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adiponectin treatment | ||
7.39 nicotinic | ||
7.58 nicotinic | ||
6.87 nicotinic | ||
7.23 nicotinic | ||
9.32 nicotinic | ||
5.72 nicotinic | ||
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3.13 nicotinic | ||
3.77 control | ||
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--- | ||
title: "Overview" | ||
subtitle: "The logic of hypothesis testing and confidence intervals" | ||
toc: true | ||
toc-location: right | ||
--- | ||
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This week we will cover the logic of consider the logic of hypothesis testing and type 1 and type 2 errors. We will also find out what the sampling distribution of the mean and the standard error are, and how to calculate confidence intervals. | ||
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![Artwork by @allison_horst: "type 1 error"](images/type-1-error.png){fig-alt="A cute population with a normal distribution with two samples, one which happens to have at mean at the low end of the population and one at the high end. The population is saying 'yes, I'm still sure I birthed both of you'. Because these samples are relatively rare - would happen less than 5% of the time - we would conclude they did not come from this population. That would be making a type 1 error." width="600"} | ||
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![Artwork by @allison_horst: "type 2 error"](images/type-2-error.png){fig-alt="Two cute populations with a normal distribution with very little overlap. There are two samples, one which happens to have at mean at the low end of one population and and the other at the high end of the other population so that the two samples are close togther. Deciding these two samples were from the same population would be making a type 2 error." width="600"} | ||
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### Learning objectives | ||
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The successful student will be able to: | ||
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- demonstrate the process of hypothesis testing with an example | ||
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- explain type 1 and type 2 errors | ||
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- define the sampling distribution of the mean and the standard error | ||
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- explain what a confidence interval is | ||
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- calculate confidence intervals for large and small samples | ||
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### Instructions | ||
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1. [Prepare](study_before_workshop.qmd) | ||
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i. 📖 Read The logic of hyothesis testing | ||
ii. 📖 Read Confidence Intervals | ||
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2. [Workshop](workshop.qmd) | ||
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i. 💻 Remind yourself how to import files | ||
ii. 💻 Calculate confidence intervals on large | ||
iii. 💻 Calculate confidence intervals on small samples. | ||
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3. [Consolidate](study_after_workshop.qmd) | ||
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i. 💻 Calculate confidence intervals for each group in a data set | ||
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--- | ||
title: "Independent Study to consolidate this week" | ||
subtitle: "The logic of hypothesis testing and confidence intervals" | ||
toc: true | ||
toc-location: right | ||
format: | ||
html: | ||
code-fold: true | ||
code-summary: "Answer - don't look until you have tried!" | ||
--- | ||
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# Set up | ||
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If you have just opened RStudio you will want to load the **`tidyverse`** package | ||
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```{r} | ||
#| code-fold: false | ||
library(tidyverse) | ||
``` | ||
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# Exercises | ||
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1. 💻 Adiponectin is exclusively secreted from adipose tissue and modulates a number of metabolic processes. Nicotinic acid can affect adiponectin secretion. 3T3-L1 adipocytes were treated with nicotinic acid or with a control treatment and adiponectin concentration (pg/mL) measured. The data are in [adipocytes.txt](data-raw/adipocytes.txt). Each row represents an independent sample of adipocytes and the first column gives the concentration adiponectin and the second column indicates whether they were treated with nicotinic acid or not. Estimate the mean Adiponectin concentration in each group - this means calculate the sample mean and construct a confidence interval around it for each group. This exercise forces you to bring together ideas from this workshop and from previous workshops | ||
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- How to calculate a confidence intervals (this workshop) | ||
- How to summarise variables in more than one group (previous workshop) | ||
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```{r} | ||
#| output: false | ||
# data import | ||
adip <- read_table("data-raw/adipocytes.txt") | ||
# examine the structure | ||
str(adip) | ||
# summarise | ||
adip_summary <- adip %>% | ||
group_by(treatment) %>% | ||
summarise(mean = mean(adiponectin), | ||
sd = sd(adiponectin), | ||
n = length(adiponectin), | ||
se = sd/sqrt(n), | ||
dif = qt(0.975, df = n - 1) * se, | ||
lower_ci = mean - dif, | ||
uppp_ci = mean + dif) | ||
# we conclude we're 95% certain the mean for the control group is | ||
# between 4.73 and 6.36 and the mean for the nicotinic group is | ||
# between 6.52 and 8.50. More usually we might put is like this: | ||
# the mean for the control group is 5.55 +/- 0.82 and that for the nicotinic group is 7.51 +/- 0.99 | ||
``` | ||
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--- | ||
title: "Independent Study to prepare for workshop" | ||
subtitle: "The logic of hypothesis testing and confidence intervals" | ||
toc: true | ||
toc-location: right | ||
--- | ||
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1. 📖 Read [The logic of hyothesis testing](https://3mmarand.github.io/comp4biosci/logic_hyopthesis_testing.html) | ||
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2. 📖 Read [Confidence Intervals](https://3mmarand.github.io/comp4biosci/confidence_intervals.html) | ||
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