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Data Set 1.
For this task I have chosen paired t-tests for all pairs of values (since there were measurements for each subject in two different conditions), and one-tail p-value, since the dive reflex is stated to work in one direction only:

1) Analyze the data to see if there is a significant difference between the means
2) Prepare a graphical representation of the data indicating which if any of the results are statistically significant. Data should be expressed as mean ± SEM.
3) Include a figure legend to accompany this graph and describe your results in the text.
4) Can we make any conclusions regarding the cue/s responsible for initiating the
dive reflex based on these results?

Significant difference between resting and simulated dive (analyzing effect of simulated dive)
Resting Simulated Dive
75 24
81 17
68 44
73 45
58 22
38 36
78 49
62 53
66 28
63 38
84 53
68 13
73 60
70 35
59 18
67 34
79 66
87 46
75 42
80 34
65 33
83 19
78 61
57 43
71 22
79 32
70 65

Paired t test
P value
The one-tailed P value is < 0.0001, considered extremely significant.
t = 9.957 with 26 degrees of freedom.
95% confidence interval
Mean difference = 32.407 (Mean of paired differences)
The 95% confidence interval of the difference: 25.717 to 39.097
Assumption test: Was the pairing effective?
Correlation coefficient (r) = 0.1740
The one-tailed P value is 0.1928, considered not significant.

Summary of Data

Parameter: Column A Column B Difference
Mean: 70.630 38.222 32.407
# of points: 27 27 27
Std deviation: 10.474 15.225 16.912
Std error: 2.016 2.930 3.255
Minimum: 38.000 13.000 2.000
Maximum: 87.000 66.000 64.000
Median: 71.000 36.000 33.000
Lower 95% CI: 66.485 32.198 25.716
Upper 95% CI: 74.774 44.246 39.099

Significant difference between resting and breath hold in air (analyzing effect of breath hold separately studied)
Resting Breath hold in air
75 60
81 79
68 82
73 76
58 65
38 35
78 59
62 61
66 60
63 61
84 85
68 68
73 70
70 48
59 46
67 67
79 78
87 82
75 69
80 68
65 61
83 78
78 62
57 54
71 65
79 60
70 78
Paired t test
P value
The one-tailed P value is 0.0035, considered very significant.
t = 2.924 with 26 degrees of freedom.
95% confidence interval
Mean difference = 4.815 (Mean of paired differences)
The 95% confidence interval of the difference: 1.430 to 8.200
Assumption test: Was the pairing effective?
Correlation coefficient (r) = 0.7146
The one-tailed P value is < 0.0001, considered extremely significant.

Summary of Data

Parameter: Column A Column B Difference
Mean: 70.630 65.815 4.815
# of points: 27 27 27
Std deviation: 10.474 11.907 8.558
Std error: 2.016 2.291 1.647
Minimum: 38.000 35.000 -14.000
Maximum: 87.000 85.000 22.000
Median: 71.000 65.000 3.000
Lower 95% CI: 66.485 61.104 1.429
Upper 95% CI: 74.774 70.526 8.201

 
Significant difference between simulated dive and breath hold in air (effect of cold water submersion in presence of apnea)

Simulated Dive Breath hold in air
24 60
17 79
44 82
45 76
22 65
36 35
49 59
53 61
28 60
38 61
53 85
13 68
60 70
35 48
18 46
34 67
66 78
46 82
42 69
34 68
33 61
19 78
61 62
43 54
22 65
32 60
65 78
Paired t test
P value
The one-tailed P value is < 0.0001, considered extremely significant.
t = 8.580 with 26 degrees of freedom.
95% confidence interval
Mean difference = -27.593 (Mean of paired differences)
The 95% confidence interval of the difference: -34.203 to -20.982
Assumption test: Was the pairing effective?
Correlation coefficient (r) = 0.2601
The one-tailed P value is 0.0950, considered not quite significant.

Summary of Data

Parameter: Column A Column B Difference
Mean: 38.222 65.815 -27.593
# of points: 27 27 27
Std deviation: 15.225 11.907 16.711
Std error: 2.930 2.291 3.216
Minimum: 13.000 35.000 -62.000
Maximum: 66.000 85.000 1.000
Median: 36.000 65.000 -28.000
Lower 95% CI: 32.198 61.104 -34.205
Upper 95% CI: 44.246 70.526 -20.981

 
Significant difference between snorkel + dive and snorkel + air (effect of cold water submersion)

Snorkel + Dive Snorkel in Air
56 55
19 73
52 57
16 76
25 64
36 38
62 67
51 67
22 33
40 77
57 83
33 41
69 70
18 60
33 48
58 61
19 28
62 77
50 70
70 78
53 66
25 79
17 17
61 50
62 83
27 74
62 68

Paired t test
P value
The one-tailed P value is < 0.0001, considered extremely significant.
t = 5.008 with 26 degrees of freedom.
95% confidence interval
Mean difference = -18.704 (Mean of paired differences)
The 95% confidence interval of the difference: -26.381 to -11.026
Assumption test: Was the pairing effective?
Correlation coefficient (r) = 0.4197
The one-tailed P value is 0.0146, considered significant.

Summary of Data

Parameter: Column A Column B Difference
Mean: 42.778 61.481 -18.704
# of points: 27 27 27
Std deviation: 18.440 17.566 19.408
Std error: 3.549 3.381 3.735
Minimum: 16.000 17.000 -60.000
Maximum: 70.000 83.000 11.000
Median: 50.000 67.000 -13.000
Lower 95% CI: 35.482 54.531 -26.383
Upper 95% CI: 50.074 68.432 -11.024

Significant difference between Cold Gel pack / breathing and Cold gel pack / breath hold (effect of breath hold in presence of cold temperature)
Cold Gel pack / breathing Cold gel pack / breath hold
56 50
31 49
62 52
20 55
57 60
37 38
38 18
61 60
33 55
53 64
77 90
53 41
68 69
34 67
53 63
57 31
15 62
65 63
55 53
66 66
50 52
73 23
38 37
50 56
36 31
44 20
68 62
Paired t test
P value
The one-tailed P value is 0.3612, considered not significant.
t = 0.3591 with 26 degrees of freedom.
95% confidence interval
Mean difference = -1.370 (Mean of paired differences)
The 95% confidence interval of the difference: -9.215 to 6.474
Assumption test: Was the pairing effective?
Correlation coefficient (r) = 0.2653
The one-tailed P value is 0.0905, considered not quite significant.

Summary of Data

Parameter: Column A Column B Difference
Mean: 50.000 51.370 -1.370
# of points: 27 27 27
Std deviation: 15.882 16.814 19.830
Std error: 3.056 3.236 3.816
Minimum: 15.000 18.000 -47.000
Maximum: 77.000 90.000 50.000
Median: 53.000 55.000 0.000
Lower 95% CI: 43.716 44.718 -9.217
Upper 95% CI: 56.284 58.023 6.476

Significant difference between RT gel pack / breathing and RT gel pack / breath hold (effect of breath hold in presence of warm temperature)

RT gel pack / breath hold RT gel pack / breathing
72 54
58 50
56 52
76 74
53 60
47 37
66 68
59 63
50 57
70 55
93 84
70 55
65 68
59 45
54 32
61 65
24 76
84 83
72 74
90 88
64 70
81 71
61 66
57 46
75 71
32 66
68 23

Paired t test
P value
The one-tailed P value is 0.2431, considered not significant.
t = 0.7065 with 26 degrees of freedom.
95% confidence interval
Mean difference = 2.370 (Mean of paired differences)
The 95% confidence interval of the difference: -4.526 to 9.267
Assumption test: Was the pairing effective?
Correlation coefficient (r) = 0.3763
The one-tailed P value is 0.0265, considered significant.
Summary of Data

Parameter: Column A Column B Difference
Mean: 63.593 61.222 2.370
# of points: 27 27 27
Std deviation: 15.485 15.732 17.434
Std error: 2.980 3.028 3.355
Minimum: 24.000 23.000 -52.000
Maximum: 93.000 88.000 45.000
Median: 64.000 65.000 2.000
Lower 95% CI: 57.465 54.998 -4.528
Upper 95% CI: 69.720 67.447 9.268

Significant difference between cold gel pack / breathing and RT gel pack / breathing (effect of cold temperature in absence of breath hold)
Cold Gel pack / breathing RT gel pack / breathing
56 54
31 50
62 52
20 74
57 60
37 37
38 68
61 63
33 57
53 55
77 84
53 55
68 68
34 45
53 32
57 65
15 76
65 83
55 74
66 88
50 70
73 71
38 66
50 46
36 71
44 66
68 23

Paired t test
P value
The one-tailed P value is 0.0058, considered very significant.
t = 2.716 with 26 degrees of freedom.
95% confidence interval
Mean difference = -11.222 (Mean of paired differences)
The 95% confidence interval of the difference: -19.714 to -2.731
Assumption test: Was the pairing effective?
Correlation coefficient (r) = 0.07789
The one-tailed P value is 0.3497, considered not significant.

Summary of Data

Parameter: Column A Column B Difference
Mean: 50.000 61.222 -11.222
# of points: 27 27 27
Std deviation: 15.882 15.732 21.466
Std error: 3.056 3.028 4.131
Minimum: 15.000 23.000 -61.000
Maximum: 77.000 88.000 45.000
Median: 53.000 65.000 -8.000
Lower 95% CI: 43.716 54.998 -19.716
Upper 95% CI: 56.284 67.447 -2.729

 
Significant difference between cold gel pack / breath hold and RT gel pack / breath hold (effect of cold temperature in presence of breath hold)

Cold gel pack / breath hold RT gel pack / breath hold
50 72
49 58
52 56
55 76
60 53
38 47
18 66
60 59
55 50
64 70
90 93
41 70
69 65
67 59
63 54
31 61
62 24
63 84
53 72
66 90
52 64
23 81
37 61
56 57
31 75
20 32
62 68

Paired t test
P value
The one-tailed P value is 0.0019, considered very significant.
t = 3.173 with 26 degrees of freedom.
95% confidence interval
Mean difference = -12.222 (Mean of paired differences)
The 95% confidence interval of the difference: -20.141 to -4.304
Assumption test: Was the pairing effective?
Correlation coefficient (r) = 0.2339
The one-tailed P value is 0.1202, considered not significant.

Summary of Data

Parameter: Column A Column B Difference
Mean: 51.370 63.593 -12.222
# of points: 27 27 27
Std deviation: 16.814 15.485 20.018
Std error: 3.236 2.980 3.852
Minimum: 18.000 24.000 -58.000
Maximum: 90.000 93.000 38.000
Median: 55.000 64.000 -9.000
Lower 95% CI: 44.718 57.465 -20.143
Upper 95% CI: 58.023 69.720 -4.302

Summary

Compared measurements Studied effect Significant difference (p-value) Significant difference (conclusion) Effective pairing (p-value) Effective pairing (conclusion)
resting and simulated dive effect of simulated dive p<0.0001 extremely significant 0.1928 not significant
resting and breath hold in air effect of breath hold 0.0035 very significant p<0.0001 extremely significant
simulated dive and breath hold in air effect of water submersion in presence of apnea p<0.0001 extremely significant 0.0950 not quite significant
snorkel + dive and snorkel + ai effect of water submersion p<0.0001 extremely significant 0.0146 significant
Cold Gel pack / breathing and Cold gel pack / breath hold effect of breath hold in presence of cold temperature 0.3612 not significant 0.2653 not quite significant
RT gel pack / breathing and RT gel pack / breath hold effect of breath hold in presence of warm temperature 0.2431 not significant 0.0265 significant
cold gel pack / breathing and RT gel pack / breathing effect of cold temperature in absence of breath hold 0.0058 very significant 0.3497 not significant
cold gel pack / breath hold and RT gel pack / breath hold effect of cold temperature in presence of breath hold 0.0019 very significant 0.1202 not significant

It is possible to see that all components of dive reflex have an influence on heart rate. First of all, dive reflex itself makes a significant difference compared to resting (in heart rate measurement). There is also significant statistical difference in heart rates concerning the effect of breath hold. Finally, cold water submersion has a considerable effect both in presence of breath hold and in absence of breath hold. Thus, we have identified two components –water submersion and breath hold – that are cues responsible for initiating the dive reflex. Applying gel packs while breath holding, however, shows no significant difference; there was no effect of breath hold in presence of cold and warm temperatures correspondingly. However, there is significant difference in heart rate when cold temperature is applied, both when breathing and during breath hold. Thus, cold temperature is also a cue responsible for the dive reflex.