CRIM 320 Lecture Notes - Lecture 8: Null Hypothesis, Statistical Hypothesis Testing, Dependent And Independent Variables

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limechimpanzee743

24 Nov 2016

School

Simon Fraser University

Department

Criminology

Course

CRIM 320

Professor

Steph Dawson

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Document Summary

Anova best thought of as an extension of t tests. Like t tests, anova starts by comparing differences in means between groups. Comparing group means of an outcome variable of interest to determine these means are significantly different from each other. Comparing group means when we have more than 2 independent groups. Categories on a variable, 3 or more groups. Spread of the data around the mean of each group. Each group will have their own mean score on the outcome. How much our group means vary from each other the logic of anova. Based on these two estimates of variability, draw conclusions about the population means what is the purpose of different categories? within-group variability - spread around the mean. Group 1 is the most spread out around the mean (most difference) Group 2 is small distribution, more clustered around the mean between-group variability - each group will have a mean score.

Related Questions

QUESTION 1What is the purpose of post hoc tests? Under what circumstances are post hoc tests not needed or appropriate?

a. Under what circumstances is ANOVA a more appropriate statistical technique to use than a t test for independent samples? Please provide an example(s) to support your answer. (2 marks)

b. (2 marks)

c. In testing the difference between group means, how are between group and within group variability related to each other? Provide an example to support your answer. (2 marks)

QUESTION 2

a. If a two-factor ANOVA results in a significant main effect for factor A and a significant AxB interaction, explain why you should be cautious in interpreting the effect of factor A. (1 mark)

b. For the following research situations what would be your main effects and interaction effect. If there was a significant interaction effect what would that mean? (please be as clear as possible in your explanation):

A researcher hypothesizes that the effect of alcohol consumption on one’s motor skills depends on the person’s weight (underweight, normal, overweight), but that this may differ for men versus women. (2 marks)
A teacher is interested in seeing how attending class and reading the assigned chapters is related to her students’ performance on tests. She assesses each student in terms of how often they attend class (rarely, sometimes, regularly) and how often they read the assigned chapters (rarely, sometimes, regularly). (2 marks)

QUESTION 3

Ethel is interested in two methods of note-taking strategies and the effect of these strategies on the overall GPAs of college freshmen. She believes that men would benefit most from Method 1, while women would benefit most from Method 2. After obtaining 30 men and 30 women volunteers in freshmen orientation, she randomly assigns 10 men and 10 women to Method 1, 10 men and 10 women to Method 2, and 10 men and 10 women to a control condition. During the first month of the spring semester individuals in the two note-taking method groups receive daily instruction on the particular note-taking method to which they were assigned. The control group receives no note-taking instruction. Fall and spring GPAs for all participants are recorded and a score that is the difference between the spring and fall semester GPAs is calculated.

Below are the results from running a two-way ANOVA. Please answer the following:

What is the dependent variable? (0.5 marks)
What are the independent variables (factors)? (0.5 marks)
What is the research question(s) being addressed? (1 mark)
What does the descriptive statistics (graphical) tell us about the effects under study?

(1 mark)
What assumptions are being tested in the R output? Are these assumptions met? Please

provide statistical evidence. (2 marks)
What effects are being tested in the R output? (1 mark)
What does output from the ANOVA table tell us? (1 mark)
What type of follow-up analyses was conducted and why? Please interpret. (2 marks)

: Men
: Method1

      median
coef.var

0.300

0.469

: Women
: Method1

      median
coef.var

0.150

0.496

: Men
: Method2

      median
coef.var

0.275

0.027

: Women
: Method2

      median
coef.var

0.600

0.629

: Men
: Control

      median
coef.var

0.175

mean 0.335

mean 0.170

mean 0.305

mean 0.640

mean 0.165

mean 0.105

skew.2SE
   0.408

SE.mean CI.mean.0.95

var 0.052

var 0.033

var 0.037

var 0.032

var 0.022

var 0.021

normtest.W
     0.936

std.dev
  0.229

0.682
    skewness

1.076
    skewness

0.630
    skewness

0.072

SE.mean CI.mean.0.95

normtest.p 0.830 -----------------------------------------------------------------------------

skew.2SE
   0.342

kurtosis
  -0.645

kurt.2SE
  -0.242

normtest.W
     0.964

0.058

SE.mean CI.mean.0.95

std.dev
  0.183

normtest.p 0.096 -----------------------------------------------------------------------------

skew.2SE
   0.361

kurtosis
  -1.363

kurt.2SE
  -0.511

normtest.W
     0.869

0.061

SE.mean CI.mean.0.95

std.dev
  0.192

normtest.p 0.857 -----------------------------------------------------------------------------

0.278
    skewness

0.904
    skewness

skew.2SE
  -0.124

kurtosis
  -1.096

kurt.2SE
  -0.411

normtest.W
     0.979

-0.171

: Women
: Control

      median
coef.var

0.100

1.392
    skewness

0.560

0.046

kurtosis
  -0.759

0.105

kurt.2SE
  -0.284

   std.dev
     0.146

normtest.p
     0.512

skew.2SE
   0.019

kurtosis
  -1.443

kurt.2SE
  -0.541

normtest.W
     0.967

skew.2SE
   0.458

kurtosis
  -0.770

kurt.2SE
  -0.289

normtest.W
     0.906

0.056

SE.mean CI.mean.0.95

std.dev
  0.178

normtest.p 0.254 -----------------------------------------------------------------------------

                                                                      std.dev
                                                                        0.149

normtest.p 0.958 -----------------------------------------------------------------------------

0.047

SE.mean CI.mean.0.95

0.164

0.131

0.137

0.127

0.107

> leveneTest(gpa$gpaimpr~gpa$gender, data=gpa,center=mean)

Levene's Test for Homogeneity of Variance (center = mean) Df F value Pr(>F)

group 1 7.09 0.01* 58

---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 > leveneTest(gpa$gpaimpr~method, data=gpa,center=mean) Levene's Test for Homogeneity of Variance (center = mean)

      Df F value Pr(>F)
group  2    1.94   0.15

> #running Levene's test for assumption of HOV (INTERACTION EFFECT)
> leveneTest(gpa$gpaimpr, interaction(gpa$gender,gpa$method),center=mean) Levene's Test for Homogeneity of Variance (center = mean)

      Df F value Pr(>F)
group  5    0.57   0.72

Df Sum Sq Mean Sq F value Pr(>F) gender 1 0.020 0.020 0.61 0.43753

method 2 1.174 0.587 17.81 1.1e-06 *** gender:method 2 0.695 0.348 10.54 0.00014 *** Residuals 54 1.780 0.033
---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

gender        0.0055
method        0.3200
gender:method 0.1894

0.011
0.397
0.281

eta.sq eta.sq.part

#selecting only Method1, run ANOVA, then follow-up tests

  Tukey multiple comparisons of means
    95% family-wise confidence level

Fit: aov(formula = gpaimpr ~ gender, data = gpaMethod1)
$`gender`
Women-Men -0.165 -0.3594851  0.02948506    0.0915581

diff        lwr        upr     p adj

#selecting only Method2, run ANOVA, then follow-up tests

  Tukey multiple comparisons of means
    95% family-wise confidence level

Fit: aov(formula = gpaimpr ~ gender, data = gpaMethod2)
$`gender`
Women-Men 0.335 0.161153 0.508847   0.000754

diff      lwr      upr    p adj

aquamarineox434

Chose the correct answers on one through 15(plese help)

1.A research group hypothesizes that successful infection by HIVdepends upon the expression of FSH3, a human gene. They overexpressthis gene in T cells (Which HIV normally infects) so that FSH3protein levels are very high in these cells. In other T-cells, theymutate FSH3 so that none of its encoded protein is made. They thenmeasure HIV infection rate in the control, overexpression, andmutant T cells. The three cultures are otherwise grown in the sameway.

What is the independent variable(s) in this experiment? (Selectall correct answers)

		FSH3 protein levels
		The medium in which cells are grown
		The temperature at which cells are grown
		HIV resistance of cells

Question 2

Which arises from an error in a measurement or observation?

		Technical variability
		Biological variability
		Standard error
		Standard deviation

Question 3

Use the following description of an experiment to answer thenext question.

A research group hypothesizes that successful infection by HIVdepends upon the expression of FSH3, a human gene. They overexpressthis gene in T cells (Which HIV normally infects) so that FSH3protein levels are very high in these cells. In other T-cells, theymutate FSH3 so that none of its encoded protein is made. They thenmeasure HIV infection rate in the control, overexpression, andmutant T cells. The three cultures are otherwise grown in the sameway.

What is the control group(s) in this experiment? (Select allcorrect answers)

		The unaltered T cells
		The medium in which cells are grown
		The T cells in which FSH3 is mutated
		The T cells overexpressing FSH3

Question 4

How many of the following statements are true?

I. All papers have an abstract, methods, results, and discussionsection

II. The methods always follows the introduction

		0
		2
		1

Question 5

If scientific convention states that when a P value of less than0.05 is considered significant (in other words, the two groupsbeing measured are actually different), this means that: (Selectall correct answers)

		If you were to repeat the experiment 100 times, there would notbe a significant difference between the groups in 5 of theexperiments
		95% of all conclusions that state two groups are not differentbased on a 0.5% p-value threshold are false negatives
		The groups are actually not different from each other 95% of thetime
		5% of all conclusions that state two groups are different basedon a 0.5% p-value threshold are false positives

What information is typically found in the introduction sectionof a paper? (Select all that apply)

		The dependent and independent variables within the study
		Which areas of the field are not well understood and whatquestion the study addresses
		How the main question of the paper is related to other researchin the field.
		How previous work forms the basis for the current study
		The purpose of the study
		Details of the approaches used
		A summary of relevant related studies

Question 7

How can you judge for yourself whether the conclusions reachedin a paper are valid? (Select all that apply)

		Read papers of other authors studying the same question or areaof inquiry
		Determine if each hypothesis is supported by different types ofevidence/approaches.
		Consider closely whether the data actually both addresses andsupports the authorâs hypothesis.
		Examine the amount of data in the paper, and how long the paperis.
		Whether the authors find a mechanism, or exactly how on variableaffects another.
		Interpret the data for yourself without looking the discussion,then compare your interpretations to that of the authorâs.

Question 8

Where can you usually find the institutional affiliations (wherethey work) of the authors?

		Within the discussion
		In the acknowledgements section
		Below the authors list
		This is not usually included in papers

Question 9

Other than publishing primary research articles, what is themain way scientists disseminate their results?

		Lab meetings
		Personal correspondence
		Conference seminars
		Public lectures

Question 10

Use the following description of an experiment to answer thenext question.

What is the experimental group(s) in this experiment? (Selectall correct answers)

		Each group is its own control
		The T cells overexpressing FSH3
		The T cells in which FSH3 is mutated
		The unaltered T cells

grayclam130

For years we have been able to analyze the fossils of extincthumans like those of Neanderthals. Their bones gave us clues to howthey looked, how they lived, and how they might be related to us.In the last few years, we have been able to get a better view intothese extinct species and their relationship to our species. Thanksto next generation genomic sequencing technologies, we have beenable to obtain genetic data on Neanderthals, Denisovans and othersthat have allowed us to make direct comparisons between our speciesand theirs. In addition, we have been able to observe the presenceof DNA from these extinct species within our own genomes which tellus that we had kids with these now extinct humans.

If we take Neanderthal DNA as an example, we find that we share99.5 percent of our DNA with them. Which means that we andNeanderthals were separated from each other for more than 500,000years. This also means that we were genetically similar enough tobe able to have offspring with each other. We see evidence of thisgenetic introgression between us and Neanderthals when we look atour DNA. Interestingly, if we obtain one thousand DNA samples fromGrossmont College students, we estimate that we would be able toextract at least 20% of the Neanderthal genome from them. Thismeans that 20% of our collective nucleotide sequences are sharedwith Neanderthals but this doesnât mean that 20% of our genes areNeanderthal specific genes. Of the twenty-one thousand genes thatNeanderthals had, only a few dozen of their genes survive withinour genome. The same holds true for Denisovans. What is moreinteresting is that older versions of ourselves have a tendency tohave higher levels of DNA from extinct humans compared toourselves. In other words, over the course of thousands of years wehave been slowly weeding out the DNA of the other humans from ourgenome in favor of our genes.

One basic question that we might like to ask is why have we beenlosing Neanderthal and Denisovan genes over time? Also, why do westill have a significant amount of DNA segments that donât seem tobe going anywhere? The answer to this has to do with selection.

The answer to the first part of the question has to do with thefact that we were not fully genetically compatible with the otherhuman species to begin with. Basically, to have had Neanderthal orDenisovan genes in the past meant that an individual's level offitness was reduced. To get rid of their genes in favor of our ownwould mean that the relative fitness of individuals would increaseovertime.

The answer to the second question has to do with the fact thatDNA segments from Neanderthals and Denisovans that did not code forproteins remained because there was little selective pressureagainst them. As far as genes are concerned, the only Neanderthaland Denisovan genes that remain only exist because they had aselective advantage or at least have been neutral to ourspecies.

DNA segments that that were neutral or that had a selectiveadvantage, whether genes or not, simply remained because they wereadvantages or there was little selective pressure against them.

Your task for this week is to look for information about oneNeanderthal or Denisovan gene that survive within our species andto tell me what function that gene has and how that gene mayincrease the fitness of modern human populations.

In your post, discussONE Neanderthal orDenisovan gene that is currently found within our species.
- Tell us about the gene and its function. Explain what it doesfor us. (Make sure you give a citation.)
- Explain in your own words any possible advantages that yourNeanderthal or Denisovan gene might have. Make sure you give ininformed opinion that is grounded in your research.

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CRIM 320 Lecture Notes - Lecture 8: Null Hypothesis, Statistical Hypothesis Testing, Dependent And Independent Variables

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