Biology Test Scores
Student Test 1 Test 2 Test 3 Test Average Test Median bins
1 78 83 85 82.0 83 75
2 77 83 82 80.7 82 80
3 70 85 86 80.3 85 85
4 88 88 87 87.7 88 90
5 85 89 90 88.0 89 95
6 83 82 91 85.3 83 100
7 80 77 85 80.7 80
8 90 89 93 90.7 90
9 72 84 89 81.7 84
10 75 84 83 80.7 83
11 85 81 92 86.0 85
12 93 92 94 93.0 93
average: 81.33 84.75 88.08 84.72222222
median: 81.5 84 88
mode: 85 83 85
SD: 7.215304 4.136863 3.98767 5.877857292
Z-Scores: Test 1 Test 2 Test 3 bins
1 -1.144 -0.293 0.047 -3
2 -1.314 -0.293 -0.463 -2.58
3 -2.505 0.047 0.217 -1.96
4 0.558 0.558 0.388 0
5 0.047 0.728 0.898 1.96
6 -0.293 -0.463 1.068 2.58
7 -0.803 -1.314 0.047 3
8 0.898 0.728 1.408
9 -2.164 -0.123 0.728
10 -1.654 -0.123 -0.293
11 0.047 -0.633 1.238
12 1.408 1.238 1.578
Did students improve between their first and third tests?
96
y = 0.3818x + 57.027
94
R² = 0.4773
3.71509E-06
92
90
Test 3
difference
88
Linear (difference)
86
84
82
80
65 70 75 80 85 90 95
Test 1
Bin Frequency
75 3 Histogram
80 4
85 14 20
Frequency
90 9 15
95 6 10
Frequency
100 0 5
0
-5 75 80 85 90 95 100
Bin
z-Test: Two Sample for Means
Variable 1 Variable 2
Mean 81.33333 88.08333
Known Variance 7.21 3.99
Observations 12 12
Hypothesized Mean Difference 0
z -6.98691
P(Z<=z) one-tail 1.41E-12
z Critical one-tail 1.644853
P(Z<=z) two-tail 2.83E-12
z Critical two-tail 1.959963
t-Test: Two-Sample Assuming Equal Variances
Section 1 Section 2
Mean 86.84262 85.22146
Variance 77.59939 90.36669
Observations 20 20
Pooled Variance 83.98304
Hypothesized Mean Difference 0
df 38
t Stat 0.55941
P(T<=t) one-tail 0.289582
t Critical one-tail 1.685953
P(T<=t) two-tail 0.579164
t Critical two-tail 2.024394
t-Test: Paired Two Sample for Means
Variable 1 Variable 2
Mean 81.33333 84.75
Variance 52.06061 17.113636
Observations 12 12
Pearson Correlation 0.526899
Hypothesized Mean Difference 0
df 11
t Stat -1.92712
P(T<=t) one-tail 0.040089
t Critical one-tail 1.795884
P(T<=t) two-tail 0.080178
t Critical two-tail 2.200986
Anova: Two-Factor Without Replication
SUMMARY Count Sum Average Variance
78 2 168 84 2
77 2 165 82.5 0.5
70 2 171 85.5 0.5
88 2 175 87.5 0.5
85 2 179 89.5 0.5
83 2 173 86.5 40.5
80 2 162 81 32
90 2 182 91 8
72 2 173 86.5 12.5
75 2 167 83.5 0.5
85 2 173 86.5 60.5
93 2 186 93 2
Test 2 12 1017 84.75 17.11364
Test 3 12 1057 88.08333 15.90152
ANOVA
Source of Variation SS df MS F P-value F crit
Rows 269.8333 11 24.5303 2.891071 0.046104 2.817927
Columns 66.66667 1 66.66667 7.857143 0.01718 4.844338
Error 93.33333 11 8.484848
Total 429.8333 23
Biology scores by class
Section 1 Section 2
85.6 99.3 (this is an example of how to do a random number generator)
97.9 73.7
95.1 88.0
77.8 75.7
87.6 90.1
85.7 78.6
75.2 73.0
74.7 89.2
98.9 75.7
98.1 79.3
81.4 99.8
77.8 93.5
91.1 80.5
93.2 73.3
81.8 73.7
85.0 74.1
83.3 99.8
88.3 81.5
97.2 83.8
90.3 77.5