# Pearsons Correlation For Location Biology Essay

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Pearsons correlation for location one shows that between the body length and abdomen length there is a significant correlation where as the body length increases so does the abdomen length, seen in figure 1. Between the body length and front wing pad length, in figure 3, there is some correlation where the two variables increases with one another (r=0.468, p=0.001, n=50). Also the abdomen length and front wing pad length show some correlation between the two variables that also increases as the other increases, in figure 2, (r=0.594, p=0.000, n=50).

Figure 3: scatter graph showing correlation between body and front wing pad length at location 1.

Figure 2: scatter graph showing correlation between abdomen and front wing pad length at location 1.

Figure 1: scatter graph showing correlation between body and abdomen length at location 1.

## Mean measurements were also calculated for location two. The body length was 2.5384 (sd=0.11956), abdomen length was 1.0919 (sd=0.06232) and front wing pad length was 1.0379 (sd=0.03874).

## For location two Pearson's correlation shows that there are correlations between all the variables. The test shows that between the body and abdomen length, in figure 4, there is some correlation (r=0.450, p=0.001, n=50) where as the body length increases the abdomen length does too. Between the body length and front wing pad length there is very little correlation, that is almost not significant, which is seen in figure 6, but the two variables do increases with one another (r=0.292, p=0.039, n=50). From figure 5 it is seen that between the abdomen and front wing pad length there is little, almost insignificant, correlation between the two variables even though as one increases so does the other increases (r=0.308, p=0.030, n=50).

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Figure 6: scatter graph showing correlation between body and front wing pad length at location 2.

Figure 5: scatter graph showing correlation between abdomen and front wing pad length at location 2.

Figure 4: scatter graph showing correlation between body and abdomen length at location 2.

## The results for the Shapiro-Wilk test are presented in Table 1.

Location

Shapiro-Wilk

Statistic

df

Sig.

1

Body Length

.988

50

.892

Abdomen Length

.985

50

.781

Front wing pad length

.984

50

.730

2

Body Length

.978

50

.469

Abdomen Length

.970

50

.235

Front wing pad length

.978

50

.477

Table 1: A table showing Shapiro-Wilk normality test.

The results of the normality test in table 1show that all the measurements for body length, abdomen length and front pad wing length for both locations are normally distributed as p>0.05 for all the data, (p50=0.892, p50=0.781, p50=0.730, p50=0.469, p50=0.235, p50=0.477). This therefore accepts the null hypothesis that the results do not deviate from normal.

Pearson's correlation was also done for both locations together. For both locations together all the results showed some correlation. Front wing pad length and abdomen length have some correlation between them (r=0.445, p=0.000, n=100). The correlation shows that as the front wing pad length increases the abdomen length increase too. There is more correlation between the front wing pad and body length (r=0.71, p=0.000, n=100) even though it is only a small correlation. This correlation also shows that as the front wing pad increases the body length increases. The other Pearson's correlation test between the abdomen length and body length also shows a higher level of correlation compare to the others (r=0.568, p =0.000, n=100).

From the t-test, in table 2, for the front wing pad length it is seen that there is no significant difference between the means from location one (m=1.0132, sd=0.05662) and location 2 (m=1.0379, sd=0.03874) of the Craspedolepta (t98=-2.544, p=0.013). There was also no significant difference between the abdomen length at location 1(m=1.0968, sd=0.8590) and location 2 (m=1.0919, sd=0.06232) of the Craspedolepta (t98=0.330, p=0.742). Different to this the t-test results for body length shows significant differences between the means of location 1 (m=2.3531, sd=0.18040) and location 2 (m=2.5384, sd=0.11956) for Craspedolepta (t98=-5.890, p=0.000).

## Independent Samples Test

Levene's Test for Equality of Variances

t-test for Equality of Means

F

Sig.

t

df

Abdomen Length

Equal variances assumed

5.714

.019

.330

98

Front wing pad length

Equal variances assumed

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3.211

.076

-2.544

98

Body Length

Equal variances assumed

8.744

.004

-5.890

98

Table 2: A table showing independent sample test.

## Heavy metals data

## At both location one and two the medians where calculated for copper, zinc and lead. In figure 7 it I seen that the median of copper at location 1 is 2120.111 and at location2 the median is 27.50. At location 1 the median for zinc is 14426.5 and location 2 is 6285, which is seen in figure 11. For lead at location 1 the median is 7152.5 and location 2 it is 9520, this is seen in figure 12.

Figure 9: box plots showing the median and ranges of lead at both locations.

Figure 8: box plots showing the median and ranges of Zinc at both locations.

Figure 7: box plots showing the median and ranges of copper at both locations.

## Spearman's rank was done for location 1. There is some positive correlation between copper and lead (rs=0.322, p=0.010, n=64). The results for copper and zinc show a significant positive correlation (rs=0.876, p=0.000, n=64). Finally there is very little insignificant positive correlation between lead and zinc (rs=0.201, p=0.111, n=64). Spearman's rank for location 2 also shows that there are some positive correlations between all the variables. The test shows that between copper and lead there a significant positive correlation (rs=0.684, p=0.000, n=64). Between copper and zinc there is also a positive correlation (rs=0.682, p=0.000, n=64). Finally the results between lead and zinc show the most significant positive correlation (rs=0.839, p=0.000, n=64).

The results of the Kolmogorov-Smirnov normality test show that the majority of data do not follow a normal distribution. At both locations, seen in figure 10 and 11, the data for zinc does not follow a normal distribution (p64=0.005, p64=0.000). The data for lead, in figures 12 and 13, also deviates from a normal distribution (p64=0.000, p64=0.000). Therefore at both locations the data for lead and zinc rejects the null hypothesis.

Figure 11: Normality plots showing the distribution of zinc at location 2.

Figure 10: Normality plots showing the distribution of zinc at location 1.

Figure 13: Normality plots showing the distribution of lead at location 2.

Figure 12: Normality plots showing the distribution of lead at location 1.

At location 1 the null hypothesis for copper is accepted as this result is normal (p64=0.064). This is the complete opposite at location 2 as the results is not normal distributed (p64=0.000). this is seen in figure 14 and 15.

Figure 15: Normality plots showing the distribution of copper at location 2.

Figure 14: Normality plots showing the distribution of copper at location 1.

## Spearman's rank was also done for both locations together. This showed that between copper and zinc there was slight positive correlation (rs=0.106, p=0.236, n=128), this is the same for lead and zinc (rs=0.453, p=0.000, n=128). This is different fro copper and zinc as there is slightly more positive correlation (rs=0.694, p=0.000, n=128).

## The mann-whitney test, seen in table 3, was done for zinc, lead and copper at both locations. There is a significant difference between the medians of zinc in both locations (U64, 64 =1008.00, p=0.000). In both locations there is no significant difference between the medians of lead (U64, 64 =1704.00, p=0.101). For copper there was significant difference between the medians of location 1 and location 2 (U64, 64 =170.500, p=0.000).

## Test Statisticsa

Copper

Lead

Zinc

Mann-Whitney U

170.500

1704.000

1008.000

Wilcoxon W

2250.500

3784.000

3088.000

Z

-8.949

-1.639

-4.956

Asymp. Sig. (2-tailed)

.000

.101

.000

Grouping Variable: Location

Table 3: A table showing mann-whitney test.