Tests Flashcards
What does standard deviation (s) show in a sample that is normally distributed?
The spread of data about the mean, 𝑥
Standard deviation helps to understand how data points deviate from the average.
What does a small value of standard deviation indicate?
Data is less scattered, more consistent and reliable
A small standard deviation suggests that the values are close to the mean.
What does a large value of standard deviation indicate?
Data is widely spread, results are less reliable
A large standard deviation suggests that the values are spread out over a wider range.
What are two other functions of standard deviation?
- To calculate standard error
- To calculate t-test value
Standard deviation is useful in various statistical analyses.
True or False: In mathematics, standard deviation is calculated for a sample.
False
In mathematics, standard deviation is typically calculated for a population.
Fill in the blank: In biology, we learn the standard deviation of a _______.
[sample]
This is distinct from the standard deviation of a population learned in mathematics.
What does Standard Error (SM) indicate?
It shows how close the mean of a sample calculated is from the true mean of the population
SM reflects the reliability of the mean
How is Standard Error (SM) used in graphical representations?
It is used to put error bars on graphs
Error bars visually represent the uncertainty in the mean value
What does a small value of Standard Error indicate?
The sample mean value is closer to the actual mean and the mean is more reliable
A small SM enhances confidence in the sample mean’s accuracy
What is the range of Standard Error (SM) values?
SM value is between 0 and 1
0 indicates no error and 1 indicates maximum error
What is required to create bar charts with error bars?
1) Mean, 𝑥 = value for y coordinates
2) Standard error, SM
3) Error bars = lines on bar charts
These elements are essential for accurately representing data variability.
How are error bars calculated?
Error bars are calculated using upper and lower limits of a 95% confidence interval, that is mean ± 2 SM
SM stands for standard error of the mean.
What is the function of error bars on bar charts?
To see if there is a significant difference between two means
Error bars help visualize the uncertainty around the mean estimates.
What is a 95% confidence interval?
Interval where 95% of the sample’s data lies around the mean
The confidence interval provides a range of values that likely contain the population parameter.
What are the upper and lower limits of the 95% confidence interval?
Min and max limit of the 95% interval
These limits indicate the range within which the true population mean is expected to fall.
How is the 95% confidence interval calculated?
Mean ± 2SM
SM stands for standard error of the mean, which is derived from the sample standard deviation.
What does it indicate when error bars overlap?
The two means are not significantly different
Null hypothesis is accepted
What does it indicate when error bars don’t overlap?
The two means are significantly different
Null hypothesis is rejected
What should be done to double check the results of error bars interpretation?
Perform a t-test
This helps confirm the significance of the difference between means.
What is a t-test used for?
To test whether data from 2 samples are significantly different
A t-test helps determine if the means of two groups are statistically different from each other.
What type of data is required for a t-test?
Continuous / interval data
Continuous data can take any value within a range, while interval data is numerical data where the difference between values is meaningful.
What distribution requirement must data meet for a t-test?
Data must be normally distributed
Normal distribution is a probability distribution that is symmetric about the mean.
What is a requirement regarding the standard deviations for a t-test?
Standard deviations are approximately the same
This assumption is known as homogeneity of variance.
What is the maximum number of values in each sample for a t-test?
Less than 30 values each
This is to ensure the validity of the t-test assumptions.
