Most research studies compare how many sets of data?
two (or more) sets
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between-subjects design
Data from two completely different
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a within-subjects or repeated-measures design
Data from the same or related participant group(s)
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Seek to prove null or alt
Null
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Null there is or is not significant difference
There is
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Estimated standard error
Measure of standard or average distance between sample statistic (M1-M2) and the population parameter
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Pooled variance
Provides an unbiased basis for calculating standard error, correcting the bias in the standard error is to combine the two sample variances into a single value
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Degrees of freedom for t test w/ two samples
Just add them both
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Steps for independent hypothesis
• State the hypothesis and select an alpha level • Locate the critical region • Collect data & compute the test statistic • Make a decision
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When to use one tail
When you know the direction
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Assumptions underlying indp. measures tests
• Observations within each sample must be independent. • The two populations must be normal (always assume normality unless told otherwise) • The two populations must have equal variances (called homogeneity of variance)
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How to test for homogeneity of variance
Use F max test
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Do you want significancy with f max test?
No
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Small value (1.00) indicates similar or different sample variances?
Similar
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If the null hypothesis is rejected the effect size should be determined by using either
Cohen's d/percentage of variance explained
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What is used to estimate the population mean difference?
M1-m2
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Estimation can provide an indication of
Size of treatment effect/significance of effect
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If interval contains 0
Not a significant effect
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Does not contain 0
Was significant
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Large variance leads to large/smaller error and what t value?
Larger error
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Larger samples produce larger/smaller error and what t values? Smaller error
larger t
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What does cohen d need to be significant?
0.5
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Variance accounted for that is best for studies
15-20% is the best
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Hypothesis testing definition
a statistical method that uses sample data to evaluate the validity of a hypothesis about a population- most commonly used w/ inferential stats
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process of hypothesis test
state hypothesis
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steps of hypothesis test
state hypothesis/ set criteria/ collect data
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symbol for null hypothesis
HO
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Null hypothesis definition
states that the treatment has no effect: there is no change
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alternative hypothesis symbol
h1
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alternative hyp definition
states that there is a change
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alpha level
α or significance level, a probability value used to define “very unlikely” outcomes.
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critical regions consist of
extreme scores, sample outcomes that are very unlikely
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how are boundaries of critical regions determined
by probility set by the alpha level
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data is always collected after...
hypothesis is stated and establishing decision criteria
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z score is the difference between what
the observed sample mean and the hypothesized population mean divided by the standard error of the mean
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if sample stat is located in critical region
null hypothesis is rejected (above 1.96)
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if sample is not located in critical region
researcher fails to reject null hypothesis
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hypothesis testing is a what process?
inferential (makes a generalization)
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type 1 errors
Researcher rejects a null hypothesis (H0) that is actually true. Researcher concludes that a treatment has an effect when it has none
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What is the probability that test will have type 1 error?
Alpha level
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Type 2 error
Harder to identify Researcher fails to reject a null hypothesis that is actually false. Researcher has failed to detect a real treatment effect.
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When is a result significant
if it is very unlikely to occur when the null hypothesis is true
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larger discrepancies mean
larger z scores
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more variability means
larger standard error
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larger n or scores in sample
smaller standard error
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assumption of hyp testing w/ z scores
Random sampling Independent observation Value of σ is not changed by the treatment Normally distributed sampling distribution
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Standard hyp is one or two tailed?
Two tailed
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Directional or one tailed test
the researcher specifies either an increase or a decrease in the population mean as a consequence of the treatment.
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one tailed rejects null with small or large difference
small provided the difference is in the predicted direction
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two tailed tests need small or large difference
large regardless of direction of difference
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should one or two tailed test be used
two unless there is a strong directional prediction
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effect size measures
the absolute magnitude of a treatment effect
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cohen's d measures
effect size simply and directly in a standardized way
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standard error describes
how much difference is reasonable to expect between population and sample mean
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cons of using z scores
The z-score requires more information than researchers typically have available Requires knowledge of the population standard deviation σ Researchers usually have only the sample data available
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What can t b considered in relation to z?
The approximate z
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The difference between the t test and z test?
Estimated standard error (sM) is used as in place of the real standard error when the value of σM is unknown
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Estimated standard error
used as estimate of the real standard error when the value of σM is unknown
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when computing the sample variance what do you need to do first?
calculate sample mean
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t distribution
• Family of distributions
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How does t distribution compare to normal dist.?
It's flatter more spread out and has more variability ("fatter tails") in t distribution
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Assumptions of t test
• Values in the sample are independent observations. • The population sampled must be normal • With large samples
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Larger the sample effect on error
Makes it smaller
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Larger the variance effect on error
Makes it larager
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Hypothesis tests determines what about the treatment effect?
If it's greater than chance
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How does cohen's d differ from t test to z test?
In t test it is estimated
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Percentage of variance explained
Determining the amount of variability in scores explained by the treatment effect is an alternative method for measuring effect size
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How to know if you have small/medium/large effect
Small=0.01 Medium=0.09 Large=0.25
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Factors affecting width of confidence interval
• Confidence level desired • More confidence desired increases interval width • Less confidence acceptable decreases interval width • Sample size • Larger sample smaller SE smaller interval • Smaller sample larger SE larger interval
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In research is 1 or 2 tailed z test used more often?
2 tailed
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Analysis of variance (ANOVA) definition
Used to evaluate mean differences between two or more treatments Uses sample data as basis for drawing general conclusions about populations
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Advantage of ANOVA over a t test
can be used to compare more than two treatments at the same time (simultaneously) between variance
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low dose has more or less variance
more variance (more variety)
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high dose (maximum dose)
less variance (less variety)
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Factor
The independent (or quasi-independent) variable that designates the groups being compared
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Levels
Individual conditions or values that make up a factor
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Factorial design
A study that combines two or more factors
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Null hypothesis
the level or value on the factor does not affect the dependent variable In the population this is equivalent to saying that the group means do not differ from each other
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Benefit of using ANOVA
ANOVA evaluates all mean differences simultaneously with one test—regardless of the number of means—and thereby avoids the problem of inflated experimentwise alpha
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F ratio
Based on variance instead of sample means
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Between-treatments variance
Variability results from general differences between the treatment conditions Variance between treatments measures differences among sample means
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Within-treatments variance
Variability within each sample Individual scores are not the same within each sample
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Sources of variability between treatments
Systematic differences caused by treatments Random
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Source of variability within treatments
No systematic differences related to treatment groups occur within each group Random, unsystematic difference (individual)
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In f ratio if h1 is true
Size of treatment effect is more than 0 F is noticeably larger than 1.00
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Denominator of the F-ratio is called
error term
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K
Number of treatment conditions (groups)
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n1
n2
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N
Total number of scores T
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GT
Grand total of all scores in study
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What will value of f be if null hypothesis is true
1.00
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F ratios are always -/+?
+
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Measuring effect size for anova
Compute percentage of variance accounted for by the treatment conditions
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