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Final

PSYC 2040 Study Guide - Final Guide: John Tukey, Type I And Type Ii Errors, Central Limit Theorem


Department
Psychology
Course Code
PSYC 2040
Professor
David Stanley
Study Guide
Final

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Introduction
Statistic - a number that describes the sample
Parameter - a number that describes the population
Unbiased Estimate - the mean of all possible values of that
statistic is equal to the parameter
Biased Estimate - the mean of all possible values of that
statistic is not equal to the parameter
Population Standard Deviation - the amount that a score differs
from the population mean
Standard Error of the Mean - the amount that sample means differ
from the population mean due to the effects of random sampling,
larger sample sizes result in smaller standard errors
Degrees of Freedom - the number of values in a data set that are
allowed to vary, the first value is the between groups degrees
of freedom while the second is the within groups degrees of
freedom
Central Limit Theorem - regardless of the shape of the
population distribution, the distribution of the sample means
will always be normal as long as we have large sample sizes and
the standard error will equal the population standard deviation
divided by the square root of the sample size
Statistics is always about ratios, more specifically:


Single Sample T-tests
We use this when we are comparing one mean to another number.
Null Hypothesis: μ = 15; any difference between the sample mean
and the hypothesized population mean is due to random sampling.
Alternative Hypothesis: μ ≠ 15; any difference between the sample
mean and the hypothesized population mean is too large to be due
to random sampling alone therefore they must be different.
We make two assumptions when conducting a simple t-test: (a)
that there was random sampling from the population and (b) that
the population values are normally distributed.

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Our p-value tells us the probability of you finding the t-value
you did when the population mean is equal to the hypothesized
population mean.
When p = .00, there is a 0% chance of obtaining that t-
value due to random sampling when a population mean is
equal to the hypothesized one. Therefore we reject the null
hypothesis because there is less than a 5% chance of
getting that t-value.
We have to be careful because sometimes our alternative
hypothesis might be that it is greater than or less than a
value (one tailed test) while SPSS gives p-values for 2-
tailed tests. This means we would have to divide the p-
value by two to get the p-value for a one sided test.
The t-value tells you that the difference between the
hypothesized population mean and the real population mean is ___
bigger than you would expect if there was only random sampling
effects involved. Typically, the larger the t-value, the smaller
the p-value and this hold for the other test statistics as well.
The degrees of freedom are calculated by: number of participants
- number of groups.
Independent Samples T-test
We do this when we have two populations and we are comparing
their means. The difference between two sample means is used to
estimate the difference between the two population means.
Null Hypothesis: μ1 = μ2; assume that mean on dependent variable
for population 1 is equal to mean on dependent variable for
population 2. Any difference seen between the two sample means
is due to random sampling alone.
Alternative Hypothesis: μ1 μ2; the difference we see with the
sample means is too large to be due to just random sampling.
Conclude that mean on dependent variable for population 1 is
different for mean on dependent variable for population 2.
We make three assumptions when conducting an independent samples
t-test: (a) that there was random sampling of the two
populations, (b) that the population values are normally
In conclusion, we do a single sample t-test when there is only one population and
it is being compared to a hypothesized mean. There is 1 independent variable
with 2 levels, which are categorical and 1 dependent variable that is continuous.

Only pages 1-3 are available for preview. Some parts have been intentionally blurred.

distributed and (c) that the variances of the two populations
are the same.
Since we are dealing with two populations we have to conduct a
Levene’s test for homogeneity of variance. This is because when
we conduct an F- or t-test we are looking to see if the between
group variance is larger than the within groups variance and to
do this ratio we can only include one within groups variance on
the bottom. Therefore it becomes:
  
    

We need to conduct a Levene‟s test to make sure it is okay to
use either or as the denominator. Our null hypothesis is that
the two variances are equal; σ1 = σ2, while our alternative
hypothesis is that the two variances are not equal; σ1 σ2. An
independent samples t-test is the only time when we can continue
if the Levene‟s test is significant. In any other test if the
Levene‟s test is significant we cannot go any further in our
analysis.
Depending on if the Levene‟s test is significant or not we use a
different line. If significant we use the “equal variances not
assumed” line, if non-significant we use the “equal variances
assumed” line. The degrees of freedom for Levene‟s test are:
(number of groups -1, number of participants - number of
groups).
The degrees of freedom are: number of participants - number of
groups as long as Levene‟s test is non-significant.
Effect size tells us how big the difference is between the
populations. We use Cohen‟s d. Our p-value only tells us that
there is a difference and only allows you to reject the null
hypothesis for d-values greater than zero (there is a
difference). P-values do not tell us about the size of the
effect, that is what reporting an effect size does. If this is
not give on output do not report it.
Small = .20
Medium = .50
Large = .80
In conclusion, we do an independent sample t-test when there are two
populations that we are comparing. There is 1 independent variable with 2
levels, which are categorical and 1 dependent variable that is continuous.
Independent samples t-test is the only time we can continue when Levene’s test
is significant.
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