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ANalysis Of VAriance

A statistical adventure guided by Laurel and Savannah

Savannah Whitington

on 4 October 2012

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Transcript of ANalysis Of VAriance

An extended examination ANalysis Of VAriance ANOVA provides an inferential statistical test to
compare the means of 2 or more independent groups
on the dependent variable. Basically, we will be able to determine if any of several means is different from each other. What is ANOVA? One-way (single factor) and two-way (factorial) ANOVA allow for the comparison of the means of 2 or more groups, therefore these tests help us to avoid committing statistical sin, or the increased chance of type 1 error attributed to doing multiple t-tests. The 2 Types of ANOVA and Why
we need them... 1. Observations are independent

2. Variance on dependent variable are equal across groups

3. Dependent variable is normally distributed for each group Assumptions of the ANOVA The output consists of 6 major sections. Interpreting SPSS Test Output:
Getting Personal with your Single Factor ANOVA Data 1. Descriptive Table: provides the sample size, mean, standard deviation, minimum, maximum, standard error, and confidence interval for each level of the independent variable
2. Test of Homogeneity of Variances: the column labeled Sig. is the p value. If the p value < α level for this test, then you can reject the H0 that the variances are equal. If the p value > α level for this test, then we fail to reject H0, thus increasing our confidence that the variances are equal (the homogeneity of variance assumption has been met). 3. ANOVA table: 6 columns provide (1) unlabeled source of variance, (2) Sum of Squares, (3) Degrees of Freedom, (4) Mean Squares/ estimates of variance, (5) F ratio, and (6) Sig. of F ratio/ p value 4. The Multiple Comparisons output gives the results of the Post-Hoc tests that you requested from SPSS. We will be using the Tukey HSD and Games-Howell tests. When the F ratio is statistically significant, we need to look at the multiple comparisons output. The output includes a separate row for each level of the independent variable. 5. Summary table for Multiple Comparisons tests 6. The final part of the SPSS output is a graph showing the dependent variable on the Y axis and the independent variable on the X axis Types of error: type 1 vs type 2

Possible sources of error To err is human: possible error in ANOVA Type 1 is a false positive error -a null hypothesis is true but has been wrongly rejected.

Type II is a false negative error -a null hypothesis is false yet fails to be rejected You're all humans -Can anyone supply a possible source of error?!? Formal Features in Children’s Science Television:
Sound Effects, Visual Pace, and Topic Shifts

Boiarsky, G., Long, M., & Thayer, G. (1999) Article 1 Discussion Certain formal features reliably draw
children’s attention to the TV screen
e.g. sound-effects, women’s voices, animation, and rapid
pace. The driving concept behind the research was
that formal features, or non-content elements of
the program, influence a child’s attention to a
program Increased attention to the screen is associated
with learning of program content

The more attention children pay to the
screen, the more they learn

The presence of some formal features can
enhance learning

Certain features can also interfere with the
learning experience Education and Formal Features Rapid presentation of information seems to
degrade learning

Rapid visual or auditory change can increase
attention to the program Interference
Children’s entertainment programs presented
formal features designed to gain attention
(rapid action, music, and visual change)

Children’s education programs presented
many features designed to encourage
thoughtful processing of content (long zooms,
moderate action, and singing) Entertainment vs. Education Do educational programs still present
formal features that encourage thoughtful

HO: The use of formal features in children’s
educational programming has not changed
from 1981 to 1995.

HA: The use of formal features in children’s
educational programming has changed from
1981 to 1995. Hypotheses 4 half-hour programs were analyzed (chosen
to capture the diversity in science education
programs today) and compared against the
findings from Huston et al. (1981)

Bill Nye The Science Guy

Magic School Bus

Newton’s Apple

Beakman’s World Method 12 episodes of each program from the 1995-1996 season were analyzed

Program characteristics coded in the study
- Number of topic shifts
- Sound effects
- Visual pacing One-Way Within Subjects ANOVA was used
to analyze the findings

The independent variable was the television

The dependent variables were the Sound
Effects per Minute, Cuts per Minute, Fades/
Dissolves per Minute, Wipes per Minute, and
Topic Shifts per Episode ANOVA Table 1
Average Number of Formal Features per Episode
by Program In general the programs in this study were fast
paced; they used frequent sound effects,
cuts, and switched topics quite

Sound Effects Pacing
• On average, the programs used more than 19
sound effects per minute
• There were significant differences among the
programs (F(3,46) = 80.42, p < .05).

Visual Pacing
• While cuts were the most used visual-pacing
effect across all programs, the programs differed
significantly in the number of cuts per minute
(F(3,46) = 24.96, p < .05)
• While fades/dissolves were used sparingly in the
4 programs, averaging just under 1 fade/dissolve
per minute, their use did differ significantly by
program (F(3,46)=3.46, p<.05)
• The programs also differed significantly in the
number of wipes per minute (F(3,46)=3.05, p<.05)

Content Pacing
• The number of content shifts was significant
between programs (F(3,46)= 34.55, p<.05) Results Why did the ANOVA fit their data? Discuss: Why ANOVA? Healthcare reform information- seeking: Relationships with uncertainty, uncertainty discrepancy, and health self-efficacy

Nasim Mirkiani Thompson, Jennifer L Bevan, Lisa Sparks Article 2 Discussion The study examines information- seeking about the 2010 Patient Protection and Affordable Care Act (i.e. healthcare reform) in relation to the potential barriers of uncertainty, uncertainty discrepancy, and low health self-efficacy. Hypotheses H1: Information-seeking is positively related to degree of uncertainty about healthcare reform.

H2: Information-seeking is positively related to uncertainty discrepancy about healthcare reform.

H3: Individuals’ health self-efficacy is posi- tively related to information-seeking about healthcare reform. Participants 18 years or older completed an online survey.

Researchers then measured information-seeking, Uncertainty, uncertainty discrepancy, and health self-efficacy. Method Researchers performed a series of univariate analysis of variances then tested the categorical health insurance and healthcare reform variables in association with their variables of interest.

Take a look at Table 2! ANOVA Their goal was to determine which potential barrier accounted for increased variance in health- care reform information-seeking. Indeed, after interpreting the ANOVA results they determined that uncertainty discrepancy was the only significant predictor, and thus accounted for the most information- seeking variance. Did ANOVA lead the researchers to their desired target information? Your turn! Prepubescent children may oxidize fat more
readily than adults. Therefore, dietary fat
needs would be higher for children compared
with adults. The dietary fat recommendations
are higher for children 4 to 18 yrs (i.e., 25 to
35% of energy) compared with adults (i.e., 20
to 35% of energy).

Can we design a study that makes use of the ANOVA? 10 children and 10 adults were fed a weight
maintenance diet for three days

Metabolic rate was measured three times
before and immediately after breakfast
and for 9 hrs using a hood system (twice) or
a room calorimeter (once) State your Variables

Write Hypotheses!

Please and Thank You...
We got y'all some data. Would ANOVA have any value in our study of exercise and the workplace?
Could you give an example Brooke? Now let's apply the ANOVA to our study!
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