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PSYC3102 - HSA3 > Week 10 > Flashcards

Week 10 Flashcards

1
Q

why Analysis of Variance (ANOVA) is needed to examine differences between multiple groups of means

A
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2
Q

Understand the philosophy underlying ANOVA

A
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3
Q

Including terminology such as between-subjects and familywise error rate

A
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4
Q

Know the assumptions that underpin ANOVA

A
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5
Q

Be able to interpret one-way between-subjects ANOVA in SPSS

A
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6
Q

Be able to interpret post-hoc testing in SPSS

A
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7
Q

Be able to write up an ANOVA in correct APA style

A
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8
Q

t-tests

A
  • Try to answer questions comparing two dependent variables
  • Is there a significant differenct between two mean variables
  • independent samples test
    e.g. rehydration vs carbohydrates
    or any combination of rehydration, carbohydrates, physio or combination
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9
Q

Problem with multiple comparisons (t-tests)

A
  • Error rate per comparison increases Type 1 Error
  • Or rejecting the null hypothesis when it is true
  • Familywise error rate:
  • Probability of making more Type 1 errors
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10
Q

Familywise Error Rate

A

The probability of making one or more Type 1 errors in a set of comparisons

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11
Q

Type 1 error

A
  • Rejecting the null hypothesis when it is true
  • Or we say something significant is happening but actually the null happening is true.
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12
Q

Alpha Value

A

= 0.05
* An acceptable level of error
* There is a 5% chance you have calculated a Type 1 error
* Connected to p value
* probability of finding a 5% magnitude difference if null is true

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13
Q

Analysis of Variance

A
  • ANOVA
  • Statistical procedure in psychology
  • guards against familywise error
  • Can analyse differences between more that one mean
  • t-tests only does two
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14
Q

One way Between-Groups ANOVA

A
  • Will tell you if there are significant differences in DV means across 3 or more groups
    *** Invented by Sir Ronald Fisher
  • F Statistic**
  • Post-hoc tests can be used to find where the differences are
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15
Q

When to use One-Way Between-Groups ANOVA

A
  • 1 Dependent variable is continuous
  • 1 Independent variable has three or more levels
  • Different participants in each level of the IV
    e.g. different football players in different groups
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16
Q

Dependent variable is continuous

A

Aa variable with many possible values.

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17
Q

Benefits of Between Groups Anova

A

Its possible to reduce the practice effect
Its possible to reduce the carry over effect.
e.g. physio could have carry over effects or other DVs could produce results when subjects practice doing the same test

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18
Q

Advantages of ANOVA

A

Can be used in wide range of experimental design
* Independent groups
* Repeated Measures
* Matched Samples
* Designs involving mixtures of independent groups and repeated measures
* More than on IV can be evaluated at once

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19
Q

Independent Groups Design

A

Between-Groups Design

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20
Q

Repeated Measures

A

Within Groups Design
Same people in each level of the IV
e.g. Each person does physio, carbs and rehydrate

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21
Q

Matched Samples

A
  • Control for confounding variables
  • Matching people to outcomes that might be important
    e.g. age and experience could influence recovery time from sport activities, so match fit people and older people for true results
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22
Q

Mixed Design ANOVA

A
  • Involves mixed IV Groups
  • Involves Repeated Measure samples
  • VCombination of a between-unit ANOVA and a within-unit ANOVA
  • Requires a minimum of two IVs called factors
  • At least one variables has to vary between-units and at least one of them has to vary within-units
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23
Q

Adjusted Factorial ANOVA

A
  • More than one IV evaluated at a time
  • Much more sophisticated
    e.g. measuring recovery time and heart rate at the same time
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24
Q

4 Assumptions of Between-Groups ANOVA

A
  1. DV must be continuous
  2. Independence: each participant must not influence the other
  3. Normality: Each group of scores should have normal distribution (No Outliers?)
  4. Homogeneity of Variance: approximatley equal variablity in each group
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25
Q

How to Check for Normality

A
  • Kolmogorov-Smirnov/Shapiro-Wilds: p > 0.05
  • Skewness & Kurtosis
  • Histograms
  • Detrended Q-Q Plots
  • Normal QQ Plots
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26
Q

Kolmogorov-Smirnov/Shapiro-Wilks:

A
  • Shapiro-Wilks: Small samples
  • Kolmogorov-Smirnov: larger samples
  • p > 0.05
  • Significant results require transformation
  • We want there to be little difference - less than 0.05
27
Q

Skewness & Kurtosis

A
  • if the z score of the statistic is < ±1.96 then it is normal
  • z score = Statistic/Std Error
28
Q

Histograms

A
  • Follows the Bell Curve
  • Similar a bar graph
  • Condenses data into a simple visua
  • Takes data points and groups them into logical ranges
29
Q

Detrended Q-Q Plots

A
  • Horizontal line representing what would be expected if the data were normally distributed.
  • Demonstrated by equal amounts of dots above & below the line
30
Q

Normal Q-Q Plots

A
  • Plots data against expected normal distribution
  • Normality is demonstrated by dots hugging the line.
31
Q

Null Hypothesis

A
  • Nothing to see here.
  • no significant difference between the averages
  • Any deviation in our sample is due to sampling error or chance.
32
Q

Alternative Hypothesis - (H1)

A

(H1): At least one of the means is different from the rest.

33
Q

Testing The Assumptions

A
  1. Convert Skewness and Kurtosis into z scores and < +-1.96
  2. Std Error should be < +-1.96
  3. Confidence Levels accuracy give or take upper and lower %
34
Q

Standard Error

A

should be < +-1.96

35
Q

5% trimmed mean

A
  • Not so important for ANOVA or t-test
  • Removes oultiers
  • If 5% trimmed mean is different to mean then data has lots of inflential scores or outliers
36
Q

Median

A
  • A better reflection of the average if the data is not normal
  • if same as mean and 5% mean indicates modal distribution or single hump
  • If different then could indicate multi modal distribution
37
Q

Uni Modal Distribution

A

When mean, 5% trimmed mean and median are the same number

38
Q

Variance

A
  • Give indication of variability in scores
  • Measure of the spread, or dispersion, of scores
  • Small variance indicates simmilarity of scores
  • Large variance indicate larger spread across the means
  • Used to measure Standard Deviation
39
Q

Standard Deviation

A
  • Measure of variability when we report our mean
  • Gives indication of distrubution of scores in each group
  • Use this in our APA Write up
40
Q

Interquartile Range

A
  • Talks about 75th & 25th percentiles
  • Reports around the median
41
Q

z scores

A
  • Convert Skewness & Kurtosis into z scores
  • Divide the Statistic Result by the Std. Error result
  • Then compare to critical value <±1.96
42
Q

Testing Assumption of Normality

A
  • Komogorov-Smirnov - p > .05 - Large sample
  • Also Shapiro-Wilks - p > .05 - Small sample
    * W = Statistic / Sig.
  • Usually a p value
  • SPSS uses a Sig. value
43
Q

Transform Data

A

When data does not meet the assumptions of normality then data can be transformed

44
Q

Outlier

A
  • Data that is 3 Standard Deviation points from Normal Data
45
Q

Anova Expample - Statistical Question

A

“Is there a significant difference among the average recovery rates of the four recovery methods. If so, what is the source of that significant difference?”

46
Q
A
  • Mu equal mean of data
  • If null is true there are no significant differences in the means of the groups
  • Any differences would be due to sampling error or chance
47
Q

Running an ANOVA

A

SPSS steps:
1. Analyse
2. Compare Means
3. One-way ANOVA
4 - Place DV in the dependent list section.
5 - Place the IV in the factor section.
6. OK

48
Q

Interpreting ANOVA

A
  • First thing is to find N
  • Then the mean for each group
  • Do differences happen due to sample error
  • Is it indicative of the population
  • Next find Standard deviation
  • Each mean and Std Deviation is used in APA Write up
49
Q

Homogeneity of Variance

A
  • Levene Statistic
  • Assumes all groups have equal variance
  • Is part of ANOVA Output
  • We want p > .05 to keep Null Hypothesis
  • ANOVA works on Means so use top row
50
Q

Anova Table

A
  • Sum of Squares
  • Divided by Degrees of Freedom
  • Gives us our Mean Square
  • Mean Square gives us the Average Variability
51
Q

The F Statistic

A
  • In and of itself is not all that meaningful
  • F = 1 means not much variability
  • We want more variablity between the groups than within the groups
  • High F is good in relation to Degrees of Freedom
  • P Value says if F is significant reject the Null
    * p < .001
52
Q

Omnibus Test

A
  • F Statistic is Omnibus Test
  • Tells you something significant is happening
  • Doesn’t tell you where the difference is
53
Q

Post-Hoc Tests

A
  • Tests carried out after finding significant overall ANOVA
  • Locates the source of the Significant F
  • Are Exploratory (cf Planned Comparisons)
  • Must be significant to Justify post-hoc test
54
Q

Follow up Significant ANOVA

A

Use post-hoc tests to control familywise error rate

55
Q

Boneferroni Adjustment a/n

A
  • Adjust significance level for each comparison
  • Alpha Divided by N - a/n
  • Acceptable p value is n
56
Q

Some Significant post-hoc tests ANOVA

A
  • Tukey’s Honestly Significant Difference Test (Tukey’s HSD)
    * Bonferroni’s test
  • Scheffe test
  • Newman-Keuls test
  • Fisher’s Least Significant Difference Test (Fisher’s LSD)
57
Q

Two most common post-hoc Tests

A
  • Tukey’s Honestly Significant Difference Test (Tukey’s HSD)
  • Bonferroni’s test
58
Q

Multiple Comparisons

A
  • Boneferroni Tests post-hoc test
  • Sig. column looking for significant differences
  • Significant at Less than 0.05
  • p < .05
  • In this example Rehydration/Carbohydrates are not significant
59
Q

Following up Significant ANOVA

A
  • Return to Descriptives Box
  • Interested in Standard Deviation and Mean values to tell the story of significance
60
Q

Calculate Effect Size

A
  • Psychology is moving away from focusing on the p value
  • Headed to confidence interals or effect size
  • Effect size for one-way ANOVA is call eta-squared
  • Eta-squared is similar to r value - Correlation Coefficient
61
Q

Write up ANOVA in APA Format

A
  • A one-way between-subjects ANOVA revealed an overall significant difference in recovery rates between the four types of recovery, F(3, 96) = 56.20, p < .001, η2 = .64.
  • Post-hoc analyses using Bonferroni adjustment found that the combined intervention had significantly higher recovery rates compared to all other interventions (all p < .001).
  • The physio group had significantly lower recovery rates compared to the other interventions (all p < .001).
  • There was no significant difference between the rehydration (M = 73.04, SD = 7.29) and the carbohydrates group (M = 77.36, SD = 7.09), p = .174.
  • Means and standard error are presented in Figure 1.
62
Q

Write up ANOVA in APA Format- step Guide

A
  • Write what test you have done – one-way between-subjects ANOVA
    F Statistic two decimals
    p value three decimals give exact p value
    eta statistic (η2) two decimals
  • Write what post-hoc test you have done – Boneferroni adjustment
  • Report all p values, the significant ones, and the non-significant ones
  • Say direction of difference and the group means (higher or lower)
  • Present figure or table
63
Q

Assumptions to Meet - Between Groups Anova

A
  • Test for Normality
  • Observe Q-Q plots, Histograms
  • Skewness & Kurtosis
  • Homogeneity of Variance - Levenne’s
64
Q

Between-groups Design

A
  • Different participants expose to each level of the IV
  • Limit practice effects, carry over effects, fatigue and minimize attrition
  • Associated with issues of individual variability
  • More than two groups

PSYC3102 - HSA3 (12 decks)

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