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77 Cards in this Set
- Front
- Back
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Which of these are typically used more? Population or Sample
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Sample: gathering data from an entire population is usually impractical
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What is assumed when collecting data for a sample
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That the sample is drawn from a population of INFINITE size
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What is the best way to achieve a representative sample
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By selecting the sample at random
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What are the different ways to do a random sampling
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1)Systematic sampling
2)stratified sampling |
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Why is it nearly impossible to do a random sampling
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Because the people still need to volunteer
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Definintion
Sampling Error |
The amount of error in estimating a population parameter (mean, SD, etc...) from a sample
-The mean of the sample might not be exactly equal to the population, so the difference is taken (Sampling error) |
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Abbriviation
SEM |
Standard Error of the Mean
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Formula
SEM = ? |
SEM = s/sq. rt. n
s = sample standard dev. n = sample size -It is the estimate of how much the sample mean differs from the population mean |
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When Sample Size increases, what happens to the Sampling Error
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it decreases
-the decrease is less noticable the larger the sample size gets |
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Definition
Research Hypothesis |
A prediction outcome based on theoretical consideration. An informed guess
-Also known as a Scientific Hypothesis |
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Definition
Null Hypothesis |
A statement about the numerical value of a unknown parameter
-Also known as a Statisical Hypothesis -The hypothesis of no difference between two groups |
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More info
Null Hypothesis |
-the hypothesis is often the reverse of what the experimenter actually believes
-Put forward to allow the data to contradict it |
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What is the purpose of the null hypothesis
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-It is important to be able to state with confidence that the effect was really due to chance
-Hypothesis tests starts with the assumption that the effect was due to chance, that there was no difference between means of the treatment group and control |
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What will the number of hypotheses depend on?
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The number of IV and DV
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With more than one IV?
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more than one hypothesis
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With more than one DV?
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Sometimes combined and sometimes stated separately
-Depends on the nature of the relationship between the DV's |
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What are some neccessities of a hypothesis in an experiment
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-elements being compared should be stated
-the hypothesis should clearly describe the relationship -hypothesis should be as concise as possible -should understand the relationship to be tested |
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What are some components of a good hypothesis
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-Concise
-Operational hunches can be emperically assessed -May be restated in null form -Stated in declarative form -Posit a relationship between variables -Reflect a theory/body of literature -Testable |
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What are some components of a bad hypothesis
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-long
-contradictory -illogical -uninterpretable -refer to "differences in the DV" -relationship and difference used in the same sentence |
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What are the characteristics of the Normal Curve
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-Unimodal
-Symmetrical -Mean, Median, Mode all the same score -Areas under the curve described by standard deviation -Tails approach, but never touch, horizontal axis (Asymptotic) |
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What is the most common standard score used with a normal distribution
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The Z-score
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Definition:
Z Score |
The standardized score used to produce a normal curve with mean=0, and s=1
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What does the Z score represent
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-A raw score expressed in standard deviation units
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Formula:
z = ? |
z =(X-Mean)/s
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What needs to be known for the raw score to be represented as a z-score
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the mean and standard deviation
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What can a z-score be used to describe for a normal distribution
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the percentage of the normal curve contained within 2 z-scores or a z-score and the mean
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+ or - 1 sd=
+ or - 2 sd= + or - 3 sd= |
68%
95% 99% |
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What is an example of a standard score
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a T score
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Formula:
Skewness (SK)= |
{n/[(n-1)(n-2)]}xsum of z^3
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Definition
Probability |
the porportion of the time you were successful
-Also known as the p value -statisical viewpoint: the likelihood that your results are due to chance |
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What is the range of probability
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0 to 1
0=no way you'll be successful 1=you will win every time -You can't have a negative probability |
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What is the probablility of an even?
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the number of favorable outcome divided by the total number of poddible outcomes
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What is a frequency distribution
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the total # of scores
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Definition:
Probability |
the number of times an event occurs of the total possible number of sample points
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Definition:
Sample Space |
The total possible sample points
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How does probability change
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based on how you state what you want your successes to be
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What formulas are used for determining sample spaces for statistical testing
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Permutation Formulas
Combination Formulas |
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What is used to compute the probability of a particular score to occure
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the z score and the corresponding area of the normal curve
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Definition
Conditional Probability |
The probability of an event given that another event has occured
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Definition
Permutation |
an arrangement of a set of objects in which their order is considered
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Formula
Permutation |
nPr = n!/(n-r)!
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Definition
Combinations |
A distinct set of objects in which the order is not considered
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Formula
Combinations |
nCr = n!/r!(n-r)!
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What are Confidence Intervals
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An actual estimate of the population mean and are based on a probability distribution
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95%CI = ?
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95%CI = Mean +or- 1.96(SEM)
SEM = s/sq.rt. n |
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When is it a Type I/Type II error
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Decision Accept Reject
Ho True: Correct TypeI Ho False: TypeII Correct |
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Type I error
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True Ho Rejected
A researcher reports a difference when there is none |
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What is the probability called when making a Type I error
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alpha level or level of significance
"the probability of observing that outcome is less than 5%" |
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What is the probability calles when making a Type II error
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Beta and is set by Power
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Formula
Power = ? |
Power = 1 - beta
typically set as 0.8 meaning that the researcher is willing to take a 20% chance of making a Type II error |
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How can a researcher control Power
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1)Increase the difference between Means
2)Decrease the Variance 3)Increase the Sample Size (easiet to control) |
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What will calculating the power allow us to do
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To determine the number of subjects needed to have adequate POWER so as to avoid the Type II error
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When is the power calculated
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Once the research is complete and be based on the data from the research
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What is the 7 step procedure for testing hypotheses with the one sampled z test
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1)State the null hypothesis
2)Do a one sample z test 3)state the level of significance for test 4)Write the tabled critical region value 5)Calculate 6)Compare calc. z score to critical z and make decision 7)state your conclusion |
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What does the one sample t test tell us
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if the smaple mean is significantly different than the population mean
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Why is the t distribution used (also called the Student's t distribution)
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it is rarely the case that all the sample data has a perfectly normal distribution
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What is the 7 step procedure of the one sampled t test
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the same as the z test but using the one sample t formula in the calculations
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What is assumed in the one-sampled t-test
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-Randomness
-Normally distributed -Interval/ratio type -mu is known |
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When is the Independent t-test (or the two-sample t-test) used
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when comparing 2 sample means rather than a sample mean to a population mean
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What is assumed in the one-sample z-test
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-Randomness
-Normally Distributed scores -Interval/ratio type -mu and sigma are know |
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what is assumed with an independent t-test
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-Randomness
-Normality -Interval/ratio data -2 independent group -10 or more participants per group -Equal variance |
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When do you have to worry about equal variances
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If the group sizes are not equal, then a test for the assumption of equal variances must be tested
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What is the test for equal variance called
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Levene's test
-if equal, avg. the variances for the groups -if unequal, the t calculated using seperate variances not avg. |
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What is the 7 step procedure for testing the hypothesis
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same as before only using the two-sample t-test when calculating
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Formula
CI for mean difference |
95%CI= mean1 - mean2 +or- (tabled critical t)(SED)
SED = sq.rt. [(s1^2/n1)+(s2^2/n2)] |
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Based on the CI, when would we reject/accept the null
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reject- the CI DOES NOT contain 0 in the range
accept- the CI DOES contain the 0 in the range |
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What is Effect size used for
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used before the study to estimate the sample size
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Effect Size
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-calculated to see the magnitude of the difference between 2 means after the study
-helps to estimate the meaningfulness of the treatment -used to describe the difference between the mean of the Exp. and the Cont. -Simply a z score (Mean_e - Mean_c)/s_c |
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in what units is the effect size expressed in
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standard deviation units
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What are the two ways of evaluating the effectiveness of a treatment
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1)Effect Size
2)Omega Squared |
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When should the Omega squared be calculated
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After a t-test if a significant difference is found
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Why is the Omega Squared calculated
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-Gives researchers and indication of how effective the treatment variable is
-Indicates the proportion of the variance in the dependent variable that is explained by the independent variable |
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What does the independent t-test assume about the groups
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that they are not related to each other in any way
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What is it meant by using related samples
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there is a single group of subjects with a dependant variable being measured on more than one occassion under more than one condition
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When do we use a paired t-test
(also known as the Dependent t-test) |
when the results of two different measurements depends on each other
-pairs of participants are matched on one or more characteristics and randomly placed into 2 groups -Twin studies |
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What are the 7 steps procedure for testing the hypothesis
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same as all the others but using a different formula
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What is assumed in the dependent t-test
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-Randomness
-normality -interval/ratio -two dependent samples of measures |
