Database Management Exam > Database Management Videos > Mastering R Programming: For Data Science and Analytics > T Distribution and t Scores in R (R Tutorial 3.4)
T Distribution and t Scores in R (R Tutorial 3.4) Video Lecture | Mastering R Programming: For Data Science and Analytics - Database Management
FAQs on T Distribution and t Scores in R (R Tutorial 3.4) Video Lecture - Mastering R Programming: For Data Science and Analytics - Database Management
| 1. What is a t-distribution and how is it different from a normal distribution? |  |
Ans. A t-distribution, also known as Student's t-distribution, is a probability distribution that arises when estimating the mean of a normally distributed population with a small sample size. It is similar to a normal distribution but has heavier tails, which means it has more probability in the extreme values. The shape of the t-distribution depends on the degrees of freedom, which is determined by the sample size minus one.
| 2. How are t-scores calculated in R? | |
Ans. To calculate t-scores in R, you can use the function `qt()`. The syntax is `qt(p, df)`, where `p` is the probability (e.g., 0.95 for a 95% confidence level) and `df` is the degrees of freedom. The function returns the t-score corresponding to the given probability and degrees of freedom.
| 3. What is the significance of degrees of freedom in t-distribution? | |
Ans. Degrees of freedom in t-distribution represent the number of independent pieces of information available after estimating one or more parameters. In the context of t-distribution, it is the sample size minus one (n-1). Degrees of freedom affect the shape of the t-distribution, with larger degrees of freedom resulting in a distribution that closely resembles a normal distribution.
| 4. How can t-distribution be used for hypothesis testing? | |
Ans. T-distribution is commonly used in hypothesis testing when the population standard deviation is unknown and the sample size is small. The steps for hypothesis testing using t-distribution are:
1. Formulate the null and alternative hypotheses.
2. Calculate the t-score using the sample data and the test statistic formula.
3. Determine the critical region or calculate the p-value.
4. Compare the t-score with the critical value or p-value to make a decision about rejecting or failing to reject the null hypothesis.
| 5. Can t-distribution be used for large sample sizes? | |
Ans. While t-distribution is primarily used for small sample sizes, it can also be used for large sample sizes. As the sample size increases, the t-distribution approaches the standard normal distribution. In practice, when the sample size is greater than 30, the t-distribution can be approximated by a normal distribution for most purposes. However, if the population standard deviation is unknown, the t-distribution should still be used.
Text Transcript from Video
hi I'm Mike Marin and in this video
we'll talk about finding probabilities
and finding percentiles for the T
distribution these can be used to find
p-values or to find critical values for
constructing confidence intervals for
statistics that follow a T distribution
throughout this video we will focus on a
statistic which follows a T distribution
with a mean of 0 standard deviation of 1
and 25 degrees of freedom we can
calculate probabilities using the PT
command in R to access the help menu
type help and in brackets the name of
the command you would like help for or
simply place a question mark in front of
the command you would like help for now
suppose that we had conducted a t-test
and obtained a test statistic of 2.3
with 25 degrees of freedom also suppose
that we would like to find the one-sided
p-value in other words we would like to
find the probability of T being greater
than 2.3 we can do this using the PT
command in R here we would like the
probability associated with a T value of
2.3 degrees of freedom are 25 and we
will set the lower tail argument equal
to false asking R for an upper tail
probability or the area above 2.3 here
we can see the one-sided p-value is 1.5
percent now suppose instead we would
like to find the two-sided p-value here
we would like to find the area above 2.3
and the area below negative 2.3 we can
calculate each of these probabilities
separately and add them together now
asking R for the area below negative two
point three degrees of freedom 25 again
we will set the lower tail equal to true
asking for a lower tail probability or
the area below negative two
three we can see the two-sided p-value
is three percent or we may simply take
the one-sided p-value and double this
now let's move into talking about
confidence intervals suppose that we
would like to construct a two-sided 95%
confidence interval here we would like
to find the T value for 95% confidence
to do this
we will use the Qt command here we would
like to find the value of T with 2.5% in
each tail we can use the Qt command to
find the quantile for the T distribution
here we would like to find the T value
associated with a probability of point
zero two five two point five percent in
the tail degrees of freedom twenty five
again we will set lower tail equal to
true asking for the value of T with two
point five percent in the lower tail
here we can see the critical value is
negative two point zero six
so a T value of two point zero six is
the critical value that would be used
for the 95 percent confidence interval
in the next video in this series we will
learn to conduct the t-test and
confidence interval using our although
it is still useful to know how to look
up these values using R as we've
discussed here you may explore the help
menus for help using the PF and the P
exp commands the PF command can be used
to look at probabilities for the F
distribution while the P exp command can
be used to look up probabilities for the
exponential distribution thanks for
watching this video and make sure to
check out my other instructional videos
we'll talk about finding probabilities
and finding percentiles for the T
distribution these can be used to find
p-values or to find critical values for
constructing confidence intervals for
statistics that follow a T distribution
throughout this video we will focus on a
statistic which follows a T distribution
with a mean of 0 standard deviation of 1
and 25 degrees of freedom we can
calculate probabilities using the PT
command in R to access the help menu
type help and in brackets the name of
the command you would like help for or
simply place a question mark in front of
the command you would like help for now
suppose that we had conducted a t-test
and obtained a test statistic of 2.3
with 25 degrees of freedom also suppose
that we would like to find the one-sided
p-value in other words we would like to
find the probability of T being greater
than 2.3 we can do this using the PT
command in R here we would like the
probability associated with a T value of
2.3 degrees of freedom are 25 and we
will set the lower tail argument equal
to false asking R for an upper tail
probability or the area above 2.3 here
we can see the one-sided p-value is 1.5
percent now suppose instead we would
like to find the two-sided p-value here
we would like to find the area above 2.3
and the area below negative 2.3 we can
calculate each of these probabilities
separately and add them together now
asking R for the area below negative two
point three degrees of freedom 25 again
we will set the lower tail equal to true
asking for a lower tail probability or
the area below negative two
three we can see the two-sided p-value
is three percent or we may simply take
the one-sided p-value and double this
now let's move into talking about
confidence intervals suppose that we
would like to construct a two-sided 95%
confidence interval here we would like
to find the T value for 95% confidence
to do this
we will use the Qt command here we would
like to find the value of T with 2.5% in
each tail we can use the Qt command to
find the quantile for the T distribution
here we would like to find the T value
associated with a probability of point
zero two five two point five percent in
the tail degrees of freedom twenty five
again we will set lower tail equal to
true asking for the value of T with two
point five percent in the lower tail
here we can see the critical value is
negative two point zero six
so a T value of two point zero six is
the critical value that would be used
for the 95 percent confidence interval
in the next video in this series we will
learn to conduct the t-test and
confidence interval using our although
it is still useful to know how to look
up these values using R as we've
discussed here you may explore the help
menus for help using the PF and the P
exp commands the PF command can be used
to look at probabilities for the F
distribution while the P exp command can
be used to look up probabilities for the
exponential distribution thanks for
watching this video and make sure to
check out my other instructional videos
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Nov 24, 2024 Last updated |
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