Reading...
Play button
Play button
Use LEFT and RIGHT arrow keys to navigate between flashcards;
Use UP and DOWN arrow keys to flip the card;
H to show hint;
A reads text to speech;
153 Cards in this Set
- Front
- Back
|
What does a bell-shaped curve of values indicate?
|
Central tendency
|
|
|
What is central tendency?
|
A trend for scores to fluctuate about the most commonly observed score, more or less equally on either side.
|
|
|
When population data are distributed normally, we use simple formulas to compute what?
|
Probability of randomly drawing samples of particular characteristics from such populations.
|
|
|
What can we do with assuming data within a sample are normally distributed?
|
Becomes relatively easy to make predictions about the data (ex. the likelihood of earning a particular exam score).
|
|
|
True or False:
All frequency distributions are normal in shape. |
FALSE: Not all frequency distributions are normal in shape.
|
|
|
What are many inferential statistical tools based on?
|
The assumption that samples are derived from normally distributed population data.
|
|
|
What is the major hallmark of parametric statistics?
|
That they are based on the presumption of normally distributed population.
|
|
|
What is parametric stats?
|
Statistics based on an entire population (s to σ)
|
|
|
Frequency distributions are often what?
|
Bell-shaped
|
|
|
How do we determine whether a set of data is normally distributed?
|
We can use formulas to determine whether data are normally, but the easiest way is to generate a histogram from the data and examine its shape.
|
|
|
What are 5 characteristics of a normal distribution shape (ex. curve)?
|
1) bell-shaped curve w/ highest point (i.e. mode) above the mean
2) symmetrical about the mean (μ, in case of a pop.) 3) the curve, even though flattens out, never touches the horizontal axis 4) pt. of transition b/w convexity and concavity on either side of the peak marks the first standard deviation (ex. μ+σ and μ-σ) 5) mode=mean=median |
|
|
True or False:
The curve, although it tends to flatten out, never touches the horizontal axis. |
TRUE
|
|
|
The point of transition b/w convexity and concavity on either side of the peak marks what?
|
The first standard deviation
|
|
|
What does a frequency histogram represent?
|
A continuous probability distribution
|
|
|
What represents a comprehensive sample space for the variable in question?
|
The entire two-dimension area under the curve
|
|
|
What is the probability of an event occurring within any sample space?
|
1
|
|
|
The entire area under the normal curve approaches what?
|
1
|
|
|
Any particular fraction of the area under the normal curve is what?
|
1
|
|
|
What percent of data will fall within 1 standard deviation of the mean?
|
68.2% (34.1% on either side)
|
|
|
What percent of data will fall within 2 standard deviations the mean?
|
95.4% (another 13.6% + 34.1% on either side)
|
|
|
What percent of data will fall within 3 standard deviations of the mean?
|
99.7% (another 2.15% + 13.6% + 34.1% on either side)
|
|
|
What shape of the curve is μ-σ?
|
Convex
|
|
|
What shape of the curve is μ+σ?
|
Concave
|
|
|
True of False:
Standard z-scores are unit-based. |
FALSE: z-scores are unitless
|
|
|
When comparing variability b/w 2 samples or populations, ideally we need what in order for it to be easier to compare frequency distributions?
|
We need a unitless measure of the mean and standard deviation
|
|
|
How are 2 normal distributions likely to differ?
|
1) absolute values of the mean and standard deviation
2) unit being used |
|
|
What formula is a simple means of transforming any set of data into a standard normal distribution, based on z-scores?
|
z = x - x (mean) / s (sample) or z = x - μ (mean) / σ (st. dev. of pop)
|
|
|
What is the z-score equal to?
|
The number of standard deviation units b/w the raw score and the mean (this number can be a fraction).
|
|
|
What is the mean equal to in any standard normal distribution?
|
0
|
|
|
What is the standard deviation equal to in any standard normal distribution?
|
1
|
|
|
If x = 0 or μ = 0, what will your z-score be?
|
0
|
|
|
If x = μ, then what does z equal?
|
0
|
|
|
If x > μ, then what does z have to be?
|
z > 0
|
|
|
If x < μ, then what does z have to be?
|
z < 0
|
|
|
What do z-scores take into account?
|
Both the mean and standard deviation, therefore one can directly compare 2 z-scores even when comparing data from entirely different distributions.
|
|
|
True or False:
One cannot compare 2 z-scores from different distributions? |
FALSE: One can directly compare 2 z-scores even when comparing data from entirely different distributions
|
|
|
What formula can we use to compute raw scores when μ and σ are known or predicted?
|
x = σz + μ
|
|
|
How can we find the areas under any standard normal curve as a fraction of the total area?
What does this boil down to? |
-By using tables
-Probability |
|
|
True or False:
Most tables include both positive and negative z-scores. |
FALSE: Only shows positive z-scores since the left half is identical to the right half.
|
|
|
What is the p value of either half to left or right of z = 0?
|
p = 0.5000
|
|
|
What should one do with raw scores of original data in order to compare?
|
Must first convert the original data into z-scores
|
|
|
What is a sampling distribution?
|
A frequency distribution is constructed based on samples (n > 1) rather than single subjects (n = 1).
|
|
|
What is described as a frequency histogram based on distribution of sample means?
|
Sampling distribution
|
|
|
What is the formula for the standard deviation of a sampling distribution (or standard error of the mean)?
|
σ = σ/ √n (sample size)
*Called standard error of the mean |
|
|
What happens to the sampling distribution's standard deviation as the sample size (n) increases?
|
The sampling distribution's standard deviation decreases.
z = x - μ / σ / √n |
|
|
Since we don't know population parameters, we can use samples to determine what?
|
1) Estimate population parameters (ex. confidence interval)
2) Formulate decisions about the populations |
|
|
What are 2 ways to formulate decisions about populations?
|
1) Use sample data to accept or reject an assumption about the population mean.
2) Determine whether 2 or more samples come from the same or different populations. (ex. T-tests) |
|
|
Any sampling distribution, regardless of the size of each sample (n), will be normal if what distribution is normal?
|
Overall x distribution is normal
|
|
|
Just like the normal distribution, a sampling distribution is also what?
|
A probability distribution
|
|
|
If you have a sampling distribution with known parameters, you can compute what?
|
The probability that the mean of a randomly selected sample will fall within a particular range.
|
|
|
What can a sampling distribution be converted into?
|
A standard normal distribution (z-score)
z = x (mean) - μ / σ σ = σ / √n |
|
|
What is the central limit theorem?
|
The sample size (n) increases, the shape of the sampling distribution will approach normality regardless of the shape of the original x distribution (ex. left-tailed skew becomes normal)
|
|
|
How can a sampling distribution become normal in shape?
|
By taking infinitely large samples from the distribution and plot as a frequency histogram.
|
|
|
True or False:
It is necessary to know or assume anything about the shape of the overall distribution. |
FALSE: It is unnecessary to know anything about the shape of the overall distribution.
|
|
|
What needs to be known in order for the central limit theorem to hold?
|
μ and σ (sigma) must be known and the sample size is very large.
|
|
|
How large of a sample size must be in order to get a normally shaped sampling distribution?
|
n = 30 or greater
|
|
|
What happens if the sample size is not infinitely large according to the central limit theorem?
|
The sampling distribution will be somewhere in b/w the "true" distribution and a normal distribution.
|
|
|
In general, what sample size will give roughly a normal distribution?
|
n = 30 or greater
|
|
|
What is an example of an inferential statistical procedure?
|
Student’s t distribution
|
|
|
What does a student’s t distribution involve?
|
Making predictions about a population based on a sample or samples from that population
|
|
|
What is a typical question we might ask by using a student’s t test?
|
may ask whether two different samples come from the same population.
|
|
|
What do we use to estimate μ based on sample data?
|
We use the confidence interval
|
|
|
What is a confidence interval?
|
A unit based range of scores w/ specific boundaries or confidence limits that should contain the population mean.
|
|
|
What is a point estimate?
|
When a single data point (e.g. the mean of a single sample) is used to estimate the population parameters.
|
|
|
What does it mean to refer to a 95% confidence interval regarding the population mean from which a sample was derived?
|
“We are 95% certain that μ is between so and so.”
|
|
|
When would s=o?
|
When 30 or more subjects are within a sample. If the sample is large (more than 30), then the standard deviation may be taken to approximate the standard deviation of the population.
|
|
|
What qualifies as being a large sample?
|
30 or more subjects
|
|
|
What can we use if s=o?
|
z-scores
|
|
|
Why is making s=o (standard deviation of a sample equally the standard deviation of the population) important?
|
it allows us to use the normal distribution in order to estimate the population mean.
|
|
|
What does estimating μ (population mean) w/ the sample mean always involve?
|
A degree of error
|
|
|
T or F: If a sample is large (having 30 or more subjects), then the degree of error is no longer a concern.
|
FALSE: Even with a large sample, there will be some degree of error.
|
|
|
What does “true” error mean?
|
The actual difference between the sample mean and population mean.
|
|
|
Can you compute a “true” error?
|
No, we cannot compute a real error, b/c we don’t know what μ (population mean) is—it can only be estimated.
|
|
|
What must we first do in order to generate confidence intervals based on clinical data?
|
We must first select a confidence level.
|
|
|
What do confidence levels refer to?
|
A probability, or area, centered about the mean of a normal distribution and are represented by areas under a curve.
|
|
|
What does the abbreviation of “c” mean?
|
Confidence levels
|
|
|
What does “c” range from?
|
0 to 1
|
|
|
What are the most common confidence levels used by statisticians?
|
90%, 95% and 99% of the area centered about the mean (c=0.90, 0.95 and 0.99)
|
|
|
What do confidence levels correspond to?
|
Pairs of z-scores
|
|
|
Areas below the normal curve and to the right of the mean can be easily translated into what?
|
Positive z-scores
|
|
|
What does the z-score table essentially correspond to w/ a particular confidence level?
|
The list of z-scores corresponds to the right half of a particular confidence level.
|
|
|
What comprises the total area of c?
|
For all confidence levels, the area under the left side of the mean is identical to the right under the curve and together they comprise the total area of c.
|
|
|
What is the absolute value of c referred to?
|
The critical value for a confidence level of c
|
|
|
What is necessary to determine confidence intervals?
|
The set of z-scores corresponding to a particular confidence level is necessary.
|
|
|
you chose c to be 95%, what would be its corresponding z score probability?
|
P=0.475 since it represents the right half of the confidence level in question. Take the positive and negative versions of this z score (±1.96)
|
|
|
If c=.90, what would our z score corresponding to a probability of?
|
P=0.45
|
|
|
If c=.99, what would our z score corresponding to a probability of?
|
P=0.495
|
|
|
If c=.80, what would our z score corresponding to a probability of?
|
P=0.40
|
|
|
What would be the critical value for a 95% confidence level?
|
Absolute z score = ± 1.96
|
|
|
What would be the critical value for a 90% confidence level?
|
Absolute z score = ± 1.645
|
|
|
What is the level of confidence for the critcal value of ± 2.58?
|
c=0.99 or 99%
|
|
|
What is the level of confidence for the critical value of ±1.44?
|
c=0.85 or 85%
|
|
|
What would be the critical value for a 80% confidence level?
|
Absolute z score = ± 1.28
|
|
|
What would be the critical value for c=0.75?
|
Absolute z score = ± 1.15
|
|
|
What equation represents the standard deviation of a sampling distribution?
|
σ = σ / √n
|
|
|
If the number of subjects increases then what happens to the standard deviation of a sampling distribution?
|
It decreases σ = σ / √n
|
|
|
What do we know zσ as?
|
E = error estimate
|
|
|
What is an error estimate (E)?
|
The difference b/w a randomly selected sample mean and the population mean (-E to +E).
|
|
|
What happens to the sampling distribution's standard deviation when the sample size gets smaller?
|
The sampling distribution's standard deviation gets larger.
|
|
|
What happens to the range when the standard distribution's standard deviation gets larger?
|
The range becomes wider.
|
|
|
What is the confidence level formula?
|
x (bar over) - E < μ < x (bar over) + E
|
|
|
What is needed in order for the standard deviation of a sample to approach that of the population?
|
A large sample size
|
|
|
What does a 95% confidence interval (c=0.95) technically mean?
|
95% of the time, we will draw a sample (of constant size) that results in a confidence interval containing the true population mean.
|
|
|
What are the 4 steps to estimate μ based on a large sample size?
|
1) select a confidence level (c)
2) obtain the z score corresponding to this level of probability 3) multiply the z score by the standard deviation of the sampling distribution (E) 4) add and subtract this value from the sample mean |
|
|
T or F: One can compute E using the standard normal (z) distribution w/ a sample size of 20 subjects.
|
FALSE: Sample sizes smaller than n=30, we cannot compute E using the standard normal (z) distribution.
|
|
|
Why can't we compute E using the standard normal (z) distribution w/ a sample size smaller than 30?
|
We cannot accurately approximate σ w/ s. We must have σ in order to be able to compute z score.
|
|
|
What test makes it possible to be able to approximate σ w/ s (compute E) in a small sample size (<30)?
|
Student's t distribution
|
|
|
What is the difference b/w z and t tests?
|
Able to compute z scores based on the sampling distribution when sample size is large (>= 30)
Std. normal distribution: z = x (bar) - μ / σ When sample size is small (n<30), we can't use std normal distribution, must use t scores t = x (bar) - μ / s s = s / √n |
|
|
As the sample gets smaller, what happens to the curve?
|
Curve gets flatter w/ more area under the tails
|
|
|
What does t distribution's shape depend on?
|
The sample size
|
|
|
T or F: There is a different curve for each sample size (numerous t distributions).
|
TRUE
|
|
|
How is the degrees of freedom denoted?
|
n-1
|
|
|
What happens to the degrees of freedom and curve when the sample size gets smaller?
|
The fewer the degrees of freedom and flatter the curve
|
|
|
What does a very flat sampling distribution indicate?
|
A high degree of sampling variability about the overall mean
|
|
|
T distributions are flatter than the standard normal (z) distribution, resulting in what?
|
Greater percentage of the total area being in the tails under the curve
|
|
|
What happens to the t value when the sample size decreases?
|
t value increases
|
|
|
What happens to the t value when the sample size increases?
|
t value decreases
|
|
|
A confidence interval based on t scores will get wider as the sample does what?
|
Gets smaller, holding all else constant
|
|
|
What is the formula for a confidence interval based on the t distribution?
|
P( -t < t < +t ) = c
|
|
|
If the t score increases, then what will happen to the confidence interval?
|
Confidence interval will expand and error (E) will increase
|
|
|
What is the formula for E using small sample sizes?
|
E = t s / √n
|
|
|
When can the t distribution only be used?
|
Only if we assume that the original x distribution is normal in shape
*Always make this assumption when using t test |
|
|
T or F: When large sample sizes are used, the sampling distribution will approach normality regardless of the original x distribution.
|
TRUE: this is the central limit theorem
|
|
|
To reject the null hypothesis is to what?
|
Accept the alternate hypothesis, which is open-ended by nature
|
|
|
T or F: We say "fail to reject" the null rather than "accept" the null.
|
TRUE
|
|
|
T or F: It is more conservative to state that not enough evidence is available to reject the null than to say the null is true.
|
TRUE
|
|
|
If we reject the null when it was actually true, we have committed what type of error?
|
Type I error (false +) alpha
|
|
|
If we fail to reject the null when it was actually false, we have committed what type of error?
|
Type II error (false -) beta
|
|
|
What is sensitivity?
|
Correctly indicating the presence of something; accuracy of the screening instrument (correct decision; no error)
|
|
|
Unless we either know or assume the value of μ, it is difficult to compute what?
|
Difficult to compute the probability of committing Type I or Type II error
|
|
|
We can compute the probability of a Type I error based on what assumption?
|
That the null hypothesis is true
|
|
|
How can you calculate the probability for a Type II error?
|
Can calculate by assuming that the null is false. Therefore, we have to assume another value for the null in order to calculate.
|
|
|
What is one way to reduce the possibility of Type I or II errors from occurring?
|
Increase sample size
|
|
|
Which is worse, type I or type II?
|
Neither is worse than the other
|
|
|
What is the probability of committing a Type I error referred to as?
|
alpha (level of significance)
|
|
|
When does Type I error occur?
|
When we incorrectly reject the null, based on the assumption null is true
|
|
|
If alpha = 0.01, then the tester wants to be at least 99% certain he/she is accurate in what?
|
Rejecting the null.
*Will reject only if their sample mean exceeds a particular distrance from μ as specified by alpha=0.01. |
|
|
If the probability of wrongly rejecting the null is alpha, then the probability of correctly failing to reject the null is what?
|
1-alpha (correct decision)
|
|
|
If we "wrongly" fail to reject the null, the Type II error is referred to as what?
|
beta
|
|
|
If the null is false, the probability of "correctly" rejecting the null must then be what?
|
1-beta (correct decision)
|
|
|
What is analogous to sensitivity?
|
1-beta
|
|
|
What is statistical power?
|
Correctly rejecting the null
*We want this power! |
|
|
What is statistical power equal to?
|
Probability (1-beta)
|
|
|
What are 3 variables that increase the "power" of a statistical test?
|
1) increasing sample size
2) increasing alpha (from 0.01 to 0.05) 3) selecting the "right" test |
|
|
T or F: Experiments are always designed w/ the intention of rejecting the null hypothesis.
|
FALSE: Experiements are usually, but not always designed to reject the null.
|
|
|
What reflects the chance that you will err in the process of rejecting the null hypothesis assuming the null is actually true.
|
Level of significance (alpha)
|
|
|
When is something considered statistically significant?
|
When observed sample mean as well as observed z score fall within the "rejection region" in a curve (less than alpha).
|
|
|
When would you have a one-tailed test?
|
When your alternate hypothesis is directional
|
|
|
Which is more common, directional or nondirectional alternate hypothesis?
|
Nondirectional
|
|
|
What kind of test would you use if your instrument of interest is still young in development? Why would you use this test?
|
Two-tailed test, b/c you are less likely to reject the null based on tails being cut in half.
|
|
|
What kind of test would you use if you were interested in using a nondirectinal alternative hypothesis?
|
Two-tailed test
|
|
|
What do you always compare the P value with no matter if it is one-tailed or two-tailed test?
|
Compare w/ alpha (level of significance)
|
|
|
P values falling short of the level of alpha are what?
|
Not statistically significant
|
