Question

Use ALL the data found in the Excel file for your analysis. Calculate the following:

• Run descriptive statistics for all the groups.
• Calculate an equal variance independent samples t-test for SysBP1 vs. SysBP2.
• Run an ANOVA for just SysBP1 and SysBP2.
• Note how the results of the t-test and ANOVA compare.
• Run an ANOVA using all three groups. If you reject the null hypothesis, use the post hoc analysis shown in the Activity 3 Excel file

• SysBP1 148 114 120 130 124 126 138 118 118 130 142 128 164 136 120 134 148 132 124 142 136 110 124 152 134 155 156 150 130 112 104 142 114 128 118 142 132 122 118 130 130 138 128 132 120 120 152 134 128 128 132 112 126 134 120 132 108 116 142 144 144 136 124 118 154 120 110 136 114 108 136 122 138 118 130 158 114 118 122 128 130 158 112 120 146 130 120 154 120 120 144 128 162 138 158 135 129 110 124 118 112 132 146 110 118 118 122 136 130 106 142 124 134 134 126 126 130 126 118 118 108 118 134 108 138 114 132 158 126 128 120 122 138 124 120 108 124 122 138 126 136 128 138 122 112 110 120 132 116 124 124 132 140 124 138 112 128 120 132 112 132 122 160 124 150 102 110 126 130 134 136 130 142 112 114 120 140 118 98 120 134 124 116 122 124 118 122 136 130 112 134 114 108 132 104 118 120 136 136 128 127 112 118 138 136 120 110 120 106 122 114 126 116 128 128 118 114 120 110 134 138 152 100 108 124 134 116 122 130 118 114 116 126 122 122 140 114 130 118 122 100 142 136 100 124 114 148 118 120 118 126 118 118 120 128 117 130 126 122 128 118 130 128 110 114 112 118 112 140 134 120

  SysBP2 152 118 124 134 128 130 142 122 122 134 146 132 168 140 124 138 152 136 128 146 140 114 128 156 138 159 160 154 134 116 108 149 121 135 125 149 139 129 125 137 137 145 135 139 127 127 159 141 135 135 139 119 133 141 127 139 115 123 149 151 151 143 131 125 161 127 117 143 121 109 137 123 139 119 131 159 115 119 123 129 131 159 113 121 147 131 121 155 121 121 145 129 163 139 159 136 130 111 122 116 110 130 144 108 116 116 120 134 128 104 140 122 132 132 124 124 128 124 116 116 106 116 132 106 136 112 130 156 124 126 139 139 131 131 135 131 123 123 113 123 139 113 143 119 137 163 131 133 125 127 143 129 125 113 129 127 143 131 141 133 143 127 117 115 125 98 106 122 126 130 132 126 138 108 110 116 136 114 94 116 130 120 112 118 120 114 118 132 126 108 130 110 104 128 100 114 116 132 132 124 123 108 114 138 136 120 110 120 106 122 114 126 116 128 128 118 114 120 110 134 138 152 100 108 124 131 113 119 127 115 111 113 123 119 119 137 111 127 115 119 97 139 133 97 121 111 145 115 117 115 123 128 128 130 138 127 140 136 132 138 128 140 138 120 124 122 128 122 150 144 130

  SysBP3 150 137 125 141 139 155 143 153 145 155 139 129 127 137 110 118 134 138 142 144 138 150 120 122 128 148 126 106 128 142 132 124 130 132 126 130 144 138 120 142 122 116 140 112 126 128 144 144 136 135 120 126 150 148 132 122 132 118 134 126 138 128 140 140 130 126 132 122 146 150 164 112 120 136 143 125 131 139 127 123 125 135 131 131 149 123 139 127 131 109 151 145 109 133 123 157 127 129 127 135 140 140 142 150 139 152 148 144 178 146 148 161 161 153 153 157 153 145 145 135 145 161 135 165 141 159 185 153 155 147 149 165 151 147 135 151 149 165 153 163 155 165 149 139 137 147 120 128 144 148 152 154 148 160 130 132 138 158 136 116 138 152 142 134 140 142 136 140 160 164 166 160 172 142 144 150 170 148 128 150 164 154 146 152 154 148 152 166 160 142 164 144 138 162 134 148 150 166 166 158 157 142 148 168 166 150 145 155 141 157 149 161 151 163 163 153 149 155 145 169 173 187 135 143 159 166 148 154 162 150 146 148 158 154 154 172 146 162 150 154 132 174 168 132 156 146 180 150 152 150 158 163 163 165 173 162 175 171 167 173 163 175 173 155 159 157 163 157 185 179 165

Answer 1

1)

SysBP1		SysBP2		SysBP3
Mean	126.1956	Mean	127.8708	Mean	145.8339
Standard Error	0.762546	Standard Error	0.829981	Standard Error	0.953128
Median	124	Median	127	Median	146
Mode	118	Mode	128	Mode	150
Standard Deviation	12.55309	Standard Deviation	13.66321	Standard Deviation	15.69047
Sample Variance	157.5801	Sample Variance	186.6833	Sample Variance	246.1908
Kurtosis	0.269935	Kurtosis	0.094393	Kurtosis	-0.299
Skewness	0.546977	Skewness	0.343876	Skewness	-0.00844
Range	66	Range	74	Range	81
Minimum	98	Minimum	94	Minimum	106
Maximum	164	Maximum	168	Maximum	187
Sum	34199	Sum	34653	Sum	39521
Count	271	Count	271	Count	271

2) equal variance independent samples t-test for SysBP1 vs. SysBP2.

t-Test: Two-Sample Assuming Equal Variances
	SysBP1	SysBP2
Mean	126.1956	127.8708
Variance	157.5801	186.6833
Observations	271	271
Pooled Variance	172.1317
Hypothesized Mean Difference	0
df	540
t Stat	-1.48637
P(T<=t) one-tail	0.068883
t Critical one-tail	1.64768
P(T<=t) two-tail	0.137766
t Critical two-tail	1.964367

for both one tail and two tail the p-value is more than level of significance 0.05 hence in both cases we fail to reject null hypothesis and conclude that there is no significant difference between the means of SysBP1 vs. SysBP2.

c) Run an ANOVA for just SysBP1 and SysBP2.

Anova: Single Factor

SUMMARY
Groups	Count	Sum	Average	Variance
SysBP1	271	34199	126.1956	157.5801
SysBP2	271	34653	127.8708	186.6833

ANOVA Table

Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	380.2878	1	380.2878	2.209284	0.137766	3.858737
Within Groups	92951.11	540	172.1317
Total	93331.4	541

From the ANOVA table we get p-value = 0.138 which is more than 0.05 hence we fail to reject null hypothesis and conclude that there is no significant difference between means of SysBP1 vs. SysBP2.

The results of t-test and ANOVA are giving same p-value for two tailed test and the test statistic F is the square of the test statistic t.

Run an ANOVA using all three groups.

One-way ANOVA: SysBP1, SysBP2, SysBP3

Method

Null hypothesis	All means are equal
Alternative hypothesis	Not all means are equal
Significance level	α = 0.05

Equal variances were assumed for the analysis.

Factor Information

Factor	Levels	Values
Factor	3	SysBP1, SysBP2, SysBP3

Analysis of Variance

Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	64240.13	2	32120.06	163.1967	2.8E-60	3.006839
Within Groups	159422.6	810	196.8181
Total	223662.8	812

From the ANOVA table we get p-value is < 0.001 which is less than 0.05 hence we reject null hypothesis and conclude that there is significant difference between means of SysBP1, SysBP2 SysBP3.

Tukey Pairwise Comparisons

Tukey Simultaneous Tests for Differences of Means

Difference of Levels	Difference of Means	SE of Difference	95% CI	T-Value	Adjusted P-Value
SysBP2 - SysBP1	1.68	1.21	(-1.15, 4.50)	1.39	0.346
SysBP3 - SysBP1	19.64	1.21	(16.82, 22.46)	16.29	0.000
SysBP3 - SysBP2	17.96	1.21	(15.14, 20.78)	14.90	0.000

Tukey Simultaneous 95% CIs

.

SysBP3-SYSBP1 and SysBP3-SysBP2, are significantly different.