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Students often go straight to the hypothesis test rather than investigating the data with summary statistics and charts first. Encourage them to summarise their data first. As well as summarising their results, charts especially can show outliers and patterns.
For continuous normally distributed data, summarise using means and standard deviations. If the data is skewed or there are influential outliers, the median (middle value) and interquartile range (Upper quartile – lower quartile) are more appropriate.
Ttests are of different types:
 Paired Ttest – dependent and independent.
 Normal Ttest
The paired ttest is used to determine paired differences. It is used in the cases where the sample is less than 50 and the sample on which the test was priory applied remains the same.
The Onesample ttest is used to compare a sample mean to a specific value.
t = (mean – comparison value)/ Standard Error
An “F Test” uses the Fdistribution. It uses an F Statistic to compare two variances.
i.e. s_{1} and s_{2}, by dividing them. A result is always a number greater than zero (as variances are always positive). The equation for comparing two variances with the ftest is:
F = s^{2}_{1} / s^{2}_{2}
It is also essential to understand the difference between a ttest and ftest as they are using interchangeably by many people.
Ttest vs Ftest
The difference between the ttest and ftest is that ttest is used to test the hypothesis whether the given mean is significantly different from the sample mean or not. On the other hand, an Ftest is used to compare the two standard deviations of two samples and check the variability.
Comparison Table Between Ttest and Ftest (in Tabular Form)
Parameter of Comparison  Ttest  Ftest 

Implication  The Ttest is used to test the hypothesis whether the given mean is significantly different from the sample mean or not  Ftest is used to compare the two standard deviations of two samples and check the variability. An Ftest is a ratio of two Chisquares. 
Types  Ttests are of different types: 1. Paired Ttest – dependent and independent. 2. Normal Ttest  There is one type if Ftest which is used to compare standard deviations of the twosample data. 
Null Hypothesis  H0: the sample mean is equal to 0.  H0: the two samples have the same variance. 
Test statistic  T = (mean – comparison value)/ Standard Error ~t(n1)  F = s21 / s22 ~ F(n11,n21) 
Degree of freedom  The degree of freedom is )n1) where n is the number of sample values  The degree of freedom is (n11,n21) where n1 and n2 are the numbers of observations in samples 1 and 2. 
What is Ttest?
T distribution or ttest is used when the sample size,n, is less than 30 and the standard deviation, sigma, is unknown.
The distribution of continuous data can often be closely approximated by the normal distribution.
T distribution is generally used to calculate numerical data.it is derived from a normal distribution and is also just a type of normal distribution.
One Sample ttest
The onesample ttest is concerned with making inferences regarding a population mean.
One sample ttest is used when we are given with only one sample and we need to run a hypothesis on that sample itself.
Two Sample ttest
This is more common in a scenario than the onesample ttest. Usually, we want to compare the means of 2 groups.
Two sample ttest is also used when we are given with only one sample and we need to run a hypothesis on that sample itself.
We can run two types of tests under this category.
 Paired test: in this the same sample population is used for testing two different treatments. compare the means of two conditions in which the same (or closely matched) participants participated.
 Unrelated Samples: In this, we compare the means of two groups of participants.
Hypothesis testing with t
 We can draw a sampling distribution of tvalues (the Student t distribution) – this shows the likelihood of each tvalue if the null hypothesis is true
 The distribution will be affected by sample size (or more precisely, by degrees of freedom)
 We evaluate the likelihood of obtaining our tvalue given the tdistribution.
Assumptions
The onesample ttest requires the following statistical assumptions:
 Random and independent sampling.
 Data are from normally distributed populations.
[Note: The onesample ttest is generally considered robust against violation of this assumption once N > 30.]
What is Ftest?
An “F Test” uses the Fdistribution. It uses an F Statistic to compare two variances.
Ftest for detecting the identity of variances of two normally distributed random variables:
Our hypothesis for the identity of the variances of two independent random variables of a normal distribution with unknown expectation and variance is checked by the socalled Ftest.
H0: σ_{1}^{2} = σ_{2}^{2}
H1: σ_{1}^{2} > σ_{2}^{2}
The test is always carried out as a onesided test.
Test statistics: F_{sz} = s_{1}^{2}/s_{2}^{2} where s_{1}^{2} > s_{2}^{2}
If H0 fulfills, then Fsz is of Fdistribution with degrees of freedom n11, n21 .
Decision principle: for Fsz ≤ Fα 0hypothesis is accepted, otherwise not.
Main Differences Between Ttest and Ftest
 The main difference between Reference and Recommendation is, that ttest is used to test the hypothesis whether the given mean is significantly different from the sample mean or not. On the other hand, an Ftest is used to compare the two standard deviations of two samples and check the variability.
 The Ttest can be conducted the twosided test or a singlesided test but the ftest is the only singlesided test as variance can not be negative.
 Ttests are of different types: Paired Ttest – dependent and independent, Normal Ttest. Whereas the ftest is only of one type.
 The Ttest is applied when the sample population is less than 30 and the standard deviation is unknown, whereas the ftest can be applied upon the large sampled population.
 The Ttest is used to check the hypothesis for the sample mean whereas the ftest is used to run the hypothesis on the variance of the samples.
Conclusion
In the world of Statistics, some tests are applied to the sample data to check the required hypothesis. Two of the tests are ttest and ftest. The Ttest is used to test the hypothesis whether the given mean is significantly different from the sample mean or not.
On the other hand, an Ftest is used to compare the two standard deviations of two samples and check the variability.
References
 https://asa.scitation.org/doi/abs/10.1121/1.417933
 https://projecteuclid.org/euclid.aoms/1177728261
 https://www.mitpressjournals.org/doi/abs/10.1162/089976699300016007
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