample test of proportions with the count option. */
. 
. prtesti 123 3 290 13, count

{txt}Two-sample test of proportions                     {res}x{txt}: Number of obs = {res}     123
                                                   y{txt}: Number of obs = {res}     290
{txt}{hline 13}{c TT}{hline 64}
    {col 14}{c |}{col 22}Mean{col 29}Std. Err.{col 44}z{col 49}P>|z|{col 59}[95% Conf. Interval]
{hline 13}{c +}{hline 64}
           x {c |}{res}{col 17} .0243902{col 28} .0139089{col 58}-.0028707{col 70} .0516512
           {txt}y {c |}{res}{col 17} .0448276{col 28} .0121511{col 58} .0210119{col 70} .0686432
{txt}{hline 13}{c +}{hline 64}
        diff {c |}{res}{col 17}-.0204373{col 28} .0184691{col 58}-.0566361{col 70} .0157614
{txt}{col 14}{c |}{col 17}under Ho:{res}{col 28} .0207648{col 38}   -0.98{col 49}0.325
{txt}{hline 13}{c BT}{hline 64}
        diff = prop({res}x{txt}) - prop({res}y{txt})                                  z = {res} -0.9842
{txt}    Ho: diff = 0

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(Z < z) = {res}0.1625         {txt}Pr(|Z| > |z|) = {res}0.3250          {txt}Pr(Z > z) = {res}0.8375
{txt}
{com}. 
. /* We could also use csi command, which has the advantage of providing exact 
> tests, which could be needed, since the number of deaths among children wearing 
> seat belts was <5. It also provides confidence intervals for the risk difference 
> and risk ratio.  In this case, the required input is the number of cases and 
> non-cases, rather than the number of cases and sample size. We have set this 
> up to treat seat belt use as exposure. */
. 
. help csi
{txt}
{com}. 
. csi 3 13 120 277, exact

{txt}{col 18}{c |}   Exposed   Unexposed  {c |}      Total
{hline 17}{c +}{hline 24}{c +}{hline 12}
           Cases {c |} {res}        3          13{txt}  {c |}  {res}       16
        {txt}Noncases {c |} {res}      120         277{txt}  {c |}  {res}      397
{txt}{hline 17}{c +}{hline 24}{c +}{hline 12}
{col 12}Total {c |} {res}      123         290{txt}  {c |}  {res}      413
{txt}{col 18}{c |}{col 43}{c |}
            Risk {c |} {res} .0243902    .0448276{txt}  {c |}  {res} .0387409
{txt}{col 18}{c |}{col 43}{c |}
{col 18}{c |}      Point estimate    {c |}    [95% Conf. Interval]
{col 18}{c LT}{hline 24}{c +}{hline 24}
 Risk difference {c |} {res}{col 27}-.0204373{txt}{col 43}{c |}   {res}-.0566361    .0157614{txt} 
      Risk ratio {c |} {res}{col 27} .5440901{txt}{col 43}{c |}   {res} .1578389    1.875545{txt} 
 Prev. frac. ex. {c |} {res}{col 27} .4559099{txt}{col 43}{c |}   {res}-.8755455    .8421611{txt} 
 Prev. frac. pop {c |} {res}{col 27} .1357795{txt}{col 43}{c |}
{col 18}{c BLC}{hline 24}{c BT}{hline 24}
{col 35}1-sided Fisher's exact P ={res} 0.2468
{txt}{col 35}2-sided Fisher's exact P ={res} 0.4126
{txt}
{com}. 
. /* At least in this case, the chi-square and exact tests give qualitatively 
> similar results. The difference may be NS, but the CIs for the risk difference 
> and risk ratio are wide. A puzzing result -- are seatbelts ineffective for 
> young children, or was the sample size too small?
> 
> ***********
> 
> Sixty-three adult males with coronary artery disease were stress-tested riding 
> a stationary bicycle until the onset of chest pain. After resting, participants 
> rode again until the repeat onset of angina, and the percent decrease in time 
> to onset of pain was recorded. This procedure was carried out twice, first with 
> clean air, and then, on a subsequent visit, when carbon monoxide had been mixed
> in the air. The sample size was 63 and the mean decreases in time to second 
> onset were 3.35% and 9.63% at the first and second visits, and the standard 
> deviation of the difference, 9.63-3.35=6.28%, was 20.3%. The research question 
> is whether carbon monoxide affected the decrease in time to onset of chest 
> pain on the second trial. 
> 
> We can test the difference using a paired t-test. */
. 
. help ttesti
{txt}
{com}. 
. /* We need the immediate for of the one sample test, with the null hypothesis 
> (the last argument to the command) of zero. */
. 
. ttesti 63 6.28 20.3 0

{txt}One-sample t test
{hline 9}{c TT}{hline 68}
{col 10}{c |}{col 16}Obs{col 27}Mean{col 35}Std. Err.{col 47}Std. Dev.{col 59}[95% Conf. Interval]
{hline 9}{c +}{hline 68}
       x {c |}{res}{col 12}     63{col 22}     6.28{col 34}  2.55756{col 46}     20.3{col 58} 1.167511{col 70} 11.39249
{txt}{hline 9}{c BT}{hline 68}
    mean = mean({res}x{txt})                                                t = {res}  2.4555
{txt}Ho: mean = {res}0                                     {txt}degrees of freedom = {res}      62

    {txt}Ha: mean < {res}0                 {txt}Ha: mean != {res}0                 {txt}Ha: mean > {res}0
 {txt}Pr(T < t) = {res}0.9916         {txt}Pr(|T| > |t|) = {res}0.0169          {txt}Pr(T > t) = {res}0.0084
{txt}
{com}. 
. /********************************************************************************
> Tests using actual data
> 
> Now we will run analogous tests using actual rather than summarized data.  
> Begin by reading in the HERS data. */
. 
. use hers.dta, clear
{txt}
{com}. 
. describe

{txt}Contains data from {res}hers.dta
{txt}  obs:{res}         2,763                          
{txt} vars:{res}            46                          23 Jul 2018 10:25
{txt} size:{res}       237,618                          
{txt}{hline}
              storage   display    value
variable name   type    format     label      variable label
{hline}
{p 0 48}{res}{bind:ptid           }{txt}{bind: int     }{bind:{txt}%9.0g     }{space 1}{bind:         }{bind:  }{res}{res}anonymized participant identifier{p_end}
{p 0 48}{bind:acei           }{txt}{bind: byte    }{bind:{txt}%9.0g     }{space 1}{bind:noyes    }{bind:  }{res}{res}use of ace-inhibitors{p_end}
{p 0 48}{bind:age            }{txt}{bind: byte    }{bind:{txt}%9.0g     }{space 1}{bind:         }{bind:  }{res}{res}age (years){p_end}
{p 0 48}{bind:anyllm         }{txt}{bind: byte    }{bind:{txt}%9.0g     }{space 1}{bind:noyes    }{bind:  }{res}{res}use of any lipid-lowering agent{p_end}
{p 0 48}{bind:aspirin        }{txt}{bind: byte    }{bind:{txt}%9.0g     }{space 1}{bind:noyes    }{bind:  }{res}{res}use of aspirin{p_end}
{p 0 48}{bind:betab          }{txt}{bind: byte    }{bind:{txt}%9.0g     }{space 1}{bind:noyes    }{bind:  }{res}{res}use of beta-blockers{p_end}
{p 0 48}{bind:bmi            }{txt}{bind: float   }{bind:{txt}%9.0g     }{space 1}{bind:         }{bind:  }{res}{res}bmi (kg/m^2){p_end}
{p 0 48}{bind:ccb            }{txt}{bind: byte    }{bind:{txt}%9.0g     }{space 1}{bind:noyes    }{bind:  }{res}{res}use of calcium channel blockers{p_end}
{p 0 48}{bind:crcl           }{txt}{bind: float   }{bind:{txt}%9.0g     }{space 1}{bind:         }{bind:  }{res}{res}creatinine clearance (ml/min){p_end}
{p 0 48}{bind:creat          }{txt}{bind: float   }{bind:{txt}%9.0g     }{space 1}{bind:         }{bind:  }{res}{res}creatinine (mg/dl) {p_end}
{p 0 48}{bind:dbp            }{txt}{bind: int     }{bind:{txt}%9.0g     }{space 1}{bind:         }{bind:  }{res}{res}diastolic blood pressure{p_end}
{p 0 48}{bind:diabetes       }{txt}{bind: byte    }{bind:{txt}%9.0g     }{space 1}{bind:noyes    }{bind:  }{res}{res}diabetes{p_end}
{p 0 48}{bind:digitali       }{txt}{bind: byte    }{bind:{txt}%9.0g     }{space 1}{bind:noyes    }{bind:  }{res}{res}use of digitalis{p_end}
{p 0 48}{bind:dmpills        }{txt}{bind: byte    }{bind:{txt}%9.0g     }{space 1}{bind:noyes    }{bind:  }{res}{res}oral dm medication by self-report{p_end}
{p 0 48}{bind:drinkany       }{txt}{bind: byte    }{bind:{txt}%9.0g     }{space 1}{bind:noyes    }{bind:  }{res}{res}any current alcohol consumption{p_end}
{p 0 48}{bind:drnkspwk       }{txt}{bind: float   }{bind:{txt}%9.0g     }{space 1}{bind:         }{bind:  }{res}{res}average drinks per week{p_end}
{p 0 48}{bind:educyrs        }{txt}{bind: byte    }{bind:{txt}%9.0g     }{space 1}{bind:         }{bind:  }{res}{res}years of education{p_end}
{p 0 48}{bind:exercise       }{txt}{bind: byte    }{bind:{txt}%9.0g     }{space 1}{bind:noyes    }{bind:  }{res}{res}exercise at least 3 times per week{p_end}
{p 0 48}{bind:globrat        }{txt}{bind: byte    }{bind:{txt}%9.0g     }{space 1}{bind:globrat  }{bind:  }{res}{res}self-reported health{p_end}
{p 0 48}{bind:glucose        }{txt}{bind: int     }{bind:{txt}%9.0g     }{space 1}{bind:         }{bind:  }{res}{res}fasting glucose (mg/dl) {p_end}
{p 0 48}{bind:hdl0           }{txt}{bind: int     }{bind:{txt}%9.0g     }{space 1}{bind:         }{bind:  }{res}{res}baseline hdl cholesterol (mg/dl){p_end}
{p 0 48}{bind:hdl1           }{txt}{bind: int     }{bind:{txt}%9.0g     }{space 1}{bind:         }{bind:  }{res}{res}year 1 hdl cholesterol (mg/dl){p_end}
{p 0 48}{bind:ht             }{txt}{bind: byte    }{bind:{txt}%15.0g    }{space 1}{bind:ht       }{bind:  }{res}{res}random assignment to hormone therapy{p_end}
{p 0 48}{bind:htnmeds        }{txt}{bind: byte    }{bind:{txt}%9.0g     }{space 1}{bind:noyes    }{bind:  }{res}{res}anti-hypertensive use{p_end}
{p 0 48}{bind:insulin        }{txt}{bind: byte    }{bind:{txt}%9.0g     }{space 1}{bind:noyes    }{bind:  }{res}{res}insulin use by self-report{p_end}
{p 0 48}{bind:ldl0           }{txt}{bind: float   }{bind:{txt}%9.0g     }{space 1}{bind:         }{bind:  }{res}{res}baseline ldl cholesterol (mg/dl){p_end}
{p 0 48}{bind:ldl1           }{txt}{bind: float   }{bind:{txt}%9.0g     }{space 1}{bind:         }{bind:  }{res}{res}year 1 ldl cholesterol (mg/dl){p_end}
{p 0 48}{bind:lpa0           }{txt}{bind: float   }{bind:{txt}%9.0g     }{space 1}{bind:         }{bind:  }{res}{res}baseline Lp(a) (mg/dl){p_end}
{p 0 48}{bind:lpa1           }{txt}{bind: float   }{bind:{txt}%9.0g     }{space 1}{bind:         }{bind:  }{res}{res}year 1 Lp(a) (mg/dl){p_end}
{p 0 48}{bind:medcond        }{txt}{bind: byte    }{bind:{txt}%9.0g     }{space 1}{bind:         }{bind:  }{res}{res}other serious conditions by self-report{p_end}
{p 0 48}{bind:nonwhite       }{txt}{bind: byte    }{bind:{txt}%9.0g     }{space 1}{bind:noyes    }{bind:  }{res}{res}nonwhite race/ethnicity{p_end}
{p 0 48}{bind:pcabg          }{txt}{bind: byte    }{bind:{txt}%9.0g     }{space 1}{bind:noyes    }{bind:  }{res}{res}pre-randomization CABG{p_end}
{p 0 48}{bind:physact        }{txt}{bind: byte    }{bind:{txt}%20.0g    }{space 1}{bind:physact  }{bind:  }{res}{res}comparative physical activity{p_end}
{p 0 48}{bind:pmi            }{txt}{bind: byte    }{bind:{txt}%9.0g     }{space 1}{bind:noyes    }{bind:  }{res}{res}pre-randomization MI{p_end}
{p 0 48}{bind:poorfair       }{txt}{bind: byte    }{bind:{txt}%9.0g     }{space 1}{bind:noyes    }{bind:  }{res}{res}poor/fair self-reported health{p_end}
{p 0 48}{bind:pptca          }{txt}{bind: byte    }{bind:{txt}%9.0g     }{space 1}{bind:noyes    }{bind:  }{res}{res}pre-randomization PTCA{p_end}
{p 0 48}{bind:raceth         }{txt}{bind: byte    }{bind:{txt}%20.0g    }{space 1}{bind:raceth   }{bind:  }{res}{res}race/ethnicity{p_end}
{p 0 48}{bind:sbp            }{txt}{bind: int     }{bind:{txt}%9.0g     }{space 1}{bind:         }{bind:  }{res}{res}systolic blood pressure{p_end}
{p 0 48}{bind:smoking        }{txt}{bind: byte    }{bind:{txt}%9.0g     }{space 1}{bind:noyes    }{bind:  }{res}{res}current smoker{p_end}
{p 0 48}{bind:statins        }{txt}{bind: byte    }{bind:{txt}%9.0g     }{space 1}{bind:noyes    }{bind:  }{res}{res}use of statins{p_end}
{p 0 48}{bind:tchol0         }{txt}{bind: int     }{bind:{txt}%9.0g     }{space 1}{bind:         }{bind:  }{res}{res}baseline total cholesterol (mg/dl){p_end}
{p 0 48}{bind:tchol1         }{txt}{bind: int     }{bind:{txt}%9.0g     }{space 1}{bind:         }{bind:  }{res}{res}year 1 total cholesterol (mg/dl){p_end}
{p 0 48}{bind:tgl0           }{txt}{bind: int     }{bind:{txt}%9.0g     }{space 1}{bind:         }{bind:  }{res}{res}baseline triglycerides (mg/dl){p_end}
{p 0 48}{bind:tgl1           }{txt}{bind: int     }{bind:{txt}%9.0g     }{space 1}{bind:         }{bind:  }{res}{res}year 1 triglycerides (mg/dl){p_end}
{p 0 48}{bind:weight         }{txt}{bind: float   }{bind:{txt}%9.0g     }{space 1}{bind:         }{bind:  }{res}{res}weight (kg){p_end}
{p 0 48}{bind:whr            }{txt}{bind: float   }{bind:{txt}%9.0g     }{space 1}{bind:         }{bind:  }{res}{res}waist/hip ratio{p_end}
{txt}{hline}
Sorted by: 

{com}. sum

{txt}    Variable {c |}        Obs        Mean    Std. Dev.       Min        Max
{hline 13}{c +}{hline 57}
{space 8}ptid {c |}{res}      2,763        1382    797.7537          1       2763
{txt}{space 8}acei {c |}{res}      2,763    .1758958    .3808004          0          1
{txt}{space 9}age {c |}{res}      2,763    66.64857    6.653081         44         79
{txt}{space 6}anyllm {c |}{res}      2,763    .4828085    .4997948          0          1
{txt}{space 5}aspirin {c |}{res}      2,763    .7915309    .4062874          0          1
{txt}{hline 13}{c +}{hline 57}
{space 7}betab {c |}{res}      2,763    .3260948    .4688673          0          1
{txt}{space 9}bmi {c |}{res}      2,758    28.57925    5.517783      15.21      54.13
{txt}{space 9}ccb {c |}{res}      2,763    .5479551    .4977851          0          1
{txt}{space 8}crcl {c |}{res}      2,760    61.30613    19.60505    6.18408   167.5208
{txt}{space 7}creat {c |}{res}      2,762    1.084432    .3163941         .4        9.3
{txt}{hline 13}{c +}{hline 57}
{space 9}dbp {c |}{res}      2,762     73.1517    9.705057         45        102
{txt}{space 4}diabetes {c |}{res}      2,763    .2645675    .4411825          0          1
{txt}{space 4}digitali {c |}{res}      2,763    .0998914    .2999095          0          1
{txt}{space 5}dmpills {c |}{res}      2,763    .0962722    .2950175          0          1
{txt}{space 4}drinkany {c |}{res}      2,761    .3915248    .4881797          0          1
{txt}{hline 13}{c +}{hline 57}
{space 4}drnkspwk {c |}{res}      2,763    1.355169    3.652089          0       49.5
{txt}{space 5}educyrs {c |}{res}      2,761    12.66932    2.645689          1         20
{txt}{space 4}exercise {c |}{res}      2,763    .3865364     .487044          0          1
{txt}{space 5}globrat {c |}{res}      2,760    3.063406     .842833          1          5
{txt}{space 5}glucose {c |}{res}      2,763    112.1516    36.84941         29        298
{txt}{hline 13}{c +}{hline 57}
{space 8}hdl0 {c |}{res}      2,752    50.26199    13.21566         14        130
{txt}{space 8}hdl1 {c |}{res}      2,608    51.78183    13.87166         14        124
{txt}{space 10}ht {c |}{res}      2,763    .4994571    .5000902          0          1
{txt}{space 5}htnmeds {c |}{res}      2,763    .8215708     .382943          0          1
{txt}{space 5}insulin {c |}{res}      2,763    .0988056    .2984549          0          1
{txt}{hline 13}{c +}{hline 57}
{space 8}ldl0 {c |}{res}      2,752    145.0385    37.80322       36.8      393.4
{txt}{space 8}ldl1 {c |}{res}      2,608    132.3915    39.02262        -20      450.2
{txt}{space 8}lpa0 {c |}{res}      2,759    33.71443    32.61081          0        236
{txt}{space 8}lpa1 {c |}{res}      2,612    30.95115    33.28073          0      201.9
{txt}{space 5}medcond {c |}{res}      2,763    .3720594    .4834416          0          1
{txt}{hline 13}{c +}{hline 57}
{space 4}nonwhite {c |}{res}      2,763    .1129207    .3165532          0          1
{txt}{space 7}pcabg {c |}{res}      2,763    .4096996    .4918673          0          1
{txt}{space 5}physact {c |}{res}      2,763    3.200145    1.083468          1          5
{txt}{space 9}pmi {c |}{res}      2,763    .5099529    .4999914          0          1
{txt}{space 4}poorfair {c |}{res}      2,760     .240942    .4277327          0          1
{txt}{hline 13}{c +}{hline 57}
{space 7}pptca {c |}{res}      2,763    .4303294    .4952118          0          1
{txt}{space 6}raceth {c |}{res}      2,763    1.146942     .439843          1          3
{txt}{space 9}sbp {c |}{res}      2,763    135.0695    19.02781         83        224
{txt}{space 5}smoking {c |}{res}      2,763    .1302932    .3366866          0          1
{txt}{space 5}statins {c |}{res}      2,763    .3731451    .4837277          0          1
{txt}{hline 13}{c +}{hline 57}
{space 6}tchol0 {c |}{res}      2,759    228.5799    41.01411        110        465
{txt}{space 6}tchol1 {c |}{res}      2,613    219.2346    41.10315         92        535
{txt}{space 8}tgl0 {c |}{res}      2,759    166.1493    63.51077         31        476
{txt}{space 8}tgl1 {c |}{res}      2,613    175.7976    84.45064         31       1016
{txt}{space 6}weight {c |}{res}      2,761     72.7305    14.70306       37.5      131.6
{txt}{hline 13}{c +}{hline 57}
{space 9}whr {c |}{res}      2,760     .869979    .0795729       .624      1.218
{txt}
{com}. 
. /* First compare baseline LDL values in smokers and non-smokers using the 
> t-test. */
. 
. ttest ldl0, by(smoking)

{txt}Two-sample t test with equal variances
{hline 9}{c TT}{hline 68}
Variable{col 10}{c |}{col 16}Obs{col 27}Mean{col 35}Std. Err.{col 47}Std. Dev.{col 59}[95% Conf. Interval]
{hline 9}{c +}{hline 68}
      no {c |}{res}{col 12}  2,397{col 22} 144.3985{col 34} .7639244{col 46}  37.4011{col 58} 142.9005{col 70} 145.8965
     {txt}yes {c |}{res}{col 12}    355{col 22}   149.36{col 34} 2.133767{col 46} 40.20324{col 58} 145.1635{col 70} 153.5565
{txt}{hline 9}{c +}{hline 68}
combined {c |}{res}{col 12}  2,752{col 22} 145.0385{col 34} .7206171{col 46} 37.80322{col 58} 143.6255{col 70} 146.4515
{txt}{hline 9}{c +}{hline 68}
    diff {c |}{res}{col 22}-4.961502{col 34} 2.148142{col 58}-9.173636{col 70}-.7493675
{txt}{hline 9}{c BT}{hline 68}
    diff = mean({res}no{txt}) - mean({res}yes{txt})                                   t = {res} -2.3097
{txt}Ho: diff = 0                                     degrees of freedom = {res}    2750

    {txt}Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = {res}0.0105         {txt}Pr(|T| > |t|) = {res}0.0210          {txt}Pr(T > t) = {res}0.9895
{txt}
{com}. 
. /* We can check whether the results are sensitive to allowing for unequal 
> variance in smoker and non-smokers. */ 
. 
. ttest ldl0, by(smoking) unequal

{txt}Two-sample t test with unequal variances
{hline 9}{c TT}{hline 68}
Variable{col 10}{c |}{col 16}Obs{col 27}Mean{col 35}Std. Err.{col 47}Std. Dev.{col 59}[95% Conf. Interval]
{hline 9}{c +}{hline 68}
      no {c |}{res}{col 12}  2,397{col 22} 144.3985{col 34} .7639244{col 46}  37.4011{col 58} 142.9005{col 70} 145.8965
     {txt}yes {c |}{res}{col 12}    355{col 22}   149.36{col 34} 2.133767{col 46} 40.20324{col 58} 145.1635{col 70} 153.5565
{txt}{hline 9}{c +}{hline 68}
combined {c |}{res}{col 12}  2,752{col 22} 145.0385{col 34} .7206171{col 46} 37.80322{col 58} 143.6255{col 70} 146.4515
{txt}{hline 9}{c +}{hline 68}
    diff {c |}{res}{col 22}-4.961502{col 34} 2.266394{col 58}-9.415545{col 70}-.5074582
{txt}{hline 9}{c BT}{hline 68}
    diff = mean({res}no{txt}) - mean({res}yes{txt})                                   t = {res} -2.1892
{txt}Ho: diff = 0                     Satterthwaite's degrees of freedom = {res} 449.474

    {txt}Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = {res}0.0145         {txt}Pr(|T| > |t|) = {res}0.0291          {txt}Pr(T > t) = {res}0.9855
{txt}
{com}. 
. /* Clearly the SDs do differ somewhat, and allowing for this inequality using 
> the unequal option increases the p-value a bit.  
> 
> We can also use a paired t-test to compare the LDL values measured at baseline 
> to the year 1 value: */
. 
. ttest ldl0 == ldl1 

{txt}Paired t test
{hline 9}{c TT}{hline 68}
Variable{col 10}{c |}{col 16}Obs{col 27}Mean{col 35}Std. Err.{col 47}Std. Dev.{col 59}[95% Conf. Interval]
{hline 9}{c +}{hline 68}
    ldl0 {c |}{res}{col 12}  2,597{col 22}  144.758{col 34} .7421193{col 46} 37.81897{col 58} 143.3028{col 70} 146.2132
    {txt}ldl1 {c |}{res}{col 12}  2,597{col 22} 132.3248{col 34} .7661903{col 46} 39.04565{col 58} 130.8224{col 70} 133.8272
{txt}{hline 9}{c +}{hline 68}
    diff {c |}{res}{col 12}  2,597{col 22} 12.43327{col 34}  .681349{col 46} 34.72207{col 58} 11.09723{col 70} 13.76931
{txt}{hline 9}{c BT}{hline 68}
     mean(diff) = mean({res}ldl0{txt} - {res}ldl1{txt})                               t = {res} 18.2480
{txt} Ho: mean(diff) = 0                              degrees of freedom = {res}    2596

 {txt}Ha: mean(diff) < 0           Ha: mean(diff) != 0           Ha: mean(diff) > 0
 Pr(T < t) = {res}1.0000         {txt}Pr(|T| > |t|) = {res}0.0000          {txt}Pr(T > t) = {res}0.0000
{txt}
{com}. 
. /* Note that the sample size goes down.  Why?
> 
> We could also use a non-parametric Wilcoxon ranksum test to compare baseline 
> LDL levels by smoking status; this method essentially operates on the ranks 
> of LDL, rather than  directly on the measured LDL values.  For within-person 
> comparisons of baseline and year 1 LDL, we can use the signrank test. */
. 
. ranksum ldl0, by(smoking)

{txt}Two-sample Wilcoxon rank-sum (Mann-Whitney) test

     smoking {c |}      obs    rank sum    expected
{hline 13}{c +}{hline 33}
          no {c |}{res}{col 17}   2397{col 26}   3265492{col 38} 3299470.5
         {txt}yes {c |}{res}{col 17}    355{col 26}    522636{col 38}  488657.5
{txt}{hline 13}{c +}{hline 33}
    combined {c |}{res}{col 17}   2752{col 26}   3788128{col 38}   3788128

{txt}unadjusted variance{col 22}{res} 1.952e+08
{txt}adjustment for ties{col 22}{res} -966.3953
{txt}{col 22}{hline 10}
adjusted variance{col 22}{res} 1.952e+08

{txt}Ho: ldl0(smoking==no) = ldl0(smoking==yes)
{col 14}z = {res} -2.432
{txt}{col 5}Prob > |z| = {res}  0.0150
{txt}
{com}. signrank ldl0 = ldl1 

{txt}Wilcoxon signed-rank test

        sign {c |}      obs   sum ranks    expected
{hline 13}{c +}{hline 33}
    positive {c |}{res}{col 17}   1714{col 26} 2399964.5{col 38}   1686741
    {txt}negative {c |}{res}{col 17}    877{col 26}  973517.5{col 38}   1686741
        {txt}zero {c |}{res}{col 17}      6{col 26}        21{col 38}        21
{txt}{hline 13}{c +}{hline 33}
         all {c |}{res}{col 17}   2597{col 26}   3373503{col 38}   3373503

{txt}unadjusted variance{col 22}{res} 1.460e+09
{txt}adjustment for ties{col 22}{res}   -2366.5
{txt}adjustment for zeros{col 22}{res}    -22.75
{txt}{col 22}{hline 10}
adjusted variance{col 22}{res} 1.460e+09

{txt}Ho: ldl0 = ldl1
{col 14}z = {res} 18.663
{txt}{col 5}Prob > |z| = {res}  0.0000
{txt}
{com}. 
. /* In both cases, the results are similar to the t-test results.  Another 
> non-parametric approach is to compare the proportions that are greater than 
> the overall median, using a chi-square test.  */
. 
. median ldl0, by(smoking)

{txt}Median test

   Greater {c |}
  than the {c |}    current smoker
    median {c |}        no        yes {c |}     Total
{hline 11}{c +}{hline 22}{c +}{hline 10}
        no {c |}{res}     1,222        157 {txt}{c |}{res}     1,379 
{txt}       yes {c |}{res}     1,175        198 {txt}{c |}{res}     1,373 
{txt}{hline 11}{c +}{hline 22}{c +}{hline 10}
     Total {c |}{res}     2,397        355 {txt}{c |}{res}     2,752 

{txt}          Pearson chi2({res}1{txt}) = {res}  5.6437  {txt} Pr = {res}0.018

{txt}   Continuity corrected:
          Pearson chi2({res}1{txt}) = {res}  5.3768{txt}   Pr = {res}0.020
{txt}
{com}. 
. /* This command has options for how ties at the median are handled; check the 
> help to learn about this. */
. 
. help median
{txt}
{com}. 
. /* For multi-category predictors, parametric and nonparametric alternatives 
> include ANOVA and Kruskal-Wallis test respectively. */
. 
. anova lpa0 raceth

                         {txt}Number of obs = {res}     2,759    {txt}R-squared     ={res}  0.0470
                         {txt}Root MSE      =   {res} 31.8468    {txt}Adj R-squared ={res}  0.0463

                  {txt}Source {c |} Partial SS         df         MS        F    Prob>F
              {hline 11}{c +}{hline 52}
                   Model {c |} {res} 137855.61          2   68927.804     67.96  0.0000
                         {txt}{c |}
                  raceth {c |} {res} 137855.61          2   68927.804     67.96  0.0000
                         {txt}{c |}
                Residual {c |} {res} 2795180.5      2,756   1014.2164  
              {txt}{hline 11}{c +}{hline 52}
                   Total {c |} {res} 2933036.1      2,758   1063.4649  
{txt}
{com}. kwallis lpa0, by(raceth)

{txt}Kruskal-Wallis equality-of-populations rank test

  {c TLC}{hline 22}{c TT}{hline 7}{c TT}{hline 11}{c TRC}
  {c |} {res}              raceth {txt}{c |} {res}  Obs {txt}{c |} {res} Rank Sum {txt}{c |}
  {c LT}{hline 22}{c +}{hline 7}{c +}{hline 11}{c RT}
  {c |} {res}               White {txt}{c |} {res}2,447 {txt}{c |} {res} 3.28e+06 {txt}{c |}
  {c |} {res}    African American {txt}{c |} {res}  218 {txt}{c |} {res}417774.50 {txt}{c |}
  {c |} {res}Latina, Asian, Other {txt}{c |} {res}   94 {txt}{c |} {res}114079.00 {txt}{c |}
  {c BLC}{hline 22}{c BT}{hline 7}{c BT}{hline 11}{c BRC}

chi-squared = {res}  109.553{txt} with {res}2{txt} d.f.
probability = {res}    0.0001

{txt}chi-squared with ties = {res}  109.653{txt} with {res}2{txt} d.f.
probability = {res}    0.0001
{txt}
{com}. 
. /* In this case, the two tests gives qualitatively identical assessments of
> the statistical significance of differences in Lp(a) by race/ethnicity.  Next
> week, we will look at the distribution of the these outcomes as well as sample 
> size to help decide whether the parametric or non-parametric test is more
> appropriate. */
. 
. log close
      {txt}name:  {res}<unnamed>
       {txt}log:  {res}/Users/eric/Work/MB/ATCR/200/Labs/lab 4.smcl
  {txt}log type:  {res}smcl
 {txt}closed on:  {res}20 Sep 2018, 11:29:52
{txt}{.-}
{smcl}
{txt}{sf}{ul off}