Module 1: development of practical skills

Question 1

Define standard deviation

Answer 1

How spread out repeats are from the mean

Question 2

Benefits of standard deviation

Answer 2

Shows the spread of data around the mean, whereas range shows difference between highest and lowest value
Reduces the effect of anomalies
Can be used to indicate whether a difference between results is significant

Question 3

Why is standard deviation useful for a conclusion

Answer 3

Add or subtract the standard deviation from mean results.
No overlap between the grouped results - likely to be a significant difference.
Overlap between grouped results - unlikely to be a significant difference

Question 4

Conclusions using S.D.

A- Mean 11, S.D 3.2
B- Mean 8, S.D 2.8
C - Mean 1, S.D 1.3

Evaluate the conclusion that there is no significant difference between the three groups. Using evidence from the results above.

Answer 4

1. Calculate the spread of data for each group by adding and subtracting the S.D. from the mean
2. Compare spread of data for any overlap
3. State evidence for and against the conclusion
4. Add context of the question (e.g. refer to the specific investigation)

The standard deviations for group A and B overlap - there is likely no significant difference between the groups.
The standard deviation for group C does not overlap with either A or B - there is likely to be a significant difference. It is significantly lower.

Question 5

What is a P-value (also significance level)

Answer 5

The probability that a result is due to chance

Question 6

How to answer statistic question

Answer 6

1. Justify use of statistic
2. Write a null hypothesis
3. State a conclusion

Question 7

Write a null hypothesis based on an investigation between two variables for a correlation coefficient statistic

Answer 7

There is NO SIGNIFICANT CORRELATION between the two variables

Question 8

When to use correlation coefficient

Answer 8

Continuous data
Investigating an association between two measurements

Question 9

Spearman’s rank correlation coefficient (rs) = 1 - 6 ∑ (d²n) divided by (n² - 1)

Answer 9

D - Difference in rank of two measurements
N - number of pairs of data

Question 10

Spearman’s rank correlation coefficient value

Answer 10

A number between -1 and +1
-1 is perfect negative correlation
+1 is perfect positive correlation
0 is no correlation

This value is then compared to a critical values table to conclude whether or not to accept the null hypothesis

Question 11

Steps to calculate spearman’s rank correlation

Answer 11

1. Rank reach set of data (1 being the smallest)
2. Find the difference in rank between the two variables
3. Square the difference
4. Substitute appropriate values into equation given to you

Question 12

How to compare the spearman’s rank correlation coefficient to a critical value table.

Answer 12

1. For the value of n, find the critical value at the 0.05 significance level/p-value
2. If the spearman’s rank correlation coefficient is lower than the critical value - accept the null hypothesis
3. If the spearman’s rank correlation coefficient is higher than the critical value - reject the null hypothesis

Question 13

If the critical value for the investigation between temperature and rate of reaction is 0.6786 and the correlation coefficient is 0.616. State the conclusion.

Answer 13

0.616 is lower than the critical value of 0.6786 at the 5% significance level.
Insufficient evidence to suggest a correlation between temperature and rate of reaction.
We accept the null hypothesis.

Question 14

When to use Student T-Test

Answer 14

Continuous data
Investigating the difference between two means

Question 15

Write a null hypothesis based on an investigation between two variables for a T-test statistic

Answer 15

There is no significant difference between the means of the two variables

Question 16

Student T-test equation
t = (X̄₁ - X̄₂) / √[(s₁² / n₁) + (s₂² / n₂)]

Answer 16

X̄₁ = mean of group 1
X̄₂ = mean of group 2
s₁² = s.d. of group 1
s₂² = s.d. of group 2
n₁ = sample size of group 1
n₂ = sample size of group 2

Question 17

Paired T-test
what type of data is used
How is degrees of freedom calculated

Answer 17

Two sets of data are from:
- from the same individual
- Both groups have the same sample size

degrees of freedom = n-1

Question 18

Unpaired T-test
What type of data is used
How is degrees of freedom calculated

Answer 18

Groups have different sample sizes

Degrees of freedom = n₁ +
n₂ - 2

Question 19

How to compare a calculated Student T-test value to a critical value

Answer 19

1. Calculate degrees of freedom
2. Find critical value for degree of freedom value at 0.05 p value
3. T test value is greater than the critical value, reject the null hypothesis
4. T test value is lower than the critical value, accept the null hypothesis

Question 20

When to use Chi-squared?

Answer 20

Frequency data - counting individuals in a category
Investigating a difference between frequencies

Question 21

Chi squared equation
χ² = ∑((O - E)² divided by E)

Answer 21

O = observed frequency
𝐸 = expected frequency

observed - expected squared
divided by the expected frequency
calculate for individual groups
Sum of these values

Question 22

How to draw conclusion with chi-squared value.

Answer 22

1. Find critical value at p-value of 0.05/5% significance level. at corresponding degree of freedom (Df = n-1)
2. if chi squared value is greater than critical value, reject null hypothesis
3. if chi squared value is smaller than critical value, accept null hypothesis

Question 23

Write a null hypothesis based on an investigation for a chi squared statistic

Answer 23

There is no significant difference between the observed and expected value for a variable.

Question 24

How to reduce uncertainty of a measurement

Answer 24

Increase the resolution of the measurement instrument
Take repeated readings
Increasing the value of what is being measured

Question 25

How to find uncertainty for a reading (single judgement) e.g. a thermometer, mass balance?

Answer 25

the uncertainty of a reading is half of the smallest division on the measuring instrument - plus or minus

Question 26

How to find uncertainty for a measurement (two judgements) e.g. a ruler, stopwatch?

Answer 26

the uncertainty of a measurement is equal to the smallest division on the measuring instrument - plus or minus

Question 27

How to find uncertainty of a given value?

Answer 27

The uncertainty is plus or minus the last significant digit of the given value e.g. 1730g is plus or minus 10g uncertainty

Question 28

Equation to calculate percentage uncertainty

Answer 28

Uncertainty divided by measured value/measured mean value

Multiplied by 100