# Research Methods 1998 Graphical design and analysis - PowerPoint PPT Presentation

1 / 29

Research Methods 1998 Graphical design and analysis. Ó Gerry Quinn, Monash University, 1998 Do not modify or distribute without expressed written permission of author. Graphical displays. Exploration assumptions (normality, equal variances) unusual values which analysis? Analysis

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

Research Methods 1998 Graphical design and analysis

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

#### Presentation Transcript

Research Methods 1998Graphical design and analysis

ÓGerry Quinn, Monash University, 1998

Do not modify or distribute without expressed written permission of author.

### Graphical displays

• Exploration

• assumptions (normality, equal variances)

• unusual values

• which analysis?

• Analysis

• model fitting

• Presentation/communication of results

### Space shuttle data

• NASA meeting Jan 27th 1986

• day before launch of shuttle Challenger

• Concern about low air temperatures at launch

• Affect O-rings that seal joints of rocket motors

• Previous data studied

3

2

Number of incidents

1

0

50

55

60

65

70

75

80

85

Joint temp. oF

O-ring failure vs temperature

Pre 1986

### Challenger flight

Jan 28th 1986 - forecast temp 31oF

3

2

Number of incidents

1

0

50

55

60

65

70

75

80

85

o

Joint temp. F

O-ring failure vs temperature

### Checking assumptions - exploratory data analysis (EDA)

• Shape of sample (and therefore population)

• is distribution normal (symmetrical) or skewed?

• are variances similar in different groups?

• Are outliers present

• observations very different from the rest of the sample?

Pr(y)

y

Pr(y)

y

### Distributions of biological data

• Bell-shaped symmetrical distribution:

• normal

• Skewed asymmetrical distribution:

• log-normal

• poisson

### Common skewed distributions

Log-normal distribution:

• m proportional to s

• measurement data, e.g. length, weight etc.

Poisson distribution:

• m = s2

• count data, e.g. numbers of individuals

## Exploring sample data

### Example data set

• Quinn & Keough (in press)

• Surveys of 8 rocky shores along Point Nepean coast

• 10 sampling times (1988 - 1993)

• 15 quadrats (0.25m2) at each site

• Numbers of all gastropod species and % cover of macroalgae recorded from each quadrat

### Frequency distributions

Observations grouped into classes

NORMAL

LOG-NORMAL

Number of observations

Value of variable (class)

Value of variable (class)

### Number of Cellana per quadrat

30

Survey 5, all shores combined

20

Frequency

10

0

0

20

40

60

80

100

### Dotplots

• Each observation represented by a dot

• Number of Cellana per quadrat, Cheviot Beach survey 5

0

10

20

30

40

outlier

*

largest value

}

25% of values

hinge

VARIABLE

}

"

median

}

"

hinge

}

"

smallest value

GROUP

### Boxplot

1. IDEAL

2. SKEWED

3. OUTLIERS

4. UNEQUAL VARIANCES

*

*

*

*

*

Boxplots of Cellana numbers in survey 5

100

80

60

40

20

0

SFPERRSPCPECBLBCPW

Site

### Scatterplots

• Plotting bivariate data

• Value of two variables recorded for each observation

• Each variable plotted on one axis (x or y)

• Symbols represent each observation

• Assess relationship between two variables

40

30

20

10

0

0

10

20

30

40

50

60

70

### Cheviot Beach survey 5 n = 15

Number of Cellana

% cover of Hormosira per quadrat

### Scatterplot matrix

• Abbreviated to SPLOM

• Extension of scatterplot

• For plotting relationships between 3 or more variables on one plot

• Bivariate plots in multiple panels on SPLOM

SPLOM for Cheviot Beach survey 5

CELLANA

- numbers of Cellana

SIPHALL

- numbers of Siphonaria

HORMOS

- % cover of Hormosira

### Transformations

• Improve normality.

• Remove relationship between mean and variance.

• Make variances more similar in different populations.

• Reduce influence of outliers.

• Make relationships between variables more linear (regression analysis).

LognormalNormal

y = log(y)

Measurement data

### Power transformation

PoissonNormal

y = Ö(y), i.e. y = y0.5, y = y0.25

Count data

### Arcsin Ö transformation

SquareNormal

y = sin-1(Ö(y))

Proportions and percentages

### Outliers

• Observations very different from rest of sample - identified in boxplots.

• Check if mistakes (e.g. typos, broken measuring device) - if so, omit.

• Extreme values in skewed distribution - transform.

• Alternatively, do analysis twice - outliers in and outliers excluded. Worry if influential.

### Assumptions not met?

• Check and deal with outliers

• Transformation

• might fix non-normality and unequal variances

• Nonparametric rank test

• does not assume normality

• does assume similar variances

• Mann-Whitney-Wilcoxon

• only suitable for simple analyses

Cheviot Beach

Sorrento

30

30

25

25

20

20

Mean number of Cellana per quadrat

15

15

10

10

5

5

0

0

1

2

3

4

5

6

7

8

9

10

1

2

3

4

5

6

7

8

9

10

Survey

### Category or line plot

Mean number of Cellana per quadrat

Survey