statistics

Question 1

What does standard deviation (s) show in a sample that is normally distributed?

Answer 1

The spread of data about the mean, 𝑥

Standard deviation helps to understand how data points deviate from the average.

Question 2

What does a small value of standard deviation indicate?

Answer 2

Data is less scattered, more consistent and reliable

A small standard deviation suggests that the values are close to the mean.

Question 3

What does a large value of standard deviation indicate?

Answer 3

Data is widely spread, results are less reliable

A large standard deviation suggests that the values are spread out over a wider range.

Question 4

What are two other functions of standard deviation?

Answer 4

• To calculate standard error
• To calculate t-test value

Standard deviation is useful in various statistical analyses.

Question 5

True or False: In mathematics, standard deviation is calculated for a sample.

Answer 5

False

In mathematics, standard deviation is typically calculated for a population.

Question 6

Fill in the blank: In biology, we learn the standard deviation of a _______.

Answer 6

[sample]

This is distinct from the standard deviation of a population learned in mathematics.

Question 7

What does Standard Error (SM) indicate?

Answer 7

It shows how close the mean of a sample calculated is from the true mean of the population

SM reflects the reliability of the mean

Question 8

How is Standard Error (SM) used in graphical representations?

Answer 8

It is used to put error bars on graphs

Error bars visually represent the uncertainty in the mean value

Question 9

What does a small value of Standard Error indicate?

Answer 9

The sample mean value is closer to the actual mean and the mean is more reliable

A small SM enhances confidence in the sample mean’s accuracy

Question 10

What is the range of Standard Error (SM) values?

Answer 10

SM value is between 0 and 1

0 indicates no error and 1 indicates maximum error

Question 11

What is required to create bar charts with error bars?

Answer 11

1) Mean, 𝑥 = value for y coordinates
2) Standard error, SM
3) Error bars = lines on bar charts

These elements are essential for accurately representing data variability.

Question 12

How are error bars calculated?

Answer 12

Error bars are calculated using upper and lower limits of a 95% confidence interval, that is mean ± 2 SM

SM stands for standard error of the mean.

Question 13

What is the function of error bars on bar charts?

Answer 13

To see if there is a significant difference between two means

Error bars help visualize the uncertainty around the mean estimates.

Question 14

What is a 95% confidence interval?

Answer 14

Interval where 95% of the sample’s data lies around the mean

The confidence interval provides a range of values that likely contain the population parameter.

Question 15

What are the upper and lower limits of the 95% confidence interval?

Answer 15

Min and max limit of the 95% interval

These limits indicate the range within which the true population mean is expected to fall.

Question 16

How is the 95% confidence interval calculated?

Answer 16

Mean ± 2SM

SM stands for standard error of the mean, which is derived from the sample standard deviation.

Question 17

What does it indicate when error bars overlap?

Answer 17

The two means are not significantly different

Null hypothesis is accepted

Question 18

What does it indicate when error bars don’t overlap?

Answer 18

The two means are significantly different

Null hypothesis is rejected

Question 19

What should be done to double check the results of error bars interpretation?

Answer 19

Perform a t-test

This helps confirm the significance of the difference between means.

Question 20

What is a t-test used for?

Answer 20

To test whether data from 2 samples are significantly different

A t-test helps determine if the means of two groups are statistically different from each other.

Question 21

What type of data is required for a t-test?

Answer 21

Continuous / interval data

Continuous data can take any value within a range, while interval data is numerical data where the difference between values is meaningful.

Question 22

What distribution requirement must data meet for a t-test?

Answer 22

Data must be normally distributed

Normal distribution is a probability distribution that is symmetric about the mean.

Question 23

What is a requirement regarding the standard deviations for a t-test?

Answer 23

Standard deviations are approximately the same

This assumption is known as homogeneity of variance.

Question 24

When value of
t calculated > critical value

Answer 24

2 sets of data are sigficantly diffrent
Null Hypothesis is rejected
diffrence is NOT due to chance

Question 25

when critival value > t calculated

Answer 25

2 sets of data are NOT significantly diffrent Null Hypothesis is accepted any diffrences are due to chance

Question 26

What is the maximum number of values in each sample for a t-test?

Answer 26

Less than 30 values each ## Footnote This is to ensure the validity of the t-test assumptions.

Question 27

testing for photosynthesis

Answer 27

Detecting for reduced NAD (redox indicators) DCPIP turns from blue to colorless when NADR releases H+ reducing DCPIP DCPIP turns from blue to colorless when electron from PSI or PSII release an electron reducing DCPIP | more light= more e- = high rate of DCPIP decolorization

Question 28

Spearman’s rank correlation test can be used to determine whether there is correlation between variables when:

Answer 28

Data is not quantitative, e.g. an abundance scale has been used rather than a count of individuals A visual inspection of data suggests a non-linear correlation Data may not be normally distributed

Question 29

Pearson's linear correlation is a statistical test that determines whether there is linear correlation between two variables The data must:

Answer 29

Be quantitative, e.g. the number of individuals has been counted and a numerical value recorded Show a linear relationship upon visual inspection Show a normal distribution

Question 30

the student analysed using spearman's rank correlation test state 3 reasons why this statistical test is a suitable way to analyse the data about species diversity | 9700/51/o/n/21

Answer 30

data is paired species and abiotic factor is independant non linear relationship data is discrete

Question 31

state why they decided to calculate standard error | 9700/51/m/j/20

Answer 31

To find the closessness to the true mean to graph error bars

Question 32

state additional informaation about the data that can ained from the calculated values of 95% CI | 9700/52/f/m/21

Answer 32

95% probability the actual mean is close within limits the diffrence b/w mean is significantt for trampled and untrampled The narrower the untrampled CI the closer the calculated mean to the true mean

Question 33

explain why they used t-test to analyse the data | 9700/51/m/j/20

Answer 33

data is continous and normally distributed comparingg the 2 sets of mean

Question 34

how is the volume of CO2 determined in an experiment

Answer 34

placing an inert material in the test tube