# statistics by 3QU3z74

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```									CHI SQUARE TEST
click on tabs on the bottom to switch to different
(if you don't see the tabs, make sure the window for this worksheet is maximized)

Steps to using Excel to do chi-square test:
First decide how many categories you have (e.g., north vs south would be 2 categories; tree, shrubs, succulents would be 3).
Use the table that has the same number of categories as you have (change categories to your's if you want).
Type your data in the gray boxes; make sure you press enter after entering all data
A p-value less than 0.05 means that the chance of the numbers being evenly randomly distributed is less than 5%.

Note: you cannot use chi square test for comparing percentages.
Note: you cannot use chi square test for sample sizes less than 30

2 categories     Category 1   Category 2
Your Data >>>       120          150                       P value       0.068      [Note: if this number = 0.000, then record p
Is the p value less than 0.05?
If no, then the totals are not significantly dif
If yes, then the totals are significantly differ
3 categories     Category 1   Category 2    Category 3
Your Data >>>                                                           P value       #DIV/0!     [Note: if this number = 0.000,
Is the p value less than 0.05
If no, then the totals are not s
If yes, then the totals are sign
4 categories     Category 1   Category 2    Category 3   Category 4
Your Data >>>        40           50            60          104                       P value         0.000

5 categories     Category 1   Category 2    Category 3   Category 4    Category 5

8 categories     Category 1   Category 2    Category 3   Category 4    Category 5    Category 6    Category 7

Example 1: if you counted 120 saguaros on the N slope and 150 saguaros on the S slope,
then p = 0.068 so there is no significant difference in # of saguaros on the two slopes.

Example 2: if you counted 40 holes on the N side, 50 on E side, 60 on W side, and 104 on S side of saguaros,
then the p < 0.01 so there is a significant difference in # of saguaros on the two slopes.

The chi square test compares the observed values to the values expected by the null hypothesis.
to different tests

bs, succulents would be 3).

is less than 5%.

umber = 0.000, then record p<0.01]
e less than 0.05?
totals are not significantly different (accept null hypothesis)
e totals are significantly different (accept alternative hypothesis)

[Note: if this number = 0.000, then record p<0.01]
Is the p value less than 0.05?
If no, then the totals are not significantly different (accept null hypothesis)
If yes, then the totals are significantly different

[Note: if this number = 0.000, then record p<0.01]
Is the p value less than 0.05?
If no, then the totals are not significantly different (accept null hypothesis)
If yes, then the totals are significantly different

#DIV/0!     [Note: if this number = 0.000, then record p<0.01]
Is the p value less than 0.05?
If no, then the totals are not significantly different (accept null hypothesis)
If yes, then the totals are significantly different
Category 8
P value     #DIV/0! [Note: if this number = 0.000, then record p<0.01]
Is the p value less than 0.05?
If no, then the totals are not significantly different (accept null hypothesis)
If yes, then the totals are significantly different

e of saguaros,
ept null hypothesis)
T-TEST
Steps to using Excel to do t-test:
Click on Group 1 and type in new name for group; do same for Group 2
Replace existing data with your data under each column name
Click into the vertical-axis label of the graph, and change the label, remembering to give the units, too

Group 1             Group 2
Your Data >>>            3.5                  1                  average Group 1          1.760
Your Data >>>            0.2                 3.2                 average Group 2          2.540
Etc.                     1.5                 4.2              standard error Group 1      0.668    These values show the variabi
3.1                 0.8              standard error Group 2      0.690

P value             0.440    [Note: if this number = 0.000, t
Is the p value less than 0.05?
If no, then the averages are no
If yes, then the averages are s
what are you
measuring (units)

0.5
1.0
1.5
2.0
2.5
3.0
3.5
0.5

0.0
Group 1
These values show the variability for each group, and are used to make the "error bars" on the graph below

[Note: if this number = 0.000, then record p<0.01]
Is the p value less than 0.05?
If no, then the averages are not significantly different (accept null hypothesis)
If yes, then the averages are significantly different
Group 1   Group 2
T-TEST: PAIRED
Steps to using Excel to do t-test:
Click on Group 1 and type in new name for group; do same for Group 2
Replace existing data with your data under each column name
Click into the vertical-axis label of the graph, and change the label, remembering to give the units, too

Group 1             Group 2
Your Data >>>            3.5                  1                  average Group 1          1.760
Your Data >>>            0.2                 3.2                 average Group 2          2.540
Etc.                     1.5                 4.2              standard error Group 1      0.668    These values show the variabi
3.1                 0.8              standard error Group 2      0.690

P value             0.581    [Note: if this number = 0.000, t
Is the p value less than 0.05?
If no, then the averages are no
If yes, then the averages are s
measuring (units)
3.5

what are you
3.0

2.5

2.0

1.5

1.0

0.5

0.0
Group 1
These values show the variability for each group, and are used to make the "error bars" on the graph below

[Note: if this number = 0.000, then record p<0.01]
Is the p value less than 0.05?
If no, then the averages are not significantly different (accept null hypothesis)
If yes, then the averages are significantly different
Group 1   Group 2
REGRESSION ANALYSIS
SAMPLE
Dexterity Productivity                                                                    Dexterity as a Predictor of Productivit
Employee          Test Score Units/Hour
A                  12         55
B                  14         63
C                  17         67

Productivity (units/hr)
75
D                  16         70
70
E                  11         51
65
SUMMARY OUTPUT                                                                                         60
55
Regression Statistics
Multiple R                 0.955                                                                       50
R Square                   0.911 91% of variation in y explained by x                                       10         12            14
Adjusted R Square          0.882                                                                                            Dexterity Test Score
Standard Error             2.757 standard error is 2.757 units/h
Observations                   5

ANOVA
df         SS           MS          F         Significance F
Regression                1          234          234       30.789          0.012      is p value
Residual                  3          22.8         7.6                                  df = n-2 = 3
Total                     4         256.8

CoefficientsStandard Error t Stat      P-value       Lower 95%                               Upper 95%Lower 95.0%
Intercept               19.2        7.669        2.504       0.087         -5.206                                  43.606    -5.206
X Variable 1              3         0.541        5.549       0.012          1.279                                   4.721     1.279
Regression Line is y = 19.2 + 3.0x            t = 5.55    p = 0.012
df = 3

RESIDUAL OUTPUT

Observation        Predicted Y Residuals
1          55.2       -0.2
2          61.2        1.8
3          70.2       -3.2
4          67.2        2.8
5          52.2       -1.2
as a Predictor of Productivity

16   18
Dexterity Test Score

Upper 95.0%
43.606
4.721
SIMPSON'S DIVERSITY INDEX
Steps to using Excel to do Simpson's diversity index:
Type in the number of individuals for each species in the gray boxes
The number in yellow is the Simpson's Diversity Index (D).
Diversity is a measure of the number of species (richness) and
how evenly spread out the individuals are among the species (evenness)
For the purposes of this class, let's say that the difference is significant if the
Simpson's diversity indices differ by more than 10 percentage points between two areas.

Area 1       Area 2
Simpson's Diversity                              Percent chance that two individuals pulled randomly from
64.8         58.1
Index [actually 1-D]                             the community will not be from the same species.
The higher the number, the more diverse the community.

N=       14          73       This is calculated for you and is total number of individuals sampled.
Richness =       4           5       This is calculated for you and is total number of species sampled.

number of species 1         1            8       You type in these
number of species 2         2           12       numbers in the gray
number of species 3         3           45       boxes which are
number of species 4                      2       the number of
number of species 5         8                    individuals of
number of species 6                      6       each species (no zeroes)
number of species 7
number of species 8
number of species 9
number of species 10
number of species 11
number of species 12
number of species 13
number of species 14
number of species 15
number of species 16
number of species 17
number of species 18
number of species 19
number of species 20
number of species 21
number of species 22
number of species 23
number of species 24
number of species 25
number of species 26
number of species 27
number of species 28
number of species 29
number of species 30
number of species 31
number of species 32
number of species 33
number of species 34
number of species 35
number of species 36
number of species 37
number of species 38
number of species 39
number of species 40
d randomly from

he community.

of individuals sampled.
of species sampled.
a3a6fff1-9fff-4226-9c95-9001906edf4c.xls

CHI SQUARE TEST
First decide how many categories you have (e.g., north vs south would be 2 categories).
Use the table that has the same number of categories as you have (change categories to yours).
Enter your data in the white boxes under "Obs"; these are your observed data.
Leave the expected values ("Exp") as they are unless you expect something other than being evenly divided.
Compare total (chi square statistic = X2) that is in the yellow box to the red number above the table (derived from statistics table

IF TOTAL IS GREATER THAN 3.84 (df=1)                              IF TOTAL IS GREATER THAN 5.99 (df=2)
THEN THERE IS SIGNIFICANT DIFFERENCE                              THEN THERE IS SIGNIFICANT DIFFERENCE
Categories       Obs         Exp       (O-E)2 (O-E)2/E            Categories      Obs        Exp      (O-E)2 (O-E)2/E
A         120         135         225         1.67             trees         0          0           0 #DIV/0!
B         150         135         225         1.67         shrubs            0          0           0 #DIV/0!
total        270         270 TOTAL               3.33             cacti         0          0           0 #DIV/0!
total        0          0 TOTAL #DIV/0!

X 2=       3.33 Significant if greater than 3.84                  X2= #DIV/0! Significant if greater than 5.99
p value =       0.068 Significant if less than 0.05               p value = #DIV/0! Significant if less than 0.05

Terms:           df= degrees of freedom = one less than the number of categories; use df to look up test statistic in statistics
p value = the probability that you conclude that there is a significant difference when there really is no difference.

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a3a6fff1-9fff-4226-9c95-9001906edf4c.xls

(derived from statistics table).

IF TOTAL IS GREATER THAN 7.81 (df=3)                               IF TOTAL IS GREATER THAN 9.49 (df=4)
THEN THERE IS SIGNIFICANT DIFFERENCE                               THEN THERE IS SIGNIFICANT DIFFERENCE
Categories       Obs        Exp       (O-E)2 (O-E)2/E             Categories      Obs        Exp      (O-E)2 (O-E)2/E
north          40        63.5     552.25           8.70             trees         0          0           0 #DIV/0!
south          50        63.5     182.25           2.87         shrubs            0          0           0 #DIV/0!
east         60        63.5      12.25           0.19        cactuses           0          0           0 #DIV/0!
west         104        63.5 1640.25             25.83             forbs         0          0           0 #DIV/0!
total       254         254 TOTAL               37.59             grass         0          0           0 #DIV/0!
total        0          0 TOTAL #DIV/0!
X 2=     37.59 Significant if greater than 7.81                   X2= #DIV/0! Significant if greater than 9.49
p value =       0.000 Significant if less than 0.05                p value = #DIV/0! Significant if less than 0.05

k up test statistic in statistics table
here really is no difference.

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a3a6fff1-9fff-4226-9c95-9001906edf4c.xls

IF TOTAL IS GREATER THAN 14.07 (df=7)
THEN THERE IS SIGNIFICANT DIFFERENCE
Categories       Obs         Exp     (O-E)2 (O-E)2/E
N           0           0          0    #DIV/0!
NE            0           0          0    #DIV/0!
E           0           0          0    #DIV/0!
SE            0           0          0    #DIV/0!
S           0           0          0    #DIV/0!
SW            0           0          0    #DIV/0!
W            0           0          0    #DIV/0!
NW             0           0          0    #DIV/0!
total          0          0      TOTAL      #DIV/0!
X2=           #DIV/0! Significant if greater than 14.067
p value =      #DIV/0! Significant if less than 0.05

Page 24
SHANNON'S DIVERSITY INDEX
Steps to using Excel to do Shannon's diversity index:
Type in the number of individuals for each species in the gray boxes
The number in yellow is the Shannon's Diversity Index (H).
Diversity is a measure of the number of species (richness) and
how evenly spread out the individuals are among the species (evenness)
For the purposes of this class, let's say that the difference is significant if the
Simpson's diversity indices differ by more than 10 percentage points between two habitats.

Area 1       Area 2
Shannon's Div. Index    66.67
n=            3            3
Richness =             2            2
Variance

ni*(ni-1)   This is the formula
number of species 1              1            1                        0   These are
number of species 2              2            2                        2   calculated for you
number of species 3                                                    0   so don't change
number of species 4                                                    0   them.
number of species 5                                                    0
number of species 6                                                    0
number of species 7                                                    0
number of species 8                                                    0
number of species 9                                                    0
number of species 10                                                   0
number of species 11                                                   0
number of species 12                                                   0
number of species 13                                                   0
number of species 14                                                   0
number of species 15                                                   0
number of species 16                                                   0
number of species 17                                                   0
number of species 18                                                   0
number of species 19                                                   0
number of species 20                                                   0
number of species 21                                                   0
number of species 22                                                   0
number of species 23                                                   0
number of species 24                                                   0
number of species 25                                                   0

log n
sum of fi log fi

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