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

by OC73429

School

University of GuelphDepartment

PsychologyCourse Code

PSYC 2040Professor

David StanleyStudy Guide

FinalThis

**preview**shows pages 1-3. to view the full**16 pages of the document.**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.

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

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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