Statistics Flashcards
Why should you study Statistics?
- objective evaluation of numbers
- population description
- estimate unknown values
What is population description?
a sample statistic to make inferences for a population because it is hard to count/analyze entire population
What is estimate unknown value?
breeding value
What is the most important value? Why?
breeding value; part of genetic variance that is passed from parent to offspring
What is an example of population desciption?
backfat thickness in Hampshire hogs
What is the formula for genetic variance?
Vg=Bv + GCV
Why do we need to measure traits?
- variation
- “raw material” breeder has available for herd improvement
What traits are the easiest to improve?
traits with highest variability
What type of traits are discontinuous variation?
qualitative traits
Are qualitative traits affected by the environment?
no
How many genes control qualitative traits?
one or few
What type of traits are continuous variation?
quantitative traits
How many genes control quantitative traits?
many genes
Is continuous variation simple or complex?
highly complex
Are discontinuous variation traits or continuous variation traits economically important?
continuous variation
What is a quality of continuous variation?
many small gradations almost imperceptible to one another
Are samples taken from a population random or specific?
random
How are continuous variation traits highly complex?
a matter of genotype and environment interaction
What is the point of taking a sample?
to make inferences about a population
How would weaning weight in cattle be inferred?
take a random sample, analyze data, and then infer weaning weight of the population
What is population parameter?
numerical descriptive measure for a population; number that describes a population
What are examples of population parameter?
population mean and variance
What is sample statistic?
numerical descriptive measures for a sample; estimate of population parameter
What is central tendency?
in normal distribution, values are clustered at the midpoint , thinning out systematically toward both extremes
How do biological measurements tend to be distributed?
normally
What happens as better traits are selected to the distribution?
mean is shifted to the right
What are the 3 measures of central tendency?
Mean, Median, and Mode
What is the median?
value half way between the 2 extreme values
What is the mode?
class with the highest frequency
What is the mean?
average of all measurements in the population (sample)
What is the most useful statistic for estimating central tendency of most populations?
mean
Formula for mean?
X (line over X) = ∑X
What can mean show in terms of distribution? (?)
Samples from a normally distributed population may
show departure from normality
What are the measures of distribution?
standard deviation, standard error, and variation (?)
What is the measure of distribution?
- describes a spread, how the data varies
- deviation about the mean
What is variance?
- the measure of distribution;
- the average squared deviation of observations from their mean
- the sum of differences between each observation and the mean in squared values
What is the formula for variance?
S^2 = = ∑ (X – X (line above) )^2
n – 1
How is variance calculated?
- each observation in a population sample first has the mean subtracted from it
- these deviations from the mean are FIRST squared
- then squared deviations are summed
- the sum of squared deviations is divided by (n-1)
What does n-1 give?
a more reliable estimate of population variance
Do limited samples account for the entire range of a population?
no
Why is variance squared?
if not, it adds up to 0
Is variance calculated useful?
yes when comparing the result to the result of another population
What is standard deviation?
“typical” deviation, in absolute value, of an observation drawn at random from the population, from its mean
What is s equal to?
√s^2
What is X (line above)?
sample mean
What is ∑ ?
sum
What is n?
number of observations in a sample
What is μ?
population mean
How is standard deviation used?
add and subtract to mean to get a range; describe variation in a population
What does standard deviation help us picture?
how much variation actually exists for a trait
What is standard error?
-how accurately the mean has been estimated
-If the mean were computed again from a different
sample of n individuals drawn at random from the
same population, how closely would the new estimate
of the mean correspond to the former one?
What is the formula for standard error?
S. E. = S. D. /√n
What makes up the measure of relationships?
- correlation
- regression
