First we need a measure to compare between plots to meet the above criteria of the unpaired, independent sample, t-test, 'dependent variable is measured on an incremental level, such as ratios or intervals.'

[32]:

myplot1 = 'BUCA'

[33]:

# Select a particular plot name based on examination of mapped data and descriptions in the plot description dataset.PLT = myplot1 # Put the name for study hear, i.e ='STRD'data1 = MSH_YEAR.where('PLOT_NAME',are.contained_in(PLT)).sort('YEAR',descending=False)data1

[33]:

PLOT_ID	PLOT_NAME	PLOT_NUMBER	YEAR	RICHNESS	COVER_%	HPRIME	EVENNESS	FREQUENCY
BUCA011980	BUCA	1	1980	10	15.5	1.886	0.819	29.5
BUCA031980	BUCA	3	1980	15	32.2	1.433	0.529	21.5
BUCA041980	BUCA	4	1980	9	18.5	1.754	0.798	31.4
BUCA011981	BUCA	1	1981	15	50.7	1.656	0.612	26.9
BUCA031981	BUCA	3	1981	17	71.2	1.324	0.467	18.8
BUCA041981	BUCA	4	1981	14	55.5	1.787	0.677	26.7
BUCA011982	BUCA	1	1982	16	39.6	1.765	0.637	26.1
BUCA031982	BUCA	3	1982	20	46.9	1.424	0.475	20.8
BUCA041982	BUCA	4	1982	16	38.7	1.931	0.697	29.5
BUCA011983	BUCA	1	1983	16	43.2	1.408	0.508	23.7

... (64 rows omitted)

[34]:

YEAR1 = data1['YEAR'].min() YEAR2 = data1['YEAR'].max()

[35]:

growth1 = data1.where('YEAR',YEAR1)['COVER_%']/data1.where('YEAR',YEAR2)['COVER_%']growth1

[35]:

array([ 0.30273438, 0.50234009, 0.33944954])

[36]:

s1 = np.std(growth1)

[37]:

myplot2 = 'PUPL'

[38]:

# Select a particular plot name based on examination of mapped data and descriptions in the plot description dataset.PLT = myplot2 # Put the name for study hear, i.e ='STRD'data2 = MSH_YEAR.where('PLOT_NAME',are.contained_in(PLT)).sort('YEAR',descending=False)data2.sort('YEAR')

[38]:

PLOT_ID	PLOT_NAME	PLOT_NUMBER	YEAR	RICHNESS	COVER_%	HPRIME	EVENNESS	FREQUENCY
PUPL011989	PUPL	1	1989	5	0.5	1.609	1	3.4
PUPL021989	PUPL	2	1989	7	0.7	1.946	1	4.1
PUPL031989	PUPL	3	1989	4	0.4	1.386	1	2.5
PUPL041989	PUPL	4	1989	7	0.7	1.946	1	2.1
PUPL051989	PUPL	5	1989	5	0.5	1.609	1	2.6
PUPL061989	PUPL	6	1989	5	0.5	1.609	1	5
PUPL071989	PUPL	7	1989	0	0	0	0	0
PUPL081989	PUPL	8	1989	1	0.1	0	0	1
PUPL091989	PUPL	9	1989	7	1	1.748	0.898	5.7
PUPL101989	PUPL	1	1989	5	0.5	1.609	1	2.4

... (242 rows omitted)

[39]:

YEAR1 = data2['YEAR'].min() YEAR2 = data2['YEAR'].max()

[40]:

growth2 = data2.where('YEAR',YEAR1)['COVER_%']/data2.where('YEAR',YEAR2)['COVER_%']growth2

[40]:

array([ 0.04385965, 0.04216867, 0.03174603, 0.03825137, 0.0625 , 0.13888889, 0. , 0.00512821, 0.03846154, 0.02645503, 0.01385042, 0. ])

[41]:

s2 = np.std(growth2)

[42]:

diffmean = np.mean(growth2) - np.mean(growth1)

[43]:

se1 = s1/np.sqrt(n)se2 = s2/np.sqrt(n)std_error = np.sqrt((se1**2+se2**2)/2)paired_std_error = s/np.sqrt(n)print(f'The mean COVER_% change is: {diff_means:.2f}')print(f'The standard deviation of the COVER_% differences is: {s:.3f}')print(f'The paired standard error is: {paired_std_error:.4f}')print(f'The degrees of freedom is: {dof}')

The mean COVER_% change is: 14.67 The standard deviation of the COVER_% differences is: 3.496 The paired standard error is: 0.2202 The degrees of freedom is: 502

[44]:

t = 14.67/0.2202print("The t value is:", t)

The t value is: 66.62125340599455

[45]:

p = 0.05

Outcome of Hypothesis Test and conclusion about selected plots...

Part 2: Testing a trend

Question 6

Now we will look at the time trend of COVER_% and RICHNESS using the changes function you developed and used in Part 2 of Lab 07. With changes we are looking at the number of increases minus decreases over the time period.

changes function:

[54]:

def diff_n(values, n): ''' Parameters: values is an array of numbers n is the offset (how far apart the numbers are in the array) ''' return np.array(values)[n:] - np.array(values)[:-n]

[55]:

def changes(array, years = 1): "Return the number of increases minus the number of decreases" differences = diff_n(array, years) increases = np.count_nonzero(differences > 0) decreases = np.count_nonzero(differences < 0) return increases - decreases

[56]:

test_stat = np.sum(....column('...'))print('Total increases minus total decreases, across all years:', test_stat)