diff --git a/paper/.~lock.weGotThePowerDraftPaper.html# b/paper/.~lock.weGotThePowerDraftPaper.html#
new file mode 100644
index 0000000000000000000000000000000000000000..045d4752318981bcc5e642447272d0850a8de33e
--- /dev/null
+++ b/paper/.~lock.weGotThePowerDraftPaper.html#
@@ -0,0 +1 @@
+Ben Anderson,ben,ou029107.otago.ac.nz,15.11.2018 14:52,file:///Users/ben/Library/Application%20Support/LibreOffice/4;
\ No newline at end of file
diff --git a/paper/figs/statPowerEsts80means_All.png b/paper/figs/statPowerEsts80means_All.png
index c0ac3a35645a1e788dd417c13d47f691c32e9339..4b491349d9bdb5abf42708bc04d7ad35704404fa 100644
Binary files a/paper/figs/statPowerEsts80means_All.png and b/paper/figs/statPowerEsts80means_All.png differ
diff --git a/paper/figs/statPowerEsts80means_p0.01.png b/paper/figs/statPowerEsts80means_p0.01.png
index 64bf64b4592b697c415c5dd2f24ca978619789e5..bb346f2ecf4ce7e104be980bcadf3f5d50b0ac49 100644
Binary files a/paper/figs/statPowerEsts80means_p0.01.png and b/paper/figs/statPowerEsts80means_p0.01.png differ
diff --git a/paper/weGotThePowerDraftPaper.Rmd b/paper/weGotThePowerDraftPaper.Rmd
index ccc7293e3672afbddda2c44478f38c05ab7b3944..52fd26341d00b217c6e0063b323e607628c10f82 100644
--- a/paper/weGotThePowerDraftPaper.Rmd
+++ b/paper/weGotThePowerDraftPaper.Rmd
@@ -51,6 +51,7 @@ rmdLibs <- c("data.table", # data munching
"dkUtils", # utilities from devtools::install_github("dataknut/dkUtils")
"forcats", # category manipulation
"pwr", # power stuff
+ "GREENGridData", # GREEN grid data loading etc from devtools::install_github("cfsOtago/GREENGridData")
"knitr" # for kable
)
# load them
@@ -73,11 +74,13 @@ labelProfilePlot <- function(plot){
myParams <- list()
myParams$repoLoc <- dkUtils::findParentDirectory("weGotThePower")
-myParams$dPath <- "~/Dropbox/Work/Otago_CfS_Ben/data/nzGREENGrid/dataExtracts/"
+myParams$dPath <- "~/Dropbox/Work/Otago_CfS_Ben/data/nzGREENGrid/"
#myParams$dPath <- "~/Data/NZ_GREENGrid/safe/gridSpy/1min/dataExtracts/"
# created from https://dx.doi.org/10.5255/UKDA-SN-853334
# using https://github.com/CfSOtago/GREENGridData/blob/master/examples/code/extractCleanGridSpy1minCircuit.R
-heatPumpData <- paste0(myParams$dPath, "Heat Pump_2015-04-01_2016-03-31_observations.csv.gz")
+heatPumpData <- paste0(myParams$dPath, "dataExtracts/Heat Pump_2015-04-01_2016-03-31_observations.csv.gz")
+ggHHData <- paste0(myParams$dPath, "ggHouseholdAttributesSafe.csv")
+
myParams$GGDataDOI <- "https://dx.doi.org/10.5255/UKDA-SN-853334"
plotCaption <- paste0("Source: ", myParams$GGDataDOI)
@@ -142,41 +145,93 @@ This report contains the analysis for a paper of the same name. The text is stor
# Load GREEN Grid Heat Pump data
if(file.exists(heatPumpData)){
message("Loading: ", heatPumpData )
- dt <- data.table::as.data.table(readr::read_csv(heatPumpData, progress = TRUE))
+ gsDT <- GREENGridData::getCleanGridSpyFile(heatPumpData) # load Grid Spy data cleanly, throws a warning about missing fields/columns
+ # dt <- data.table::as.data.table(readr::read_csv(heatPumpData,
+ # progress = FALSE,
+ # col_types = list(col_character(), # hhid
+ # col_character(), # linkID
+ # col_datetime(format = ""), # dateTime
+ # col_character(), # circuit
+ # col_double()) # power
+ # )
+ # )
} else {
message("No such file: ", heatPumpData )
stop()
}
-dt <- dt[, month := lubridate::month(r_dateTime)]
-dt <- dt[, year := lubridate::year(r_dateTime)]
+gst <- summary(gsDT)
+
+gsDT <- gsDT[, month := lubridate::month(r_dateTime)]
+gsDT <- gsDT[, year := lubridate::year(r_dateTime)]
# add southern hemisphere season
-dt <- dt[, tmpM := lubridate::month(r_dateTime)] # sets 1 (Jan) - 12 (Dec). May already exist but we can't rely on it
-dt <- dt[, season := "Summer"] # easiest to set the default to be the one that bridges years
-dt <- dt[tmpM >= 3 & tmpM <= 5, season := "Autumn"]
-dt <- dt[tmpM >= 6 & tmpM <= 8 , season := "Winter"]
-dt <- dt[tmpM >= 9 & tmpM <= 11, season := "Spring"]
+gsDT <- gsDT[, tmpM := lubridate::month(r_dateTime)] # sets 1 (Jan) - 12 (Dec). May already exist but we can't rely on it
+gsDT <- gsDT[, season := "Summer"] # easiest to set the default to be the one that bridges years
+gsDT <- gsDT[tmpM >= 3 & tmpM <= 5, season := "Autumn"]
+gsDT <- gsDT[tmpM >= 6 & tmpM <= 8 , season := "Winter"]
+gsDT <- gsDT[tmpM >= 9 & tmpM <= 11, season := "Spring"]
# re-order to make sense
-dt <- dt[, season := factor(season, levels = c("Spring", "Summer", "Autumn", "Winter"))]
+gsDT <- gsDT[, season := factor(season, levels = c("Spring", "Summer", "Autumn", "Winter"))]
+
+# Load GREEN Grid household data
+if(file.exists(ggHHData)){
+ message("Loading: ", ggHHData )
+ hhDT <- data.table::as.data.table(readr::read_csv(ggHHData))
+} else {
+ message("No such file: ", ggHHData )
+ stop()
+}
+
+knitr::kable(caption = "Summary of grid spy data", gst)
+
+# there are negawatts!
+gsDT <- gsDT[, negW := "PosW"]
+gsDT <- gsDT[ powerW < 0, negW := "NegaW"]
+
+t <- table(gsDT$linkID,gsDT$negW)
+t
+prop.table(t)
+
```
```{r dataPrep}
-testDT <- dt[lubridate::hour(r_dateTime) > 15 & # 16:00 ->
+
+hhDT <- hhDT[Q57 == 1, nPeople := "1"]
+hhDT <- hhDT[Q57 == 2, nPeople := "2"]
+hhDT <- hhDT[Q57 == 3, nPeople := "3"]
+hhDT <- hhDT[Q57 > 3, nPeople := "4+"]
+
+
+setkey(hhDT, linkID)
+
+testDT <- gsDT[lubridate::hour(r_dateTime) > 15 & # 16:00 ->
lubridate::hour(r_dateTime) < 20 & # <- 20:00
lubridate::wday(r_dateTime) != 6 & # not Saturday
lubridate::wday(r_dateTime) != 7 & # not Sunday
- year == 2015,
+ year == 2015 & negW == "PosW", # remove the negawatts (see https://github.com/CfSOtago/GREENGridData/issues/6)
.(meanW = mean(powerW, na.rm = TRUE),
sdW = sd(powerW, na.rm = TRUE)), keyby = .(season, linkID)]
+setkey(testDT, linkID)
+linkedTestDT <- hhDT[testDT]
+
-testTable <- testDT[, .(meanMeanW = mean(meanW),
- sdMeanW = sd(meanW)), keyby = .(season)]
+testTable <- linkedTestDT[, .(meanMeanW = mean(meanW),
+ sdMeanW = sd(meanW),
+ nHouseholds = .N), keyby = .(season, nPeople)]
knitr::kable(caption = "Summary of mean consumption per household by season", testTable)
-ggplot2::ggplot(testDT, aes(y = meanW, x = fct_reorder(linkID, meanW, .desc = TRUE), colour = season)) +
- geom_point()
+testTable <- linkedTestDT[season == "Winter", .(meanMeanW = mean(meanW),
+ sdMeanW = sd(meanW),
+ nHouseholds = .N)]
+
+knitr::kable(caption = "Summary of mean consumption per household in winter", testTable)
+
+# plot distn
+ggplot2::ggplot(linkedTestDT, aes(y = meanW, x = fct_reorder(linkID, meanW, .desc = TRUE), colour = nPeople)) +
+ geom_point() +
+ facet_wrap(. ~ season)
```
Observations are summarised to mean W per household during 16:00 - 20:00 on weekdays for year = 2015.
@@ -186,8 +241,9 @@ Observations are summarised to mean W per household during 16:00 - 20:00 on week
testSamples <- seq(50,3000,50)
testPower <- 0.8
-testMean <- mean(testDT[season == "Winter"]$meanW)
-testSD <- sd(testDT[season == "Winter"]$meanW)
+# overall mean
+testMean <- mean(linkedTestDT[season == "Winter"]$meanW)
+testSD <- sd(linkedTestDT[season == "Winter"]$meanW)
# use package function
meansPowerDT <- weGotThePower::estimateMeanEffectSizes(testMean,testSD,testSamples,testPower) # auto-produces range of p values
@@ -260,7 +316,7 @@ p <- p + labs(caption = myCaption) +
p <- p +
geom_hline(yintercept = y001, colour = "red") +
geom_segment(x = x001, y = y001, xend = x001, yend = 0, alpha = vLineAlpha,
- colour = cbPalette[2])
+ colour = cbPalette[1])
p <- p +
annotate(geom = "text",
@@ -269,13 +325,6 @@ p <- p +
label = paste0("Effect size = ", round(y001, 2) ,"% with \n p = 0.01, power = 0.8 and n = 1000"),
hjust = 0) # https://stackoverflow.com/questions/26684023/how-to-left-align-text-in-annotate-from-ggplot2
-# add vline at 0.01 effect size for p = 0.01, n = 1000
-p001Ref <- meansPowerDT[pValue == "p = 0.01" &
- effectSize < ceiling(p001Ref$effectSize) &
- effectSize > floor(p001Ref$effectSize)] # for reference line
-x001 <- mean(p001Ref$sampleN)
-p <- p + geom_segment(x = x001, y = y001, xend = x001, yend = 0, alpha = vLineAlpha,
- colour = cbPalette[1])
# add vline at 0.05 effect size for p = 0.01, n = 1000
p005Ref <- meansPowerDT[pValue == "p = 0.05" &
@@ -295,8 +344,8 @@ p <- p + geom_segment(x = x01, y = y001, xend = x01, yend = 0, alpha = vLineAlp
# add vline at 0.2 effect size for p = 0.01, n = 1000
p02Ref <- meansPowerDT[pValue == "p = 0.2" &
- effectSize < ceiling(p001Ref$effectSize+2) &
- effectSize > floor(p001Ref$effectSize-2)] # for reference line
+ effectSize < ceiling(p001Ref$effectSize) &
+ effectSize > floor(p001Ref$effectSize)] # for reference line
x02 <- mean(p02Ref$sampleN)
p <- p + geom_segment(x = x02, y = y001, xend = x02, yend = 0, alpha = vLineAlpha,
colour = cbPalette[4])
@@ -305,6 +354,13 @@ p
ggplot2::ggsave("figs/statPowerEsts80means_All.png", p)
```
+At same effect size (`r y001`%, n = 1000, p = 0.01):
+
+ * p = 0.05, n = `r x005`
+ * p = 0.1, n = `r x01`
+ * p = 0.2, n = `r x02`
+
+
Full table of results:
```{r meansPowerTable}
@@ -390,44 +446,50 @@ This may be far too wide an error margin for our purposes so we may instead have
## Getting it 'wrong'
+Use base GREENGrid and number of people but re-sample slightly.
-
+> NB: we create a small sample roughly 2 * the size of the GREEN Grid data. Due to small numbers and the random re-sampling with replacement process, there will be random fluctuations in the results with each run. As a result the results in this section will probably not match the results in the paper...
```{r smallNTable}
-# mimic an intervention using seasons
-testDT <- testDT[season == "Winter", group := "Control"]
-testDT <- testDT[season == "Spring", group := "Intervention 1"]
-testDT <- testDT[season == "Summer", group := "Intervention 2"]
-testDT <- testDT[season == "Autumn", group := "Intervention 3"]
-t <- testDT[, .("mean W" = mean(meanW),
+# group will be NA where we have no survey data
+# select just wnter
+linkedTestDT <- linkedTestDT[season == "Winter" & !is.na(nPeople)]
+
+# create small sample - be warned, this is a random process so you will get different results each time you run it
+
+smallTestDT <- sample_frac(linkedTestDT, 2, replace = TRUE)
+
+t <- smallTestDT[, .("mean W" = mean(meanW),
"sd W" = sd(meanW),
"n households" = .N),
- keyby = .(group)]
+ keyby = .(nPeople)]
-knitr::kable(t, caption = "Number of households and summary statistics per group")
+knitr::kable(t, caption = "Number of households and summary statistics per group (winter heat pump use)")
```
+So a sample of `r nrow(smallTestDT)`.
+
```{r ggMeanDiffs, fig.caption = "Mean W demand per group (Error bars = 95% confidence intervals for the sample mean)"}
-plotDT <- testDT[, .(meanW = mean(meanW),
+plotDT <- smallTestDT[, .(meanW = mean(meanW),
sdW = sd(meanW),
nObs = .N),
- keyby = .(group)
+ keyby = .(nPeople)
]
-myCaption <- paste0("Hypothetical small n sample",
+myCaption <- paste0("Hypothetical (very) small n sample",
"\nStatistic: mean W, weekdays 16:00 - 20:00")
makeMeanCIPlot <- function(dt){
# makes the plot, assumes meanW & sdW - not flexible but it does the job
dt <- dt[, ci_upper := meanW + (qnorm(0.975) * sdW/sqrt(nObs))]
dt <- dt[, ci_lower := meanW - (qnorm(0.975) * sdW/sqrt(nObs))]
- p <- ggplot2::ggplot(dt, aes(x = group, y = meanW, fill = group)) +
+ p <- ggplot2::ggplot(dt, aes(x = nPeople, y = meanW, fill = nPeople)) +
geom_col() +
geom_errorbar(aes(ymin = ci_lower, ymax = ci_upper), width = 0.25) +
guides(fill = guide_legend(title = "Group")) +
labs(y = "Mean W",
- x = "Trial group",
+ x = "N people in household",
caption = myCaption)
return(p)
}
@@ -436,21 +498,21 @@ makeMeanCIPlot(plotDT)
```
-T test group 1
+T test 1 <-> 3
```{r tTestTabG1}
# fix
# we are going to compare winter with summer to get a large effect. This is not what we would really do as it is a repeat measures dataset but this is irrelevant for our current purposes.
-tTest <- t.test(testDT[group == "Intervention 1"]$meanW, testDT[group == "Control"]$meanW)
+tTest <- t.test(smallTestDT[nPeople == "1"]$meanW, smallTestDT[nPeople == "3"]$meanW)
tTestTidy <- broom::tidy(tTest)
-tTestTidy$`Control mean` <- tTestTidy$estimate2
-tTestTidy$`Intervention 1 mean` <- tTestTidy$estimate1
+tTestTidy$`1 person mean` <- tTestTidy$estimate1
+tTestTidy$`3 persons mean` <- tTestTidy$estimate2
tTestTidy$`Mean difference` <- tTestTidy$estimate
-knitr::kable(tTestTidy[c("Control mean", "Intervention 1 mean", "Mean difference",
- "statistic", "p.value", "conf.low", "conf.high")], caption = "T test results (Group 1 vs Control)")
+knitr::kable(tTestTidy[c("1 person mean", "3 persons mean", "Mean difference",
+ "statistic", "p.value", "conf.low", "conf.high")], caption = "T test results (1 vs 3)")
controlW <- tTest$estimate[[2]]
intW <- tTest$estimate[[1]]
@@ -465,24 +527,25 @@ The results show that the mean power demand for the control group was `r round(c
* 95% confidence interval for the test = `r round(cil,2)` to `r round(ciu,2)` representing _considerable_ uncertainty/variation;
* p value of `r round(tTest$p.value,3)` representing a _relatively low_ risk of a false positive result but which (just) fails the conventional p < 0.05 threshold.
-T test Group 2
+T test 1 <-> 4+
```{r tTestTabG2}
# fix
# now compare winter & spring for a smaller effect
-tTest <- t.test(testDT[group == "Intervention 2"]$meanW, testDT[group == "Control"]$meanW)
+tTest <- t.test(smallTestDT[nPeople == "1"]$meanW, smallTestDT[nPeople == "4+"]$meanW)
tTestTidy <- broom::tidy(tTest)
-tTestTidy$`Control mean` <- tTestTidy$estimate2
-tTestTidy$`Intervention 2 mean` <- tTestTidy$estimate1
+tTestTidy$`1 person mean` <- tTestTidy$estimate1
+tTestTidy$`4+ persons mean` <- tTestTidy$estimate2
tTestTidy$`Mean difference` <- tTestTidy$estimate
-knitr::kable(tTestTidy[c("Control mean", "Intervention 2 mean", "Mean difference",
- "statistic", "p.value", "conf.low", "conf.high")], caption = "T test results (Group 2 vs Control)")
+knitr::kable(tTestTidy[c("1 person mean", "4+ persons mean", "Mean difference",
+ "statistic", "p.value", "conf.low", "conf.high")], caption = "T test results (1 vs 4+)")
controlW <- tTest$estimate[[2]]
intW <- tTest$estimate[[1]]
+
cil <- tTest$conf.int[[1]]
ciu <- tTest$conf.int[[2]]
```
@@ -494,43 +557,30 @@ Now:
* p value of `r round(tTest$p.value,3)` representing a _higher_ risk of a false positive result which fails the conventional p < 0.05 threshold and also the less conservative p < 0.1.
-```{r getN}
-# get sample size required for Int Group 2
-sd <- testDT[, sd(meanW)]
-result <- power.t.test(
- n = NULL,
- delta = controlW - intW,
- sd = sd,
- sig.level = 0.05,
- power = 0.8,
- alternative = c("one.sided")
- )
-```
-
-To detect Intervention Group 2's effect size of `r round(100 * (1-(intW/controlW)),2)`% would have required control and trial group sizes of `r round(result$n)` respectively.
-
-
## Getting it 'right'
+> NB: we create a larger sample roughly 40 * the size of the GREEN Grid data. Due to the random re-sampling with replacement process, there will be random fluctuations in the results with each run. As a result the results in this section will probably not exactly match the results in the paper but as the sample is large they should be quite close...
```{r creatLargeN}
# fix.
# we just randomly re-sample the GREEN Grid data
-largeTestDT <- sample_frac(testDT, 40, replace = TRUE)
+largeTestDT <- sample_frac(linkedTestDT, 40, replace = TRUE)
t <- largeTestDT[, .("mean W" = mean(meanW),
"sd W" = sd(meanW),
"n households" = .N),
- keyby = .(group)]
+ keyby = .(nPeople)]
knitr::kable(t, caption = "Number of households and summary statistics per group")
```
+So n = `r nrow(largeTestDT)`
+
```{r largeNmeanDiffs, fig.cap="Mean W demand per group for large sample (Error bars = 95% confidence intervals for the sample mean)"}
plotDT <- largeTestDT[, .(meanW = mean(meanW),
sdW = sd(meanW),
nObs = .N),
- keyby = .(group)
+ keyby = .(nPeople)
]
myCaption <- paste0("Hypothetical large n sample",
@@ -538,23 +588,24 @@ myCaption <- paste0("Hypothetical large n sample",
makeMeanCIPlot(plotDT)
```
-re-run T tests Control vs Group 1
+re-run T tests 1 vs 3
```{r largeNtTestControl-1}
-# now compare winter & spring for a smaller effect
-tTest <- t.test(largeTestDT[group == "Control"]$meanW, largeTestDT[group == "Intervention 1"]$meanW)
+
+tTest <- t.test(largeTestDT[nPeople == "1"]$meanW, largeTestDT[nPeople == "3"]$meanW)
tTestTidy <- broom::tidy(tTest)
-tTestTidy$`Control mean` <- tTestTidy$estimate1
-tTestTidy$`Intervention 1 mean` <- tTestTidy$estimate2
+tTestTidy$`1 person mean` <- tTestTidy$estimate1
+tTestTidy$`3 persons mean` <- tTestTidy$estimate2
tTestTidy$`Mean difference` <- tTestTidy$estimate
-knitr::kable(tTestTidy[c("Control mean", "Intervention 1 mean", "Mean difference",
- "statistic", "p.value", "conf.low", "conf.high")], caption = "T test results (Intervention 2 vs Control)")
+knitr::kable(tTestTidy[c("1 person mean", "3 persons mean", "Mean difference",
+ "statistic", "p.value", "conf.low", "conf.high")], caption = "T test results (1 vs 3)")
+
+controlW <- tTest$estimate[[2]]
+intW <- tTest$estimate[[1]]
-controlW <- tTest$estimate[[1]]
-intW <- tTest$estimate[[2]]
cil <- tTest$conf.int[[1]]
ciu <- tTest$conf.int[[2]]
```
@@ -565,23 +616,22 @@ In this case:
* 95% confidence interval for the test = `r round(cil,2)` to `r round(ciu,2)` representing _much less_ uncertainty/variation;
* p value of `r round(tTest$p.value,4)` representing a _very low_ risk of a false positive result as it passes all conventional thresholds.
-re-run T tests Control vs Group 2
+re-run T tests 1 person vs 4+
```{r largeNtTestControl-2}
-# now compare winter & spring for a smaller effect
-
-tTest <- t.test(largeTestDT[group == "Control"]$meanW, largeTestDT[group == "Intervention 2"]$meanW)
+tTest <- t.test(largeTestDT[nPeople == "1"]$meanW, largeTestDT[nPeople == "4+"]$meanW)
tTestTidy <- broom::tidy(tTest)
-tTestTidy$`Control mean` <- tTestTidy$estimate1
-tTestTidy$`Intervention 2 mean` <- tTestTidy$estimate2
+tTestTidy$`1 person mean` <- tTestTidy$estimate1
+tTestTidy$`4+ persons mean` <- tTestTidy$estimate2
tTestTidy$`Mean difference` <- tTestTidy$estimate
-knitr::kable(tTestTidy[c("Control mean", "Intervention 2 mean", "Mean difference",
- "statistic", "p.value", "conf.low", "conf.high")], caption = "T test results (Intervention 2 vs Control)")
+knitr::kable(tTestTidy[c("1 person mean", "4+ persons mean", "Mean difference",
+ "statistic", "p.value", "conf.low", "conf.high")], caption = "T test results (1 vs 4+)")
+
+controlW <- tTest$estimate[[2]]
+intW <- tTest$estimate[[1]]
-controlW <- tTest$estimate[[1]]
-intW <- tTest$estimate[[2]]
cil <- tTest$conf.int[[1]]
ciu <- tTest$conf.int[[2]]
```
diff --git a/paper/weGotThePowerDraftPaper.html b/paper/weGotThePowerDraftPaper.html
index 48f310fdd0aeb0b1bc35722d3faa4f42dc1dcfb9..bccb2d44b4febd7e763b3c2963e6c734d4932a5d 100644
--- a/paper/weGotThePowerDraftPaper.html
+++ b/paper/weGotThePowerDraftPaper.html
@@ -239,7 +239,7 @@ div.tocify {
<h1 class="title toc-ignore">Statistical Power, Statistical Significance, Study Design and Decision Making: A Worked Example</h1>
<h3 class="subtitle"><em>Sizing Demand Response Trials in New Zealand</em></h3>
<h4 class="author"><em>Ben Anderson and Tom Rushby (Contact: <a href="mailto:b.anderson@soton.ac.uk">b.anderson@soton.ac.uk</a>, <code>@dataknut</code>)</em></h4>
-<h4 class="date"><em>Last run at: 2018-11-13 13:49:39</em></h4>
+<h4 class="date"><em>Last run at: 2018-11-15 14:49:28</em></h4>
</div>
@@ -301,30 +301,162 @@ div.tocify {
<thead>
<tr class="header">
<th align="left">season</th>
+<th align="left">nPeople</th>
<th align="right">meanMeanW</th>
<th align="right">sdMeanW</th>
+<th align="right">nHouseholds</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td align="left">Spring</td>
-<td align="right">58.80597</td>
-<td align="right">113.53102</td>
+<td align="left">NA</td>
+<td align="right">595.994212</td>
+<td align="right">443.635765</td>
+<td align="right">2</td>
+</tr>
+<tr class="even">
+<td align="left">Spring</td>
+<td align="left">1</td>
+<td align="right">92.230234</td>
+<td align="right">103.648048</td>
+<td align="right">2</td>
+</tr>
+<tr class="odd">
+<td align="left">Spring</td>
+<td align="left">2</td>
+<td align="right">89.339624</td>
+<td align="right">44.338145</td>
+<td align="right">4</td>
+</tr>
+<tr class="even">
+<td align="left">Spring</td>
+<td align="left">3</td>
+<td align="right">207.619377</td>
+<td align="right">171.401166</td>
+<td align="right">7</td>
+</tr>
+<tr class="odd">
+<td align="left">Spring</td>
+<td align="left">4+</td>
+<td align="right">175.856103</td>
+<td align="right">148.738840</td>
+<td align="right">11</td>
</tr>
<tr class="even">
<td align="left">Summer</td>
-<td align="right">35.13947</td>
-<td align="right">83.90258</td>
+<td align="left">1</td>
+<td align="right">4.019881</td>
+<td align="right">3.746534</td>
+<td align="right">2</td>
+</tr>
+<tr class="odd">
+<td align="left">Summer</td>
+<td align="left">2</td>
+<td align="right">35.275766</td>
+<td align="right">61.099420</td>
+<td align="right">3</td>
+</tr>
+<tr class="even">
+<td align="left">Summer</td>
+<td align="left">3</td>
+<td align="right">87.760306</td>
+<td align="right">133.023910</td>
+<td align="right">7</td>
+</tr>
+<tr class="odd">
+<td align="left">Summer</td>
+<td align="left">4+</td>
+<td align="right">33.637416</td>
+<td align="right">74.408925</td>
+<td align="right">10</td>
+</tr>
+<tr class="even">
+<td align="left">Autumn</td>
+<td align="left">NA</td>
+<td align="right">387.203399</td>
+<td align="right">316.302379</td>
+<td align="right">2</td>
</tr>
<tr class="odd">
<td align="left">Autumn</td>
-<td align="right">68.37439</td>
-<td align="right">147.37279</td>
+<td align="left">1</td>
+<td align="right">70.587984</td>
+<td align="right">79.862519</td>
+<td align="right">2</td>
</tr>
<tr class="even">
+<td align="left">Autumn</td>
+<td align="left">2</td>
+<td align="right">73.233719</td>
+<td align="right">56.284769</td>
+<td align="right">4</td>
+</tr>
+<tr class="odd">
+<td align="left">Autumn</td>
+<td align="left">3</td>
+<td align="right">245.971947</td>
+<td align="right">194.352385</td>
+<td align="right">8</td>
+</tr>
+<tr class="even">
+<td align="left">Autumn</td>
+<td align="left">4+</td>
+<td align="right">199.479290</td>
+<td align="right">165.371666</td>
+<td align="right">13</td>
+</tr>
+<tr class="odd">
+<td align="left">Winter</td>
+<td align="left">NA</td>
+<td align="right">661.964787</td>
+<td align="right">275.647550</td>
+<td align="right">2</td>
+</tr>
+<tr class="even">
+<td align="left">Winter</td>
+<td align="left">1</td>
+<td align="right">169.532436</td>
+<td align="right">213.880258</td>
+<td align="right">2</td>
+</tr>
+<tr class="odd">
<td align="left">Winter</td>
-<td align="right">162.66915</td>
-<td align="right">325.51171</td>
+<td align="left">2</td>
+<td align="right">282.138922</td>
+<td align="right">71.265180</td>
+<td align="right">4</td>
+</tr>
+<tr class="even">
+<td align="left">Winter</td>
+<td align="left">3</td>
+<td align="right">475.616350</td>
+<td align="right">280.427370</td>
+<td align="right">8</td>
+</tr>
+<tr class="odd">
+<td align="left">Winter</td>
+<td align="left">4+</td>
+<td align="right">413.121623</td>
+<td align="right">279.067726</td>
+<td align="right">12</td>
+</tr>
+</tbody>
+</table>
+<table>
+<caption><span id="tab:dataPrep">Table 4.1: </span>Summary of mean consumption per household in winter</caption>
+<thead>
+<tr class="header">
+<th align="right">meanMeanW</th>
+<th align="right">sdMeanW</th>
+<th align="right">nHouseholds</th>
+</tr>
+</thead>
+<tbody>
+<tr class="odd">
+<td align="right">412.6407</td>
+<td align="right">264.3291</td>
+<td align="right">28</td>
</tr>
</tbody>
</table>
@@ -344,7 +476,7 @@ Figure 4.1: Power analysis results (p = 0.01, power = 0.8)
</p>
</div>
<pre><code>## Saving 7 x 5 in image</code></pre>
-<p>Effect size at n = 1000: 28.37.</p>
+<p>Effect size at n = 1000: 9.08.</p>
<p>Figure <a href="#fig:ggHPSampleSizeFig80all">4.2</a> shows the plot for all results.</p>
<pre><code>## Scale for 'y' is already present. Adding another scale for 'y', which
## will replace the existing scale.</code></pre>
@@ -355,6 +487,12 @@ Figure 4.2: Power analysis results (power = 0.8)
</p>
</div>
<pre><code>## Saving 7 x 5 in image</code></pre>
+<p>At same effect size (9.0816159%, n = 1000, p = 0.01):</p>
+<ul>
+<li>p = 0.05, n = 575</li>
+<li>p = 0.1, n = 425</li>
+<li>p = 0.2, n = 250</li>
+</ul>
<p>Full table of results:</p>
<pre><code>## Using 'effectSize' as value column. Use 'value.var' to override</code></pre>
<table>
@@ -371,143 +509,143 @@ Figure 4.2: Power analysis results (power = 0.8)
<tbody>
<tr class="odd">
<td align="right">50</td>
-<td align="right">128.57</td>
-<td align="right">100.21</td>
-<td align="right">85.33</td>
-<td align="right">67.49</td>
+<td align="right">41.16</td>
+<td align="right">32.08</td>
+<td align="right">27.32</td>
+<td align="right">21.60</td>
</tr>
<tr class="even">
<td align="right">100</td>
-<td align="right">90.27</td>
-<td align="right">70.61</td>
-<td align="right">60.21</td>
-<td align="right">47.68</td>
+<td align="right">28.90</td>
+<td align="right">22.60</td>
+<td align="right">19.27</td>
+<td align="right">15.26</td>
</tr>
<tr class="odd">
<td align="right">150</td>
-<td align="right">73.53</td>
-<td align="right">57.58</td>
-<td align="right">49.13</td>
-<td align="right">38.92</td>
+<td align="right">23.54</td>
+<td align="right">18.43</td>
+<td align="right">15.73</td>
+<td align="right">12.46</td>
</tr>
<tr class="even">
<td align="right">200</td>
-<td align="right">63.61</td>
-<td align="right">49.84</td>
-<td align="right">42.53</td>
-<td align="right">33.70</td>
+<td align="right">20.36</td>
+<td align="right">15.95</td>
+<td align="right">13.61</td>
+<td align="right">10.79</td>
</tr>
<tr class="odd">
<td align="right">250</td>
-<td align="right">56.86</td>
-<td align="right">44.56</td>
-<td align="right">38.03</td>
-<td align="right">30.14</td>
+<td align="right">18.20</td>
+<td align="right">14.27</td>
+<td align="right">12.17</td>
+<td align="right">9.65</td>
</tr>
<tr class="even">
<td align="right">300</td>
-<td align="right">51.88</td>
-<td align="right">40.67</td>
-<td align="right">34.71</td>
-<td align="right">27.51</td>
+<td align="right">16.61</td>
+<td align="right">13.02</td>
+<td align="right">11.11</td>
+<td align="right">8.81</td>
</tr>
<tr class="odd">
<td align="right">350</td>
-<td align="right">48.01</td>
-<td align="right">37.65</td>
-<td align="right">32.14</td>
-<td align="right">25.47</td>
+<td align="right">15.37</td>
+<td align="right">12.05</td>
+<td align="right">10.29</td>
+<td align="right">8.15</td>
</tr>
<tr class="even">
<td align="right">400</td>
-<td align="right">44.90</td>
-<td align="right">35.21</td>
-<td align="right">30.06</td>
-<td align="right">23.82</td>
+<td align="right">14.37</td>
+<td align="right">11.27</td>
+<td align="right">9.62</td>
+<td align="right">7.63</td>
</tr>
<tr class="odd">
<td align="right">450</td>
-<td align="right">42.33</td>
-<td align="right">33.20</td>
-<td align="right">28.34</td>
-<td align="right">22.46</td>
+<td align="right">13.55</td>
+<td align="right">10.63</td>
+<td align="right">9.07</td>
+<td align="right">7.19</td>
</tr>
<tr class="even">
<td align="right">500</td>
-<td align="right">40.15</td>
-<td align="right">31.49</td>
-<td align="right">26.88</td>
-<td align="right">21.31</td>
+<td align="right">12.85</td>
+<td align="right">10.08</td>
+<td align="right">8.61</td>
+<td align="right">6.82</td>
</tr>
<tr class="odd">
<td align="right">550</td>
-<td align="right">38.27</td>
-<td align="right">30.02</td>
-<td align="right">25.63</td>
-<td align="right">20.31</td>
+<td align="right">12.25</td>
+<td align="right">9.61</td>
+<td align="right">8.20</td>
+<td align="right">6.50</td>
</tr>
<tr class="even">
<td align="right">600</td>
-<td align="right">36.64</td>
-<td align="right">28.74</td>
-<td align="right">24.54</td>
-<td align="right">19.45</td>
+<td align="right">11.73</td>
+<td align="right">9.20</td>
+<td align="right">7.86</td>
+<td align="right">6.23</td>
</tr>
<tr class="odd">
<td align="right">650</td>
-<td align="right">35.20</td>
-<td align="right">27.61</td>
-<td align="right">23.57</td>
-<td align="right">18.69</td>
+<td align="right">11.27</td>
+<td align="right">8.84</td>
+<td align="right">7.55</td>
+<td align="right">5.98</td>
</tr>
<tr class="even">
<td align="right">700</td>
-<td align="right">33.92</td>
-<td align="right">26.61</td>
-<td align="right">22.72</td>
-<td align="right">18.01</td>
+<td align="right">10.86</td>
+<td align="right">8.52</td>
+<td align="right">7.27</td>
+<td align="right">5.76</td>
</tr>
<tr class="odd">
<td align="right">750</td>
-<td align="right">32.77</td>
-<td align="right">25.71</td>
-<td align="right">21.95</td>
-<td align="right">17.40</td>
+<td align="right">10.49</td>
+<td align="right">8.23</td>
+<td align="right">7.03</td>
+<td align="right">5.57</td>
</tr>
<tr class="even">
<td align="right">800</td>
-<td align="right">31.72</td>
-<td align="right">24.89</td>
-<td align="right">21.25</td>
-<td align="right">16.84</td>
+<td align="right">10.16</td>
+<td align="right">7.97</td>
+<td align="right">6.80</td>
+<td align="right">5.39</td>
</tr>
<tr class="odd">
<td align="right">850</td>
-<td align="right">30.77</td>
-<td align="right">24.14</td>
-<td align="right">20.61</td>
-<td align="right">16.34</td>
+<td align="right">9.85</td>
+<td align="right">7.73</td>
+<td align="right">6.60</td>
+<td align="right">5.23</td>
</tr>
<tr class="even">
<td align="right">900</td>
-<td align="right">29.91</td>
-<td align="right">23.46</td>
-<td align="right">20.03</td>
-<td align="right">15.88</td>
+<td align="right">9.57</td>
+<td align="right">7.51</td>
+<td align="right">6.41</td>
+<td align="right">5.08</td>
</tr>
<tr class="odd">
<td align="right">950</td>
-<td align="right">29.11</td>
-<td align="right">22.84</td>
-<td align="right">19.50</td>
-<td align="right">15.46</td>
+<td align="right">9.32</td>
+<td align="right">7.31</td>
+<td align="right">6.24</td>
+<td align="right">4.95</td>
</tr>
<tr class="even">
<td align="right">1000</td>
-<td align="right">28.37</td>
-<td align="right">22.26</td>
-<td align="right">19.00</td>
-<td align="right">15.06</td>
+<td align="right">9.08</td>
+<td align="right">7.13</td>
+<td align="right">6.08</td>
+<td align="right">4.82</td>
</tr>
</tbody>
</table>
@@ -607,11 +745,15 @@ Figure 4.2: Power analysis results (power = 0.8)
<h1><span class="header-section-number">5</span> Testing for differences: effect sizes, confidence intervals and p values</h1>
<div id="getting-it-wrong" class="section level2">
<h2><span class="header-section-number">5.1</span> Getting it ‘wrong’</h2>
+<p>Use base GREENGrid and number of people but re-sample slightly.</p>
+<blockquote>
+<p>NB: we create a small sample roughly 2 * the size of the GREEN Grid data. Due to small numbers and the random re-sampling with replacement process, there will be random fluctuations in the results with each run. As a result the results in this section will probably not match the results in the paper…</p>
+</blockquote>
<table>
-<caption><span id="tab:smallNTable">Table 5.1: </span>Number of households and summary statistics per group</caption>
+<caption><span id="tab:smallNTable">Table 5.1: </span>Number of households and summary statistics per group (winter heat pump use)</caption>
<thead>
<tr class="header">
-<th align="left">group</th>
+<th align="left">nPeople</th>
<th align="right">mean W</th>
<th align="right">sd W</th>
<th align="right">n households</th>
@@ -619,39 +761,40 @@ Figure 4.2: Power analysis results (power = 0.8)
</thead>
<tbody>
<tr class="odd">
-<td align="left">Control</td>
-<td align="right">162.66915</td>
-<td align="right">325.51171</td>
-<td align="right">28</td>
+<td align="left">1</td>
+<td align="right">147.9273</td>
+<td align="right">161.6783</td>
+<td align="right">7</td>
</tr>
<tr class="even">
-<td align="left">Intervention 1</td>
-<td align="right">58.80597</td>
-<td align="right">113.53102</td>
-<td align="right">26</td>
+<td align="left">2</td>
+<td align="right">301.9291</td>
+<td align="right">76.8570</td>
+<td align="right">7</td>
</tr>
<tr class="odd">
-<td align="left">Intervention 2</td>
-<td align="right">35.13947</td>
-<td align="right">83.90258</td>
-<td align="right">22</td>
+<td align="left">3</td>
+<td align="right">429.2748</td>
+<td align="right">248.5965</td>
+<td align="right">14</td>
</tr>
<tr class="even">
-<td align="left">Intervention 3</td>
-<td align="right">68.37439</td>
-<td align="right">147.37279</td>
-<td align="right">29</td>
+<td align="left">4+</td>
+<td align="right">470.3224</td>
+<td align="right">297.9899</td>
+<td align="right">24</td>
</tr>
</tbody>
</table>
+<p>So a sample of 52.</p>
<p><img src="weGotThePowerDraftPaper_files/figure-html/ggMeanDiffs-1.png" width="672" /></p>
-<p>T test group 1</p>
+<p>T test 1 <-> 3</p>
<table>
-<caption><span id="tab:tTestTabG1">Table 5.2: </span>T test results (Group 1 vs Control)</caption>
+<caption><span id="tab:tTestTabG1">Table 5.2: </span>T test results (1 vs 3)</caption>
<thead>
<tr class="header">
-<th align="right">Control mean</th>
-<th align="right">Intervention 1 mean</th>
+<th align="right">1 person mean</th>
+<th align="right">3 persons mean</th>
<th align="right">Mean difference</th>
<th align="right">statistic</th>
<th align="right">p.value</th>
@@ -661,29 +804,29 @@ Figure 4.2: Power analysis results (power = 0.8)
</thead>
<tbody>
<tr class="odd">
-<td align="right">162.6691</td>
-<td align="right">58.80597</td>
-<td align="right">-103.8632</td>
-<td align="right">-1.587604</td>
-<td align="right">0.1216582</td>
-<td align="right">-236.8285</td>
-<td align="right">29.10212</td>
+<td align="right">147.9273</td>
+<td align="right">429.2748</td>
+<td align="right">-281.3475</td>
+<td align="right">-3.116754</td>
+<td align="right">0.0061527</td>
+<td align="right">-471.4924</td>
+<td align="right">-91.20272</td>
</tr>
</tbody>
</table>
-<p>The results show that the mean power demand for the control group was 162.67W and for Intervention 1 was 58.81W. This is a (very) large difference in the mean of 103.86. The results of the t test are:</p>
+<p>The results show that the mean power demand for the control group was 429.27W and for Intervention 1 was 147.93W. This is a (very) large difference in the mean of 281.35. The results of the t test are:</p>
<ul>
-<li>effect size = 104W or 64% representing a <em>substantial bang for buck</em> for whatever caused the difference;</li>
-<li>95% confidence interval for the test = -236.83 to 29.1 representing <em>considerable</em> uncertainty/variation;</li>
-<li>p value of 0.122 representing a <em>relatively low</em> risk of a false positive result but which (just) fails the conventional p < 0.05 threshold.</li>
+<li>effect size = 281W or 66% representing a <em>substantial bang for buck</em> for whatever caused the difference;</li>
+<li>95% confidence interval for the test = -471.49 to -91.2 representing <em>considerable</em> uncertainty/variation;</li>
+<li>p value of 0.006 representing a <em>relatively low</em> risk of a false positive result but which (just) fails the conventional p < 0.05 threshold.</li>
</ul>
-<p>T test Group 2</p>
+<p>T test 1 <-> 4+</p>
<table>
-<caption><span id="tab:tTestTabG2">Table 5.3: </span>T test results (Group 2 vs Control)</caption>
+<caption><span id="tab:tTestTabG2">Table 5.3: </span>T test results (1 vs 4+)</caption>
<thead>
<tr class="header">
-<th align="right">Control mean</th>
-<th align="right">Intervention 2 mean</th>
+<th align="right">1 person mean</th>
+<th align="right">4+ persons mean</th>
<th align="right">Mean difference</th>
<th align="right">statistic</th>
<th align="right">p.value</th>
@@ -693,31 +836,33 @@ Figure 4.2: Power analysis results (power = 0.8)
</thead>
<tbody>
<tr class="odd">
-<td align="right">162.6691</td>
-<td align="right">35.13947</td>
-<td align="right">-127.5297</td>
-<td align="right">-1.990661</td>
-<td align="right">0.0552626</td>
-<td align="right">-258.11</td>
-<td align="right">3.050644</td>
+<td align="right">147.9273</td>
+<td align="right">470.3224</td>
+<td align="right">-322.3952</td>
+<td align="right">-3.739141</td>
+<td align="right">0.0013971</td>
+<td align="right">-502.9035</td>
+<td align="right">-141.8869</td>
</tr>
</tbody>
</table>
<p>Now:</p>
<ul>
-<li>effect size = 128W or 78.4% representing a still <em>reasonable bang for buck</em> for whatever caused the difference;</li>
-<li>95% confidence interval for the test = -258.11 to 3.05 representing <em>even greater</em> uncertainty/variation;</li>
-<li>p value of 0.055 representing a <em>higher</em> risk of a false positive result which fails the conventional p < 0.05 threshold and also the less conservative p < 0.1.</li>
+<li>effect size = 322W or 68.55% representing a still <em>reasonable bang for buck</em> for whatever caused the difference;</li>
+<li>95% confidence interval for the test = -502.9 to -141.89 representing <em>even greater</em> uncertainty/variation;</li>
+<li>p value of 0.001 representing a <em>higher</em> risk of a false positive result which fails the conventional p < 0.05 threshold and also the less conservative p < 0.1.</li>
</ul>
-<p>To detect Intervention Group 2’s effect size of 78.4% would have required control and trial group sizes of 31 respectively.</p>
</div>
<div id="getting-it-right" class="section level2">
<h2><span class="header-section-number">5.2</span> Getting it ‘right’</h2>
+<blockquote>
+<p>NB: we create a larger sample roughly 40 * the size of the GREEN Grid data. Due to the random re-sampling with replacement process, there will be random fluctuations in the results with each run. As a result the results in this section will probably not exactly match the results in the paper but as the sample is large they should be quite close…</p>
+</blockquote>
<table>
<caption><span id="tab:creatLargeN">Table 5.4: </span>Number of households and summary statistics per group</caption>
<thead>
<tr class="header">
-<th align="left">group</th>
+<th align="left">nPeople</th>
<th align="right">mean W</th>
<th align="right">sd W</th>
<th align="right">n households</th>
@@ -725,44 +870,45 @@ Figure 4.2: Power analysis results (power = 0.8)
</thead>
<tbody>
<tr class="odd">
-<td align="left">Control</td>
-<td align="right">160.44582</td>
-<td align="right">317.03541</td>
-<td align="right">1128</td>
+<td align="left">1</td>
+<td align="right">159.2209</td>
+<td align="right">151.7489</td>
+<td align="right">88</td>
</tr>
<tr class="even">
-<td align="left">Intervention 1</td>
-<td align="right">58.51839</td>
-<td align="right">109.58111</td>
-<td align="right">984</td>
+<td align="left">2</td>
+<td align="right">285.1232</td>
+<td align="right">63.8895</td>
+<td align="right">149</td>
</tr>
<tr class="odd">
-<td align="left">Intervention 2</td>
-<td align="right">36.35177</td>
-<td align="right">83.36952</td>
-<td align="right">903</td>
+<td align="left">3</td>
+<td align="right">511.0046</td>
+<td align="right">279.3558</td>
+<td align="right">308</td>
</tr>
<tr class="even">
-<td align="left">Intervention 3</td>
-<td align="right">70.69426</td>
-<td align="right">147.43129</td>
-<td align="right">1185</td>
+<td align="left">4+</td>
+<td align="right">417.3538</td>
+<td align="right">267.6910</td>
+<td align="right">495</td>
</tr>
</tbody>
</table>
+<p>So n = 1040</p>
<div class="figure"><span id="fig:largeNmeanDiffs"></span>
<img src="weGotThePowerDraftPaper_files/figure-html/largeNmeanDiffs-1.png" alt="Mean W demand per group for large sample (Error bars = 95% confidence intervals for the sample mean)" width="672" />
<p class="caption">
Figure 5.1: Mean W demand per group for large sample (Error bars = 95% confidence intervals for the sample mean)
</p>
</div>
-<p>re-run T tests Control vs Group 1</p>
+<p>re-run T tests 1 vs 3</p>
<table>
-<caption><span id="tab:largeNtTestControl-1">Table 5.5: </span>T test results (Intervention 2 vs Control)</caption>
+<caption><span id="tab:largeNtTestControl-1">Table 5.5: </span>T test results (1 vs 3)</caption>
<thead>
<tr class="header">
-<th align="right">Control mean</th>
-<th align="right">Intervention 1 mean</th>
+<th align="right">1 person mean</th>
+<th align="right">3 persons mean</th>
<th align="right">Mean difference</th>
<th align="right">statistic</th>
<th align="right">p.value</th>
@@ -772,29 +918,29 @@ Figure 5.1: Mean W demand per group for large sample (Error bars = 95% confidenc
</thead>
<tbody>
<tr class="odd">
-<td align="right">160.4458</td>
-<td align="right">58.51839</td>
-<td align="right">101.9274</td>
-<td align="right">10.12667</td>
+<td align="right">159.2209</td>
+<td align="right">511.0046</td>
+<td align="right">-351.7837</td>
+<td align="right">-15.50063</td>
<td align="right">0</td>
-<td align="right">82.18316</td>
-<td align="right">121.6717</td>
+<td align="right">-396.4678</td>
+<td align="right">-307.0996</td>
</tr>
</tbody>
</table>
<p>In this case:</p>
<ul>
-<li>effect size = 101.9274343W or 63.53% representing a still <em>reasonable bang for buck</em> for whatever caused the difference;</li>
-<li>95% confidence interval for the test = 82.18 to 121.67 representing <em>much less</em> uncertainty/variation;</li>
+<li>effect size = 351.7837236W or 68.84% representing a still <em>reasonable bang for buck</em> for whatever caused the difference;</li>
+<li>95% confidence interval for the test = -396.47 to -307.1 representing <em>much less</em> uncertainty/variation;</li>
<li>p value of 0 representing a <em>very low</em> risk of a false positive result as it passes all conventional thresholds.</li>
</ul>
-<p>re-run T tests Control vs Group 2</p>
+<p>re-run T tests 1 person vs 4+</p>
<table>
-<caption><span id="tab:largeNtTestControl-2">Table 5.6: </span>T test results (Intervention 2 vs Control)</caption>
+<caption><span id="tab:largeNtTestControl-2">Table 5.6: </span>T test results (1 vs 4+)</caption>
<thead>
<tr class="header">
-<th align="right">Control mean</th>
-<th align="right">Intervention 2 mean</th>
+<th align="right">1 person mean</th>
+<th align="right">4+ persons mean</th>
<th align="right">Mean difference</th>
<th align="right">statistic</th>
<th align="right">p.value</th>
@@ -804,20 +950,20 @@ Figure 5.1: Mean W demand per group for large sample (Error bars = 95% confidenc
</thead>
<tbody>
<tr class="odd">
-<td align="right">160.4458</td>
-<td align="right">36.35177</td>
-<td align="right">124.0941</td>
-<td align="right">12.61266</td>
+<td align="right">159.2209</td>
+<td align="right">417.3538</td>
+<td align="right">-258.1329</td>
+<td align="right">-12.80393</td>
<td align="right">0</td>
-<td align="right">104.7925</td>
-<td align="right">143.3956</td>
+<td align="right">-297.8882</td>
+<td align="right">-218.3776</td>
</tr>
</tbody>
</table>
<p>In this case:</p>
<ul>
-<li>effect size = 124.0940533W or 77.34% representing a still <em>reasonable bang for buck</em> for whatever caused the difference;</li>
-<li>95% confidence interval for the test = 104.79 to 143.4 representing <em>much less</em> uncertainty/variation;</li>
+<li>effect size = 258.1328841W or 61.85% representing a still <em>reasonable bang for buck</em> for whatever caused the difference;</li>
+<li>95% confidence interval for the test = -297.89 to -218.38 representing <em>much less</em> uncertainty/variation;</li>
<li>p value of 0 representing a <em>very low</em> risk of a false positive result as it passes all conventional thresholds.</li>
</ul>
</div>
@@ -839,7 +985,7 @@ Figure 5.1: Mean W demand per group for large sample (Error bars = 95% confidenc
</div>
<div id="runtime" class="section level1">
<h1><span class="header-section-number">8</span> Runtime</h1>
-<p>Analysis completed in 46.02 seconds ( 0.77 minutes) using <a href="https://cran.r-project.org/package=knitr">knitr</a> in <a href="http://www.rstudio.com">RStudio</a> with R version 3.5.1 (2018-07-02) running on x86_64-apple-darwin15.6.0.</p>
+<p>Analysis completed in 42.5 seconds ( 0.71 minutes) using <a href="https://cran.r-project.org/package=knitr">knitr</a> in <a href="http://www.rstudio.com">RStudio</a> with R version 3.5.1 (2018-07-02) running on x86_64-apple-darwin15.6.0.</p>
</div>
<div id="r-environment" class="section level1">
<h1><span class="header-section-number">9</span> R environment</h1>
@@ -872,28 +1018,28 @@ Figure 5.1: Mean W demand per group for large sample (Error bars = 95% confidenc
## [1] stats graphics grDevices utils datasets methods base
##
## other attached packages:
-## [1] knitr_1.20 pwr_1.2-2 forcats_0.3.0
-## [4] broom_0.5.0 lubridate_1.7.4 readr_1.1.1
-## [7] ggplot2_3.1.0 dplyr_0.7.7 data.table_1.11.8
-## [10] dkUtils_0.0.0.9000
+## [1] knitr_1.20 GREENGridData_1.0 pwr_1.2-2
+## [4] forcats_0.3.0 broom_0.5.0 lubridate_1.7.4
+## [7] readr_1.1.1 ggplot2_3.1.0 dplyr_0.7.7
+## [10] data.table_1.11.8 dkUtils_0.0.0.9000
##
## loaded via a namespace (and not attached):
-## [1] Rcpp_0.12.19 highr_0.7 pillar_1.3.0
-## [4] compiler_3.5.1 plyr_1.8.4 bindr_0.1.1
-## [7] tools_3.5.1 digest_0.6.18 lattice_0.20-35
-## [10] nlme_3.1-137 evaluate_0.12 tibble_1.4.2
-## [13] gtable_0.2.0 pkgconfig_2.0.2 rlang_0.3.0.1
-## [16] cli_1.0.1 yaml_2.2.0 xfun_0.4
-## [19] bindrcpp_0.2.2 withr_2.1.2 stringr_1.3.1
-## [22] hms_0.4.2 rprojroot_1.3-2 grid_3.5.1
-## [25] tidyselect_0.2.5 glue_1.3.0 R6_2.3.0
-## [28] fansi_0.4.0 rmarkdown_1.10 bookdown_0.7
-## [31] reshape2_1.4.3 weGotThePower_0.1 tidyr_0.8.1
-## [34] purrr_0.2.5 magrittr_1.5 backports_1.1.2
-## [37] scales_1.0.0 htmltools_0.3.6 assertthat_0.2.0
-## [40] colorspace_1.3-2 labeling_0.3 utf8_1.1.4
-## [43] stringi_1.2.4 lazyeval_0.2.1 munsell_0.5.0
-## [46] crayon_1.3.4</code></pre>
+## [1] Rcpp_0.12.19 highr_0.7 cellranger_1.1.0
+## [4] pillar_1.3.0 compiler_3.5.1 plyr_1.8.4
+## [7] bindr_0.1.1 prettyunits_1.0.2 progress_1.2.0
+## [10] tools_3.5.1 digest_0.6.18 lattice_0.20-35
+## [13] nlme_3.1-137 evaluate_0.12 tibble_1.4.2
+## [16] gtable_0.2.0 pkgconfig_2.0.2 rlang_0.3.0.1
+## [19] yaml_2.2.0 xfun_0.4 bindrcpp_0.2.2
+## [22] withr_2.1.2 stringr_1.3.1 hms_0.4.2
+## [25] rprojroot_1.3-2 grid_3.5.1 tidyselect_0.2.5
+## [28] glue_1.3.0 R6_2.3.0 readxl_1.1.0
+## [31] rmarkdown_1.10 bookdown_0.7 weGotThePower_0.1
+## [34] reshape2_1.4.3 tidyr_0.8.1 purrr_0.2.5
+## [37] magrittr_1.5 backports_1.1.2 scales_1.0.0
+## [40] htmltools_0.3.6 assertthat_0.2.0 colorspace_1.3-2
+## [43] labeling_0.3 stringi_1.2.4 lazyeval_0.2.1
+## [46] munsell_0.5.0 crayon_1.3.4</code></pre>
</div>
<div id="references" class="section level1 unnumbered">
<h1>References</h1>
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