T-tests Flashcards
What do statistical procedures allow?
–statistical procedures allow us to make probability statements about the likelihood of a given pattern occurring if the observed means were based on samples drawn randomly from the same population.
–If that likelihood is low (typically less than 1 in 20; i.e., 5%) then the observed difference is unlikely to occur if the samples were drawn from the same population.
what is one of the main approaches to statistical inference?
What does this involve?
significance testing:
given degree of confidence we can therefore reject the null hypothesis (Ho ; that ‘nothing has happened’ — i.e., that the manipulation of the independent variable has had no effect, or there is **no difference between groups). **
When is signifiance- testing/hypothesis -testing conducted
in experiments or studies or questionnaires
There is an alternative/ research hypothesis (difference between groups) and a null hypothesis (where there is no difference between groups)
do we always test the null hypothesis, if so why?
we always test the Null Hypothesis (Ho)
Therefore we usually aim to reject the null-hypothesis (Ho), and accept the alternative hypothesis (H1)
statement of what shall occur when observing random process
We need to assume that there is no difference between means until we are certain that some sort of difference exists.
what percentage is usually used to reject null hypothesis?
probability the two means coming from the same population is small enough to conclude the two means were unlikely to have been drawn from same population
5% or less
what happens after the null hypothesis is rejected?
significantly more likely for the mean to be drawn from the same population
what happpens if the likelihoodof the two means being different by chance alone is p>0.05
Therefore, fail to reject Ho and conclude that people are just as likely to consider a child running and a stroller as equally threatening to the driving situation
what are two type of errors made in significance testing?
Type I error is when you incorrectly reject Ho (i.e., say that there is a difference between the means when there really isn’t)
A Type II error is when you incorrectly not reject Ho (i.e., say that there is no difference between our means, when in fact there is)
How is t-test influenced by the research design?
If the variable is manipulated within-subjects, then you use a **within-subjects t-test. **
If the variable is manipulated between-subjects, then you use a between-subjects t-test.
when is the t-test used?
compare the means of 2 groups
compare the means of groups i.e., do the means of our experimental and control conditions differ?
when we compare means, we test the
we test the null-hypothesis (Ho), not the experimental hypothesis (H1)
t-distribution
sampling distrubition used to test the difference between means when population standard deviation is unknown
when is a within-subject t-tet used?
comparing means based on sets of data collected in pairs from same participant
independent variable manipulated within subjects
what happens when the value of t is very large?
(either positive or negative) then the probability that a random process could have produced a difference this large will be small
therefore, we will have low inferential uncertainty and be confident results are not due to random error or chance
what happens if t corresponds to small probability i.e one less than 5 in 1000?
since this is less than P<5% (1 in 200) chance, we reject the null hypothesis. results not due to chance or random error. students were not responding randomly
how to calculate degree of freedom? (df)
N (sample size)
N-1
t test
t(N-1) = x̄ - x/ sx / rootN
when gleaning on data that is different, what other question could be asked?
what can answer this?
whether the means are sufficiently different to infer thatthey reflect a real underlying difference
inferential statistics can tell how likely it is the two sets of repsonses are different if this would have been randomly drawn from same population
between subject t-test
compare means from different groups of participants
ise difference score D to compare difference between pairs of scores from same participant
hwow can you be confident the two conditions in two gropus reflect real underlying different between groups?
greater dispersion of two sets of responses
more data = more evidence
difference in means relative to amount of error is greater
Larger t-values,
small standard deviation
large sample
large difference between means
what is the alternative hypothesis H1
there is a significant difference in research.
two means are drawn from 2 different populations with different means
when there is high inferential uncertainty, do we reject or accept null hypothesis?
what about if there is low inferential uncertainty?
not reject null hypothesis (never entitled to accept null hypothesis because statistics cannot prove random process has yielded results)
We reject null hypothesis and accept alternative hypothesis that there is a difference
in the t-distribution, where does the rejection regions?
what do we conclude if t-value falls in the rejection region?
the small regions at the tail on both sides where few extreme t-values lie
reject null hypothesis because means are statisically different and accept alternative hypothesis i.e low inferential uncertainty
what are critical values?
the values that cuts off rejection region
what alpha level correponds to rejection region of 5%?
what do we say when t value exceeds critical value and falls in rejection region?
0.05
p< 0.05 (alpha level)
wat happpens if t-value falls outside rejection region?
null hypothesis is not rejected
what do we call when the obtained value of t fall in either tail? Test two possibilities (one has to be larger than other)
what happens when we hypothesize one mean will be greater than other?
two-tailed test
use one-tailed test / directional test by using single rejection region at end of distribution
when is one-tailed test used?
researchers know that one mean cannot possibly be larger than other
what is alpha level
largest propbability that researcher is prepared to accept in order to reject nul hypothesis
what happens when you compare t value (t-obtained), to the critical t-value and t value obtained is > critical t-value?
If tobt > tcrit, then reject Ho
what is correlation?
the relationship between two variables
what is a common way of displaying and observing correlation?
on a scatterplot graph
what does negative correlation look like?
what does no correlation look like
what are examples of correlation questions in experiments and surveys
–what is the relationship between the amount of physical contact and attraction),
but is also typically used in surveys — where you have multiple values of each variable (i.e., lots of different levels of contact (not just two) and lots of levels of attraction.
difference between positive and negative correlation
positive correlation: one value increases, the other increaes
negative correlation: one value increases, the other decreases
how do we tell from a scatterplot graph the relationship is stronger?
what inference can be made?
the less scattered the various points are from a straight line —
the more confidently we would be able to estimate or predict one variable on the basis of the other
to estimate from someone’s reaction time how much they had drunk, or to estimate from how much someone had drunk what their reaction time would be
most frequently, correlations are measured by? an example of this is
–correlation coefficients. and example of this is the Pearson product-moment correlation
what does value of r in pearson’s r reveal?
–The value of r indicates how strong a correlation is and it can vary between –1.00 and + 1.00.
what does r in pearson’s r show?
allow us to establish whether high scores on one variable are associated with high scores on the other, and low scores on one variable associated with low scores on the other
what does r=1 look like?
what can you say from r=1?
A correlation of r=1, also means that any one value is totally predictable from
Knowledge of the associated value of the other factor
what does r= .75 look like? and how often will you get this?
it is unlikely to obtain r=.75
what happens if you get r=-0.75? how unlikely?
very unlikely
what is a more likely r value one may obtain?
r = 0.45
if we obtain r =0.45, how certain are we?
We can still predict one variablefrom the other, but we become less certain
if we get r=0, or zero correlation, how likely is our prediciton?
it is impossible to
predict one variable from the other
when is correlational analysis appropriate?
Correlational analysis is only appropriate for linear relationships
when we are using 2 different populations, would displaying results on scatterplot graph be appropriate?
no as this would produce a very strong correlation, but it would be more appropriate to simply do a t-test, because we are clearly dealing with two different populations.
what can outliers do in a scatterplot graph?
Outliers can make a huge difference to your correlation coefficient (r)
it is easy to spot outliers in scatterplot graph
what is scatterplot graph useful for
in determining the nature of the relationship between variables
what is Ho in correlational analysis?
our hypothesis of no correlation.
what is the alternative hypothesis in correlational studies?
there is a positive/negative correlation between two variables
if r obt is > than r critical, what do we do?
reject Ho
what happens if r value obtained is < critical value?
retain Ho and conclude that there is not sufficiently strong evidence to indicate that there is a relationship between the variables.
how do u calculate degree of freedom in correlational studies?
df=N-2
steps of calculating r value
–Determine your Ho and H1
–Plot the data on a scatterplot to see what it looks like
–Calculate df (for a correlation, df=N-2)
–Calculate r (this can be done by hand or with a stats package)
–Compare calculated r with critical values for r (from back of book) for the df and the a you decide to use.
–If your obtained or calculated r is greater than your critical r, then reject Ho, and conclude that there is a significant correlation between your two variables.
what happens if r is very low?
s relationship may be statistically significant where r is very low
how may a researcher’s ability to detect correlation be limited?
give an example
if one (or both) of the variables whose relationship is being assessed has a low variance, or **restricted range. **
–extreme case, this is because if there is no variation at all in one variable (e.g., if all values of X are the same — say because all participants in a study consume the same amounts of alcohol) then necessarily r = 0.
what is an example of restricted range?
one or more subgroups demonstrate a ceiling effect, or a floor effect.
how does floor effect come about?
when there is small variance in samples eg. taking away good readers and poor readers perform poorly
what does ceiling effect look like?
good readers are performing at
ceiling level with little variability.
what happens if we take the group clustered at the ceiling away?
and correlation
drops
what is correlational fallacy?
by researchers is to assume that just because two variables are highly correlated, this means that one is responsible for variation in the other.
correlation does not equal correlation
why does correlation not equal to causation?
causal relationship between these variables may be reversed (aggressiveness may cause people to drink more), or the relationship may be the product of a third factor, like a person’s upbringing. third factor lead to increase in both variables rather than the variables having an influence on one another
what does hypothesis testing in correlation methodology consist of?
Ho: r = 0,
H1: r cannot equal to 0.
difference between t-test and correlational test
A t-test is a measure of whether the means of two samples may be due to chance. Whereas a correlational test is a measure of whether the linear relationship between two variables may be due to chance.
