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FANR 3000: TEST 1
closeness of a measured value to the true value
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accuracy
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closeness of 2 or more measurements to each other
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precision
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incorrect measurements due to carelessness
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gross errors
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errors of same size and magnitude
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systematic errors
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errors that are always present in measurement
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random errors
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linear version of cumulative histogram
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ogive
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display change in one variable in relation to another
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line graph
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similar to histogram but usually associated with categories
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bar graph
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circular graph showing how total quantitiy is distributed among group of categories
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pie charts
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Equation for outliers
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Q1 - (1.5*IQR)
Q3 + (1.5*IQR)
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measure of how spread out the data is
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variance
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square root of the variance
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standard deviation
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What is the empirical rule?
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- 68% of data falls within 1 standard dev
- 95% of data falls within 2 standard dev
- 99.7% of data falls within 3 standard dev
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value that represents how many standard deviations a value is from the mean
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z score
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how do you calculate standard error
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Standard deviation divided by square root of n
(SD/sqrt(n))
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What do these symbols stand for:
- Mu
- sigma
- sigma squared
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- population mean
- population standard deviation
- population variance
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What do these symbols stand for:
- N
- n
- x bar
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- total number in population
- total number in sample
- sample mean
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What do these symbols stand for:
- S of SD
- S squared
- sigma sub x bar
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- sample standard deviation
- sample variance
- sample standard error
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What do these symbols stand for:
- alpha
- v (nu)
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- significance level in hypothesis test
- degrees of freedom
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the most commonly observed value in the data set
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mode |
what is the range?
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highest value - lowest value
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A high variance would mean that the data will be ____
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spread out
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What is the formula for variance?
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E(xi-xbar)2/(n-1)
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What is the formula for standard error?
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SD/sqrt(n)
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What is the mean plus or minus the SD?
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it is a descriptive statistic that shows how the observations within the sample differ from the sample mean
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what is the mean plus or minus the standard error?
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this is a description of the bound on the estimate of the population mean/how likely the sample mean is the population mean
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set of all individuals possessing the particular attribute which we describe
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population
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values that summarize properties of the population
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parameters
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what are some common parameters
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population mean (mu) and the population variance (sigma squared)
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the portion or subset of the population that we actually count or measure
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sample
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what is a key assumption concerning the sample
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the information obtained from the sample must reliably reflect the population
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three types of samples
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- simple random sample
- systematic sample
- stratified sample
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taking a random sample of n units from a population of size N
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simple random sample
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sampling every kth unit from a population
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systematic sample
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dividing the population into non-overlapping blocks (strata) and taking a random sample within strata
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stratified sample
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the measurable characteristics of the samples of interest
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variables
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example variables
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- age
- gender
- volume
- length
- density
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two types or categories of variables
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quantitative and qualitiative
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Quantitative variables
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numbers or data that can be measured
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qualitative variables
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words or data that can be observed but not really measured
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two types of quantitative data
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discrete - counts (integer values only)
continuous - measurement (any value withing a given range)
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two types of qualitative data
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Nominal - no natural ordering
Ordinal - have a natural order or rank
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the set of measurements we have obtained
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observations |
Value which summarizes a property of the sample
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statistic
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You measure the height of a tree five times:
10.1, 10.0, 9.9, 10.1, and 10.0
The true height is 15.7
Is this low or high precision?
Is this low or high accuracy?
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low accuracy and high precision
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number of observations in each variable class
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frequency
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fraction of the total observations in each variable class
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relative frequency
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the frequency of a variable class plus the frequency of the classes below it
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cumulative frequency
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the relative frequencies plus the relative frequencies of the classes below it
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cumulative relative frequency
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bar graphs are similar to histograms but they are usually associated with _____ common with qualitative data
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categories
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used to display the change in one variable in relation to another
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line graph
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data is "distributed normally" if:
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- distribution is symmetrical and bell shaped
- measures of central tendency are the same
- variable of interest has an infinite range
- the practical range is plus or minus 3 standard deviations above and below the mean
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How many standard deviations is a score of 83 from the mean?
Mean is 87.5
SD = 3.75
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(score - mean)/SD
(83 - 87.5)/3.75
= -1.2
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What is the formula to find a z score
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(x - xbar)/SD
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Find probability that in any given year, more than 5000 acres will be burned? given mu = 4300 sd = 750
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z score = (5000-4300)/750
z score = 0.93
(look up 0.93 in z score table)
= 0.3238
Greater than that is .5-.3238 =0.1762
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equation for confidence interval
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CI = xbar +- tn-1,a/2(SE)
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what does the central limit theorem say?
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regardless of the shape of the original distribution of data, the sampling distribution of the mean will be approximately normally distributed
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What is a 90% confidence interval for a sample (n=26) of fish weights with a mean of 8.7lbs and a sample SE of 1.3lbs?
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a = .10 (so a/2=.05)
df = 26-1 = 25
Look these up in t table = 1.7081
90% CI = 8.7 + or - 1.7081(1.3) =
8.7+ or - 2.22
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Three things that impact the width of the confidence interval?
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- confidence interval - as interval increases, it gets wider
- variability - populations with more variability generate wider CI's
- sample size - smaller samples sizes generate wider intervals
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Steps for determining confidence interval
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1. calculate mean of sample
2. calculate variance
3. determine critical t or z value
4. plug all those into CI formula
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when would u use a critical z value or the z distribution table?
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when the standard deviation of the population is known
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