Me, Myself and I

Question 1

What can we find in the natural world?

Answer 1

Massive amounts of diversity within and between: plants, animals, bacteria, fungi and so on. To understand this diversity we will need to be able to quantifiably measure it.

Question 2

Give examples of variations in humans.

Answer 2

Examples of variations within humans include:

• cognitive ability
• personality
• physical appearance (body shape, skin color, etc.)
• immunology
• height

Question 3

What can we do once we understand a set of data?

Answer 3

Once we can understand a set of data we can use it to make helpful and meaningful predictions. For example, trends in global warming and predict how it will progress and affect the climate.

Question 4

Code for a histogram on R.

Answer 4

You can simply make a histogram by using the hist() function.

Question 5

Code for a specific column of a dataset.

Answer 5

select only a specific column of a dataset, x, to make a histogram, you will have to use the hist() function with the dataset name (x) in combination with the $ sign, followed by the column name

Question 6

How would you present data from a histogram on a finer scale?

Answer 6

One would use the hist() function with the “, breaks = n”. Like so:

hist(x, breaks = 50)

Question 7

What is a sampling error?

Answer 7

Sampling error is the random variation introduced into a dataset as a function of only sampling a subset of the total population [or possible experiments].

Question 8

How would you obtain a numerical description of a datacolumn within a dataset? In this case the dataset will be named, “x” and the datacolumn in question will be named, “age”.

Answer 8

To obtain a numerical description of a datacolumn within a dataset one would use the function:

summary(x$age)

It will present the minimum value, the maximum value, the median value, the mean and the lower and upper quartiles.

Question 9

How would you find the mean, median, max, min values of the “age” data column within dataset “x”?

Answer 9

You’d get the mean, median, max, min values of the “age” data column within dataset “x” with the following functions:

• mean(x$age)
• median(x$age)
• max(x$age)
• min(x$age)

Question 10

What is a data population?

Answer 10

A data population is all members of a defined group.

Question 11

What is a sample?

Question 12

What is a sampling bias?

Answer 12

In statistics, sampling bias is a bias in which a sample is collected in such a way that some members of the intended population have a lower or higher sampling probability than others.

Question 13

How would you obtain a numerical description of 10 random values in the datacolumn of “age” from dataset “x”?

Answer 13

To obtain a numerical description of 10 random values in the datacolumn of “age” from dataset “x” you would use the function:

summary(sample(x$age, 10)).

Question 14

Why are humans different heights?

Answer 14

Humans are different heights for the following reasons:

• genetics (nature): The main factor that influences a person’s height is their genetic makeup. However, many other factors can influence height during development, including nutrition, hormones, activity levels, and medical conditions. Scientists believe that genetic makeup, or DNA, is responsible for about 80% of a person’s height
• environment (nurture): environmental factors such as nutrition and exercise can affect growth during development

Question 15

What is a factor in R?

Answer 15

Conceptually, factors are variables in R which take on a limited number of different values; such variables are often refered to as categorical variables.

Question 16

GIve an example of what would class as a factor in R

Answer 16

An example of what would class as a factor in R would be sex for example. Male/Female.

Question 17

How would you create a barchart to compare two datacolumns of “sex” in the dataset “x”?

Answer 17

To create a barchart in R you would use the function:

barplot(table(x$age))

Question 18

How would you form a table in R?

Answer 18

You can form a table with the function:

table()

Question 19

How would you form a barchart for “sex” based on proportions from dataset “x”?

Answer 19

You would form a barchart for sex based on proprtions by using the function:

prop.table(table(x$sex))

You can also make the proportions show on the barchart scale by nesting the above function into the barplot() function as so:

barplot(prop.table(table(x$sex)))

Question 20

What is the Null Hypothesis?

Answer 20

A Null Hypothesis isthe default expectation that there is no relationship between two measured phenomena, that categorical outcomes are all equally likely, or there is no association between groups.

Question 21

What is H₁ (an alternative hypthesis)?

Answer 21

H₁ is the expectation that there is a relationship between two measured phenomena, or an association among groups, or that categorical outcomes are not all equally likely.

Question 22

When can the chi squared test (X²) be used?

Answer 22

The chi squared test (X²) can be used where the observations are assigned into mutually exclusive classes.

Question 23

Breakdown chi squared test (X²).

Answer 23

In the chi squared test (X²) the number of observations in each mutually exclusive class i.e. “male or female” are compared to those under the Null Hypothesis.

X² = Σ(d²/e)

d (difference) = o (observed) - e (expected)

Σ = Sum of

Question 24

How would one calculate the number of degrees of freedom?

Answer 24

The No. of degrees of freedom = (no. of rows - 1) x (no. columns -1)

if there is only one column, the degrees of freedom = No. of rows - 1 instead.

Question 25

What are the degrees of freedom and why is it impossible for it be 0?

Answer 25

Degrees of Freedom refers to the maximum number of logically independent values, which are values that have the freedom to vary, in the data sample. So if there were 0 independent values there wouldn’t be anything to test!

Question 26

What is the p-value?

Answer 26

The p-value is the probability of obtaining test results at least as extreme as the results actually observed, under the assumption that the null hypothesis is correct.

Question 27

How would you add purple colour in R?

Answer 27

You’d add purple colour in R with the function:

col = c(“purple”)

Question 28

How would you perform a chi squareed test for sex in dataset x in R?

Answer 28

You’d perform a chi squared test as follows:

chisq.test(table(x$sex))

Question 29

What should you be more inclined to do if the p value in a chi squared test is very small?

Answer 29

If p is very small, we are more inclined to believe that our data diverges from the null hypothesis. We are also more inclined to believe that an alternative hypothesis explains our data.

Question 30

How would you look at the height of males in sex data column of dataset x in R?

Answer 30

hist(x$sex ==”Male”)

To add women into the same graph you code:

hist(x$sex ==”Female”) , add TRUE

Question 31

What is the rgb function?

Answer 31

This function creates colors corresponding to the given intensities (between 0 and max) of the red, green and blue primaries. The colour specification refers to the standard sRGB colorspace (IEC standard 61966).

An alpha transparency value can also be specified (as an opacity, so 0 means fully transparent and max means opaque). If alpha is not specified, an opaque colour is generated.

The names argument may be used to provide names for the colors.

The values returned by these functions can be used with a col= specification in graphics functions or in par

Question 32

What is a type 1 and type 2 error?

Answer 32

In statistical hypothesis testing, a type I error is the rejection of a true null hypothesis, while a type II error is the non-rejection of a false null hypothesis.

Question 33

What is a post hoc test?

Answer 33

In a scientific study, post hoc analysis consists of statistical analyses that were specified after the data were seen.

Question 34

What does the t-test determine?

Answer 34

The t-test determines whether the mean of one group is statistically different from the mean of another group.

Question 35

What is the t-test function in R?

Answer 35

The t-test function in R is as follows

t.test()

Question 36

What is the version of the t-test that R uses?

Answer 36

The version of the t-test that R uses is the Welch t-test.

Question 37

What is the t value in the t test?

Answer 37

The t-value measures the size of the difference relative to the variation in your sample data. Put another way, T is simply the calculated difference represented in units of standard error. The greater the magnitude of T, the greater the evidence against the null hypothesis.

Question 38

How would you plot two continuous variables?

Answer 38

You would plot two continuous variables on a line graph.

Question 39

What is the function for a scatter plot?

Answer 39

The function for a scatter plot is:

plot()

Question 40

What are explanatory and response variables?

Answer 40

The response variable is the focus of a question in a study or experiment. An explanatory variable is one that explains changes in that variable. It can be anything that might affect the response variable.

Question 41

What are residuals in a scatter plot with a line of best fit?

Answer 41

Residuals are the differences between the observed values and those predicted by the regression line.

Question 42

How can one determine the line of best fit using R?

Answer 42

To determine the line of best fit on R is as follows:

lm(response data ~ explanatory data)

Question 43

What does the abline function do?

Answer 43

Fits the line of best fit onto lm function:

abline(lm(response data ~ explanatory data)))

This data can be summarised by nesting it into the summary() function.

Question 44

What is the formula for a straight line on a graph?

Answer 44

The formula for a straight line on a graph is:

y = mx + c

Question 45

What is a linear regression model?

Answer 45

In statistics, linear regression is a linear approach to modeling the relationship between a scalar response (or dependent variable) and one or more explanatory variables (or independent variables).

Question 46

What is the y intercept?

Answer 46

The y-intercept or vertical intercept is a point where the graph of a function or relation intersects the y-axis of the coordinate system. As such, these points satisfy x = 0.

Question 47

How is the gradient of a line on a graph calculated?

Answer 47

For a straight-line graph, pick two points on the graph. The gradient of the line = (change in y-coordinate)/(change in x-coordinate) . We can, of course, use this to find the equation of the line.

Question 48

What does the Welch’s and Student’s t-test assume?

Answer 48

Assumptions. Student’s t-test assumes that the two population(being compared) distributions are normally distributed with equal variance. Welch’s t-test is designed for unequal sample distribution variance, but the assumption of sample distribution normality is maintained.

Question 49

What is the variance?

Answer 49

Variance measures how far a set of data is spread out. A variance of zero indicates that all of the data values are identical. A high variance indicates that the data points are very spread out from the mean, and from one another. Variance is the average of the squared distances from each point to the mean.

Question 50

What is the R squared value?

Answer 50

R-squared is a statistical measure of how close the data are to the fitted regression line. It is also known as the coefficient of determination, or the coefficient of multiple determination for multiple regression. … 100% indicates that the model explains all the variability of the response data around its mean.

Question 51

What is the adjusted R square Value?

Answer 51

Adjusted R-squared, a modified version of R-squared, adds precision and reliability by considering the impact of additional independent variables that tend to skew the results of R-squared measurements.

Question 52

What is the General Linear Model Overview?

Answer 52

GLM Overview

Data = Model + Error

Model ususally takes the format of:

Y = B + MX

M being the gradient of the regression line

X being the explanatory variable

Y being the response variable

B is essentially the y intercept/ The satrting point of the ab line.

Question 53

What is error?

Answer 53

Error doesn’t mean the data is incorrect, it is a deviation from the regression model. The data isn’t wrong, the model is.

Question 54

What does it mean if adjusted R squared value is negative?

Answer 54

Means there’s no association between the two variables.

Question 55

What is a biphasic response in a regression model?

Answer 55

A biphasic response is observed in a regression model when the response variable displays two different correlations with the explanatory variable.

Question 56

What does the R squared value tell you?

Answer 56

R-squared (R²) is a statistical measure that represents the proportion of the variance for a dependent variable that’s explained by an independent variable or variables in a regression model.

Question 57

What is an ordinal scale?

Answer 57

Ordinal Scale is defined as a variable measurement scale used to simply depict the order of variables and not the difference between each of the variables. These scales are generally used to depict non-mathematical ideas such as frequency, satisfaction, happiness, a degree of pain, etc.

E.g. How was work today?

1 - Good

2 - Meh

3 - Shit

Question 58

What is variance? How is it calculated?

Answer 58

The variance is the average of the squared differences from the Mean.

• Work out the Mean (the simple average of the numbers)
• Then for each number: subtract the Mean and square the result (the squared difference).
• Then work out the average of those squared differences.

Question 59

What is a 95% confidence interval?

Answer 59

A Confidence Interval is a range of values we are fairly sure our true value lies in.

The “95%” says that 95% of experiments like we just did will include the true mean, but 5% won’t.

So there is a 1-in-20 chance (5%) that our Confidence Interval does NOT include the true mean.

Question 60

What is a point estimate?

Answer 60

In statistics, point estimation involves the use of sample data to calculate a single value which is to serve as a “best guess” or “best estimate” of an unknown population parameter.

Question 61

What is meta-analysis in research?

Answer 61

A meta-analysis is a statistical analysis that combines the results of multiple scientific studies.

Question 62

What is the Fisher’s exact test and how is it calculated?

Answer 62

Fisher’s exact test is a statistical significance test used in the analysis of contingency tables. Although in practice it is employed when sample sizes are small, it is valid for all sample sizes.

Question 63

What is a multivariate model?

Answer 63

The multivariate model is a popular statistical tool that uses multiple variables to forecast possible outcomes.

Question 64

What are the components of the ideal experiment?

Answer 64

The components of the ideal experiment:

• Define your hypothesis
• Design an experiment to collect the data
• Design your statistical testing plan in advance
• Conduct your experiment
• Analyse the data
• Publish the results (positive or negative)
• [conduct any post hoc analyses]
• Formulate new hypotheses.

Question 65

What is cross sectional and longitudinal research?

Answer 65

A longitudinal study requires a researcher to revisit participants of the study at proper intervals. Cross-sectional study is conducted with different samples. Longitudinal study is conducted with the same sample over the years. Cross-sectional studies cannot pin down cause-and-effect relationship.