How do you report a paired samples t

We’ll use some data from a paper by Faaborg et al on bird populations in Puerto Rico. We’ll look at 9 species of warblers, and compare the number of birds captured in mist nests in 1991 and in 2005 to determine if on average birds are declining at this study site

#make a vector of species names.
species <- c("OVEN","WEWA","NOWA",
             "BWWA","HOWA","AMRE",
             "CMWA","NOPA","PRWA")

#Number of birds of each species captured in 1991 
N.1991 <- c(29, 6, 4, 60, 8, 19, 9, 7, 4)
N.2005 <- c(24, 5, 0, 16, 3, 9, 2, 5, 8)

#make dataframe
dat <- data.frame(species,
                  N.1991,
                  N.2005)

Take alook at the dataframe; we have 3 columns, one with the names of the 9 species, one with the number caught in 1991, and one with the nubmer caught in 2005

##   species N.1991 N.2005
## 1    OVEN     29     24
## 2    WEWA      6      5
## 3    NOWA      4      0
## 4    BWWA     60     16
## 5    HOWA      8      3
## 6    AMRE     19      9

Paired t-test

Its a bit confusing, but there are multiple ways to do a paired t-test in R. (I can think about about 6, will focus on the 2 easiest ones). Paired t-tests are actually just a 1-sample t-test where the “1 sample” is a set of differnces between pairs of data points. Each one of our species has a pair of data points: abundance in 1991 and abundance in 2005. We can give R the raw data and t.test will calcaulte the differnce on the fly, or we can calculate the difference ourselvres. If we let R calcualte the difference, we must tell it that we are looking for a paired t-test by telling it “paired = TRUE”. If we calcualte the difference ourselvees we must tell it we want a 1-sample t-test, which is done by giving it a mean value against which to test the null hypothesis (“mu = 0”).

Paired t-test, Version 1

Paired t-test carried out by giving the t.test() function 2 columns from from a dataframe.

• Note there is no “~”, just the name of each column, followed by a comma
• must include paired = TRUE

t.test(dat$N.1991,    #column 1, then a comma
       dat$N.2005,    #column 2; 
       paired = TRUE)

## 
##  Paired t-test
## 
## data:  dat$N.1991 and dat$N.2005
## t = 1.7644, df = 8, p-value = 0.1157
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -2.523868 18.968313
## sample estimates:
## mean of the differences 
##                8.222222

Paired t-test, Version 2

Paired t-test as a 1-sample t-test on the difference between two columns.

• First calcualte the difference between the columns
• T-test is given one column
• Note there is no “~”, just the name of the column that has the differnces
• must set mu = 0
• there is NO “paired = TRUE”

#make new column with the differencce between 1991 an 2005
dat$difference <- dat$N.1991 - dat$N.2005

#t.test() on difference
t.test(dat$difference, 
       mu = 0)

## 
##  One Sample t-test
## 
## data:  dat$difference
## t = 1.7644, df = 8, p-value = 0.1157
## alternative hypothesis: true mean is not equal to 0
## 95 percent confidence interval:
##  -2.523868 18.968313
## sample estimates:
## mean of x 
##  8.222222

Reporting the results of a paired t-test

When we report a paired t-test we should give the p-value, the t statistic, and the degrees of freedom (df). NOte that for a paired t-test the df are equal to n-1, where n is the number of pairs in the data set (eg, the number of differences calculated), not the total number of seperate datapoinots.

We shoudl also report the effect size, which for a paried t-test is mean difference between the pairs; we should also report the 95% confidence interval for the effect size. Here, the mean difference is 8.2, which means on average there were 8 fewer individuals of each species captured in 2005 versus 1991. The 95 CI around this difference is large, from -2.5 to 19. Since it contains 0.0, the p value is greater than 0.05.

I would report the results of the t-test like this:

“There was a marginally significant difference in the number of birds of the 9 species captured in 1991 versus 2005 (paired t-test: t = 1.76, df = 8, p = 0.12). The mean difference in the number captured between years was 8.2 birds (95%CI: -2.5 to 19).”

We can use the following format to report the results of an independent two samples t-test:

A two sample t-test was performed to compare [response variable of interest] in [group 1] and [group 2].

 

There [was or was not] a significant difference in [response variable of interest] between [group1] (M = [Mean], SD = [standard deviation]) and [group2] (M = [Mean], SD = [standard deviation]); t(df) = [t-value], p = [p-value].

We can use the following format to report the results of a paired samples t-test:

A paired samples t-test was performed to compare [response variable of interest] in [group 1] and [group 2].

 

There [was or was not] a significant difference in [response variable of interest] between [group1] (M = [Mean], SD = [standard deviation]) and [group2] (M = [Mean], SD = [standard deviation]); t(df) = [t-value], p = [p-value].

Note: The “M” in the results stands for sample mean, the “SD” stands for sample standard deviation, and “df” stands for degrees of freedom associated with the t-test statistic.

The following examples show how to report the results of each type of t-test in practice.

Example: Reporting Results of a One Sample T-Test

A botanist wants to know if the mean height of a certain species of plant is equal to 15 inches. She collects a random sample of 12 plants and performs a one sample-test.

The following screenshot shows the results of the test:

Here’s how to report the results of the test:

A one sample t-test was performed to compare the mean height of a certain species of plant against the population mean.

 

The mean value of height (M = 14.33, SD = 1.37) was not significantly different than the population mean; t(11) = -1.685, p = .120.

Example: Reporting Results of an Independent Samples T-Test

Researchers want to know if a new fuel treatment leads to a change in the average miles per gallon of a certain car. To test this, they conduct an experiment in which 12 cars receive the new fuel treatment and 12 cars do not.

The following screenshot shows the results of the independent samples t-test:

Here’s how to report the results of the test:

A two sample t-test was performed to compare miles per gallon between fuel treatment and no fuel treatment.

 

There was not a significant difference in miles per gallon between fuel treatment (M = 22.75, SD = 3.25) and no fuel treatment (M = 21, SD = 2.73); t(22) = -1.428, p = .167.

Example: Reporting Results of a Paired Samples T-Test

Researchers want to know if a new fuel treatment leads to a change in the average mpg of a certain car. To test this, they conduct an experiment in which they measure the mpg of 12 cars with and without the fuel treatment.

The following screenshot shows the results of the paired samples t-test:

Here’s how to report the results of the test:

A paired samples t-test was performed to compare miles per gallon between fuel treatment and no fuel treatment.

 

There was a significant difference in miles per gallon between fuel treatment (M = 22.75, SD = 3.25) and no fuel treatment (M = 21, SD = 2.73); t(11) = -2.244, p = .046.

How do you write a paired samples t

t = x_diff / (s_diff/√n) where: x_diff: sample mean of the differences. s: sample standard deviation of the differences. n: sample size (i.e. number of pairs)

How do I report a paired sample t

Step-by-Step Instructions for Running the Paired t-Test in Excel.

In Excel, click Data Analysis on the Data tab..

From the Data Analysis popup, choose t-Test: Paired Two Sample for Means..

Under Input, select the ranges for both Variable 1 and Variable 2..

In Hypothesized Mean Difference, you'll typically enter zero..

How do you interpret a paired two sample t test?

Assuming that the population means are equal: If t < 0, P(T <= t) one-tail is the probability that a value of the t-Statistic would be observed that is more negative than t. If t >0, P(T<=t) one tail is the probability that a value of the t-Statistic would be observed that is more positive than t.

How do you report a two sample t test?

We can use the following format to report the results of an independent two samples t-test: A two sample t-test was performed to compare [response variable of interest] in [group 1] and [group 2].