Statistics
Biology
STATISTICS Accuracy - closest to true value
Precision
uncertainty with expiramenrs Reliability
[ Digital equipment stopwatch .
digital thermometer ]
1- 1- the smallest unit eg .
thermometer
22 . I
↳ unit
uncertainty + 1- 0 . I ← smallest
[ Analog manually reading units ]
eg .
Reading volume of water
+ / - half the smallest Unit ( in beaker )
Per measurement 34.5
/
reading 0.5<=2 =
F- 0.25
µ← sticks to the equipment
water
Always read the meniscus
curvature
-
the lowest point causing .
if there are no intervals on equipment / donor estimate .
measuring cylinder does not have 0.5 . Do not write 34.5
* Rulers are an exception .
2 points of uncertainty .
170--15
So the halved then doubled ( ✗ 2) the 0 Where it ends
uncertainty is
(the length of thing
therefore it remains the smallest unit
I ÷ 2 =
0.5×2 = 1
Average = Mean sum of group of number
a divided by
the number of numbers .
Median = The middle number if the group of numbers
are in order ( ascending)
Mode The number that
= shows up the most frequently
standard deviation .
Number which determines how far ir strays from
the mean .
SMALL
°
if number is .
Clustered no
Big . Fav from mean .
very
spread apart
how to calculate STANDARD DEVIATION
1 .
Calculate the mean for a set of dara
mean = 169.5
2 .
Subtract each individual data with the
MEAN [M -
N = Difference]
Equation :
Jie
- = mean
sunny y
169.5-157 = 1215
eg .
g ,
→ sample size
3. Square each Difference
eg . ( 12.55 = 156.25
4 .
Add all the savored difference & calculate
the mean of squared difference
total = 642.5
mean =
64,2¥ = 64.25
5 .
Square root the mean of square differences
fig =
8.02¢
M.P .
ya
SIGNATURE 2022
January
6
64
PROJECT
.
how to calculate standard deviation
with a calculator CGDC )
I = Mean
Ix '
= Sum of squared difference
I. ✗ = sum
0 ✗ = standard deviation
IN = Sample size
raw data = What you
measure
processed = After calculation
data
collecting Data
( DATA TABLE )
I. V D. V. (unit ) C. V.
Independent Variable
Control Variable
C What You Change ) Dependent Variable
( what stays the same )
( wna , you measure ,
E✗T,-zt3|Mem|s#
( F- Oil
Cmj
111
Distance on ruler
writing hand
Non -
writing
¥EÉ
PROCESSED DATA
Standard Deviation On Spreadsheets
☒•
[ MEAN] = AVERAGE ( : ) Highlight data cells
DEVIATION ]
[STANDARD =
STDEVPA ( : 7
* Number of decimal places THE SAME
use
.O← or .
OQ ,
f) + I 5. D. Bar graph
line
-
Discrete data
continuous data
/}
graph -
Dependent
-
I 5. D.
Variable
( Distance )
key to determine
what the error bars
vepevsent .
X
Independent Variable
( hands )
The bars SD shows the stray from the
error repevsenr uncertainty .
mean
Error Bars
the longer the error bars the [ less reliable ] your data is because
there are a bigger spread of data & it is less consistence
↳ around the mean value
small SD bar = more reliable Larger SD bar = less reliable
because biological data is variable
" "
it doesn't mean it is nor valid
SIGNIFICANT DIFFERENCE
↳ Results that due to
are seen are most likely not
chance or
sampling error .
there will always be a chance that the
"
significant result
"
was due to an error , however ,
it may just be reflecting the
nature of your set of data .
Rather than "
error
"
Graphs is
' '
can show whether it significant or not .
-
-
T T T
/
f- |
OVERLAP
I |
- -
| -
lap
-
I y
1-
When SD bars overlap when SD Bars overlap when SD bars do not overlap
a lot . Difference may less .
It may not be it may be that the difference
not be
statistically statistically significant may be significant
significant .
Bigger overlap the lower the VALIDITY ( statistically insig )
cannot draw a conclusion ,
no comparison
Better to be statistically significant As there is less
Overlap ,
There is an obvious difference .
( }
Ho is the belief that there
null hypothesis , the are no
relationship . eg . There are no correlation between 2 variables
H , is the alternative hypothesis ,
the belief that there is a
relationship 2 means different or there is correlation
eg are
.
.
Null hypothesis ( Ho ) -
no significant difference between the 2
Sers of data
Alternative hypothesis (H ) .
- There Is a significant difference
between the 2 sets of data
if less overlapping , means MORE likely
to be significantly different .
if more overlapping ,
means LESS likely
to be significantly different
c- value > C. V. .
Difference between 2 are significantly dif
Difference beheler 2 are nor Sig dif
c- valve { C. V.
Annalysis of graph
Writing hand faster reaction
time
-
Mean .
compare the mean and interpret the data
ie w is lower that N W
-
.
S D
.
.
-
length of error bars
compare the length
larger spread more variable data
longer error bar =
less reliable
[ Interpret
-
spread ,
reliability
1.
'
Overlapping of error bar
compare the overlap
N - W W if less overlapping , means MORE likely
to be significantly different .
if more overlapping ,
means LESS likely
to be significantly different
To determine the significance of the different between 2 Sers
of data using calculated values of t
T -
Test -
statistical test
keys
/Ñ ,
-
Ñz / I ,
= mean value of set 1
take a true
/ vehicle lines 1 =
value . positive
t¥ S
n =
= Standard deviation
no
'
of measurements
OVERLAP
1- test provides a
way of measuring
if 2 Sets of data have widely separated means & small variances
( data is clustered around mean ) they will have little overlap & a
Big Valve of T this shows significant difference
if 2 sets of dara have close means & large valences . They win have large
overlap & small valve of T .
this shows little significant difference
large valve T -
little overlap & significant difference
small valve T -
big overlap & no Sig dif
the T
judge whether is big
valve or small
To
A table of critical valve is consulted
the value that
is used is the Degrees Of Freedom
"
To work out the Degrees of Freedom
"
Degrees of freedom = number of class -
l
if there are 21 individuals in each sample
(21-1) -1 (21-1) =
40¢
investigations that will be
analysed using statistical test
scientists usually make
a
hull hypothesis The null
.
hypothesis
usually states that there is no significant difference benteen 2 samples
If the value of T is greater or equal to the critical value
than the null hypothesis can be rejected and ir can be
stated that the IS a significant different
critical value found if you have your degrees of freedom
and at 5% ( chance different due to chance )
ARE 5. D.
T > C. V.
determining statistically
radiation different
seeds B → gamma
example A → normal
① calculate T Valve
| { |
A B
|io.9-2 7,84
10 9 2.3 =
mean length "÷+"÷É
.
Of leaf
, .gg
3. a ,
S D
- .
② calculate Degrees of Freedom
28
sample size
15 15 (15-1)-1 (15-1) =
③ consult the table & find ④ compare 1- valve and C. V.
critical value at [ 5% )
level 2-048 7,84 7 2.048
CV at 5% significant
=
T is bigger so in fact is
⑤ accept hypothesis statistically different
reject null hypo ( no Sis dif )
accept alternate
can draw a more definite answer . objections determine the
significance of difference of the data
Analysis of graph
§
①
-
Trends
positive
( shape
correlation
of graph ]
É
I
gy•°É
increased too ) of 1-
( one increased , the other
'
. not linear
! { z
- 0.75 → 1,25
increase in % loss in
largest
mass -
compared to 1.25 → 2-5
② Error bars
i ) length ( variation in data )
largest block =
largest variation → this means less
realiable
ii )
overlapping
eg .
0,75 & 1.25 -
overlap
↳ suggest data is not
statistically different
( can't determine without 1- test )
1. 25 - 2.5 no overlap
③ Uncertainties
-
Saturation of water ? [ how sure
variables
are the controlled
]
blocks identical ?
not
[ may
controlled variables
]
-
possible disintegration nor have been
the same
-
systematic uncertainties [ in equipment
]
environmental factors
-
may change
Conclusion of graph
① conclusion statement
-
How hell does the result support the hypothesis
does not FULLY
M support
hypothesis results -
Both positive
but one is linear the ☐the plater
②
-
Explanation
scientific reasoning / context
ie SA ;v ratio size 8
]
.
us
-
significance in bio
in dept reasoning for why your results came to be
Evaluation
not done by the same people
-
limitations # Precision
""
of cutting
- a controlled environment
-
improvements
( nor monitored ]
Strengths _- C ( time , material
V
)
- -
-
\ 5 repeats
very repeatable
how significant did the limitations affect the results
when doing expiramenrs with natural organism
BIOLOGICAL VARIATION
accounts for the largest variation
