Research Methods 1998
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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

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Research methods 1998 graphical design and analysis

Research Methods 1998Graphical design and analysis

ÓGerry Quinn, Monash University, 1998

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


Graphical displays

Graphical displays

  • Exploration

    • assumptions (normality, equal variances)

    • unusual values

    • which analysis?

  • Analysis

    • model fitting

  • Presentation/communication of results


Space shuttle data

Space shuttle data


Space shuttle data1

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


Research methods 1998 graphical design and analysis

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

Challenger flight

Jan 28th 1986 - forecast temp 31oF


Research methods 1998 graphical design and analysis

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

Checking assumptions - exploratory data analysis (EDA)

  • Shape of sample (and therefore population)

    • is distribution normal (symmetrical) or skewed?

  • Spread of sample

    • are variances similar in different groups?

  • Are outliers present

    • observations very different from the rest of the sample?


Distributions of biological data

Pr(y)

y

Pr(y)

y

Distributions of biological data

  • Bell-shaped symmetrical distribution:

  • normal

  • Skewed asymmetrical distribution:

  • log-normal

  • poisson


Common skewed distributions

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

Exploring sample data


Example data set

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

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

Number of Cellana per quadrat

30

Survey 5, all shores combined

Total no. quadrats = 120

20

Frequency

10

0

0

20

40

60

80

100

Number of Cellana per quadrat


Dotplots

Dotplots

  • Each observation represented by a dot

  • Number of Cellana per quadrat, Cheviot Beach survey 5

  • No. quadrats = 15

0

10

20

30

40

Number of Cellana per quadrat


Boxplot

outlier

*

largest value

}

25% of values

hinge

VARIABLE

}

"

median

spread

}

"

hinge

}

"

smallest value

GROUP

Boxplot


Research methods 1998 graphical design and analysis

1. IDEAL

2. SKEWED

3. OUTLIERS

4. UNEQUAL VARIANCES

*

*

*

*

*


Research methods 1998 graphical design and analysis

Boxplots of Cellana numbers in survey 5

100

80

60

Number of Cellana per quadrat

40

20

0

SFPERRSPCPECBLBCPW

Site


Scatterplots

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


Cheviot beach survey 5 n 15

40

30

20

10

0

0

10

20

30

40

50

60

70

Cheviot Beach survey 5 n = 15

Number of Cellana

per quadrat

% cover of Hormosira per quadrat


Scatterplot matrix

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


Research methods 1998 graphical design and analysis

SPLOM for Cheviot Beach survey 5

CELLANA

- numbers of Cellana

SIPHALL

- numbers of Siphonaria

HORMOS

- % cover of Hormosira

n = 15 quadrats


Transformations

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).


Log transformation

Log transformation

LognormalNormal

y = log(y)

Measurement data


Power transformation

Power transformation

PoissonNormal

y = Ö(y), i.e. y = y0.5, y = y0.25

Count data


Arcsin transformation

Arcsin Ö transformation

SquareNormal

y = sin-1(Ö(y))

Proportions and percentages


Outliers

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

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


Category or line plot

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


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