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.**Research Statistics Lecture Summaries

Lecture 1: Introduction

- The purpose of statistics is to make a conclusion about a large group of people (a

population) from a small group of people (a sample).

Describing the Population

- Population mean is an average

oIdeally we would like to be able to describe the population using this

population mean

oHowever this is impractical, we cannot survey everyone

oThis is why we use a sample mean to estimate the population mean

o We are usually interested in a sample only to the extent that it tells us

something about the population

- Population standard deviation

oThe larger the SD is, the larger the differences

oIt is used to describe how accurate the mean is in describing everyone in

the population

oIt is “roughly, on average, the amount that a score differs from the

population mean”

- Standard error of the mean

oRoughly, on average, the amount that sample means differ from the

population mean due to the effects of random sampling

oIt is the amount of variability in sample means that we would expect if we

used random sampling

oDescribes the variability

oLarger sample sizes result in small standard errors, that means there is less

variability

- Estimated Standard deviation

oRoughly, on average, the amount that a score differs from the sample

mean

oBased on our single sample, this is our best guess of what the population

standard deviation is

- Estimated standard error of the mean

oRoughly, on average, the amount that a sample means differ from the

population mean

oBased on our single sample, this is our best guess of what the Standard

Error of sample means would be with repeated sampling

oYou can also think of SE based on your sample as our best guess of the

amount of variability in sample means that we would expect if we used

random sampling

oNote that when researchers say “Standard Error‟, they are usually

referring to “Estimated Standard Error”

oRatios are extremely important way of comparing 2 things in statistics

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- We typically based the denominator on standard error (standard error squared) in

these ratios

Central Limit Theorem

- Regardless of the shape of the population distribution, the distribution of sample

means will

o Always be roughly normal

oHave a standard error equal to the population standard deviation divided

by the square root of sample size

Lecture 2: T-tests

1. Single-Sample T-test

- The focus is on 1 population

Communicate Findings

I examined the intelligence quotient (IQ) of University of Guelph graduate students using

a random sample of 200 students. A two-tailed single-sample t-test revealed that the

average IQ of University of Guelph graduate students (M = 120.53, SE = .77) was

significantly higher, t(199) = 26.60, p < .001, than 100. Thus, University of Guelph

graduate students may be smarter than the average person.

- Identify

oWho the participants are

oHow many

oDependent variable (IQ)

oType of test (1 or 2 tail)

oSignificant or non-significant

oHigher/lower

oRandom sampling

op or ns

Hypothesis

Null Hypothesis: H0: μ = 100

oAny difference between the sample mean and the hypothesized population

mean is simply due to random sampling error

oAssuming alpha is .05, p > .05 is non-significant and just due to random

sampling

- Alternative Hypothesis: H1: μ „ 100

oIf you reject the null hypothesis, you conclude that the alternative

hypothesis is correct

oSpecifically you conclude that the difference between the sample mean

and the hypothesized population mean is so large, that it could not be due

to random sampling

oAssuming alpha is .05, p < .05 is significant and more than just random

sampling o We reject it if the p-value is less than 5% chance

Assumptions

1. Random sampling from a clearly defined population

2. Population values are normally distributed

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- P-value indicates the probability that you would obtain a t-value as extreme as you did

when the population mean is the hypothesized one

2. Independent-Groups T-test

- The focus is on 1 independent variable with 2 levels/groups and no repeated measures

Communicate findings

I examined the extent to which University (University of Waterloo, University of Guelph)

influenced ratings of movie enjoyment using a two-tailed independent-groups t-test. The

homogeneity of variance assumptions was violated, Levene’s F(1, 98) = 5.21, p < .05,

therefore I used the t-test formula based on separate variance estimates (rather than

pooled). University of Guelph students (M = 82.98, SE = .44) rated the movie

significantly higher t(89) = 2.45, p <.05, Cohen’s d = .49, than University of Waterloo

students (M = 84.80, SE = .60). Moreover, this difference can be considered medium,

using Cohen’s standards. Thus, University of Guelph students enjoyed the movie more

than University of Waterloo Students

- Identify

oIndependent/dependent variables

oIndicate the name of the test

oReport the mean and standard error

oReport tests of assumptions

oReport primary test results and effect sizes

oUse the word “significant‟ and “non-significant‟ where appropriate

oUse ns, p < .05, p < .01, p < .001 as needed

oConcluding sentence for a general audience

Hypothesis

- Null Hypothesis: H0: m

Guelph = m

Waterloo

oThe assumption is that the mean of Group 1 is the same as the mean of

Group 2

oTherefore, any differences between the group’s means is due to random

sampling error

oAssuming alpha is .05, p > .05 is non-significant and just due to random

sampling

- Alternative Hypothesis: H1: m

Guelph „ m

Waterloo.

oIf you reject the null hypothesis, you conclude that the alternative

hypothesis is correct

oSpecifically you conclude that the sample means are so different that it

could not be due to random sampling

oAssuming alpha is .05, p < .05 is significant and more than just random

sampling o We reject it if the p-value is less than 5% chance

Assumptions

1. Random sampling from 2 clearly defined populations

2. Population values are normally distributed

3. Variances of the 2 populations are the same, known as the homogeneity of

variance

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