Week 2 Statistics Af

Front 1

Variability

Back 1

Is a measure of the dispersion or spread of scores in a distribution and ranges from 0 to infinity. A measure of variability is a way to measure the dispersion or spread of scores around the mean.

Front 2

What is the simplest way to describe how dispersed scores are?

Back 2

It is to identify the range of scores in a distribution.

Front 3

The range

Back 3

Is the difference between the largest value and the smallest value in a data set.

Range= L-S

Front 4

Why is the range the most informative for data sets without outliers?

Back 4

Because the range can change dramatically with the presence of one outlier.

Front 5

Fractiles

Back 5

Are measures that divide data sets into two or more equal parts. The median is an example of a fractile, you also have quartiles (4), deciles(10) and percentiles(100).

Front 6

What are the 4 quartiles and what do they do?

Back 6

They split a data set into 4 equal parts. 25th percentile, 50th percentile, 75th percentile, 100th percentile.

Front 7

The lower quartile

Back 7

Is the median value of the lower half of a data set at the 25th percentile.

Front 8

The median quartile

Back 8

Is the median value of a data set at the 50th percentile of a distirbution.

Front 9

The upper quartile

Back 9

Is the median value of the upper half of the data set at te 75th percentile of a distribution.

Front 10

Interquartile range (IQR)

Back 10

Is the range of scores in a distribution between Q1 and Q3. Thus, the IQr is the range of scores, minus the top and the bottom 25% of scores, in a distribution.

Front 11

Semi-interquartile range

Back 11

Is used as a measure of half the distance between the upper and lower of a distributions, you can think of it as the mean IQR. So basically the IQR divided by 2.

Front 12

Variance

Back 12

Is a measure of variability for the average squared distance that scores deviate from their mean.

Front 13

Population variance

Back 13

Is a measure of variability for the average square distance that score in a population deviate from the mean. It is computed only when all scores ina given population are recorded. Population variance is stated as the symbol sigma squared. The formulation for it is in notion.

Front 14

The sum of squares (SS)

Back 14

Is the sum of the squared deviations of scores from tgeir mean.

Front 15

Sample variance

Back 15

Is a measure of variabilitt for the average squared difference that scores in a sample deviate from the mean. It is computed when only a portion or sample of data is measured in a population. The formula is in notion.

Front 16

To compute variance, we square each deviation, why do we do this?

Back 16

Basically, we need to compute a positive value for variance that is not zero. Think of any solution to avoid this zero result as intentionally making an error. To minimize error, we need to ensure that the result we obtain is the smallest possible positive value, or the value with minimal error. So basically, we do it because it provides a solution with minimal error. So squaring each deviation provides a solution for the minimal erro that we then correct by taking the square root of the variance.

Front 17

The degrees of freedom for sample variance

Back 17

Are the number of scores in a sample that are free to vary. All scores except one are free to vary in a sample.

Front 18

The standard deviation (SD)

Back 18

Also caleld the root mean square deviation, is a measure of variability for the average distance that scores deviate from their mean. It is calculated by taking the square root of the variance.

Front 19

Standard deviation formula

Back 19

write it down and check notion.

Front 20

How do we find the Standard deviation?

Back 20

We first compute the variance and then take the square root of that answer remember that our objective is to find the average distance that scores deviate from their mean and not the average squared distance that scores deviate from their mean. Taking the square root of the variance will allow us to reach this objective.

Front 21

What does the Standard deviation tell us?

Back 21

It is an estimate for the average distance that scores deviate from the mean. When scores are concentrated near the mean, the Sd is small; when scores are scattered far from the mean, the SD is larger.

Front 22

Which 3 statements can be made for normal distributions with any mean and any variance?

Back 22

1. at least 68% of all scores lie within 1 Sd of the mean.

2. At least 95% of all scores lie within 2 SD of the mean.

3. At least 99.7% of all scores lie within 3 SD of the mean.

Front 23

The empirical rule

Back 23

68% 1 SD of the mean, 95% 2 SD of the mean, 99.7% 3 SD of the mean.

The name of this rule arises because so many of the behaviours researchers observe are normally distributed. The rule is then an approximation of the fact that the percentages are correct.

Front 24

Characteristics of the SD

Back 24

1. The SD is always positive

2. The SD is used to describe quantitative data.

3. The SD is most informative when reported with the mean.

4. The value for the SD is affected by the value of each score in a distribution.

Front 25

The correlational method

Back 25

Is to treat each factor like a dependent variable and measure the relationship between each pair of variables.

Front 26

Correlation coefficient

Back 26

The statistics we use to measure correlations. The value of a correlation ranges from -1.0 to +1.0. Values closer to +1.0 indicates stronger correlations.

Front 27

What can you use a correlation for?

Back 27

1. To describe the pattern of data points for the values of two factors.

2. To determine whether the pattern observed in a sample is also present in the population from which the sample was selected.

Front 28

A correlation

Back 28

A statistical procedure used to describe the strength and direction of the linear relationship between two factors.

Front 29

A scatterplot

Back 29

Is a common way to illustrate a correlation, The data points are plotted along the x-and-y axis of the graph to see if a pattern emerges. The pattern that emerges is described by the value and sign of a correlation. A scatterplot is also called a scattergram.

Front 30

A positive correlation

Back 30

Means that as the value of one factor increase, the values of the second factor also increase; as the values of one factor decrease, the value of the other factor also decrease, if two factors have values that change in the same direction, we can graoh the correlation using a straight line. A perfect positive correlation occurs when each data point falls exactly on a straight line. It basically indicated that the values of two factors change in the same direction.

Front 31

A negative correlation

Back 31

Means that as the values of one factor increase, the values of the second factor decrease. If two factors have values that change in the opposite direction, we can graph the correlation using a straight line. It is a negative value of r that indicates that the values of two factors change in different directions, meaning that as the values of one factor increase the values of the second factor decrease.

Front 32

A regression line

Back 32

Is the best-fitting straight line to a set of data points. A best-fitting line is the line that minimizes the istance of all data points that fall from it. The closer a set of data points falls to a regression line, the stronger the correlation.

Front 33

The Pearson correlation coefficient (R)

Back 33

Also called Pearson product-moment correlation coefficient, is a measure of the direction and strength of the linear relationship of two factors in which the data for both factors are measured on an interval or ratio scale of measurement.

Front 34

Covariance

Back 34

Is the extent to which the values of two factors vary together. The closer data points fall to the regression line, the more that values of two factors vary together.

Front 35

Name the 4 steps of hypothesis testing

Back 35

Step 1: state the hypotheses, the null and the alternative hypothesis.

Step 2: set the criteria for a decision.

Step 3: compute the test statistic.

Step 4: make a decision.

Front 36

What are the key 3 assumptions we make to test for significance of a linear correlation?

Back 36

1. Homoscedasticity.

2. Linearity.

3. Normality.

Front 37

Homoscedasticity

Back 37

Is the assumption of constant variance among data points. We assume that there is an equal variance or scatter of data points dispersed aloing the regression line.

Front 38

Linearity

Back 38

Linearity is the assumption that the best way to describe a pattern of data is using a straight line. In truth, we could fit just about any set of data points to a best fitting straight line, but the data may actually conform better to other shapes, such as curvilinear shaper. Linearity is thus the assumption that the best way to describe a pattern of data is using a straight line.

Front 39

Normality

Back 39

To test for linear correlations, we must assume that the data points are normally distributed. For a linear correlations between two factors, the assumption of normality requires that a population of X and Y scores for two factors forms a bivariate normal distribution. Violating the assumption of normality can distort or bias the value of the correlation coefficient.

Front 40

Reverse causality

Back 40

Is a problem that arises when the causality between two factors can be in either direction.

Front 41

Outliers

Back 41

Can obscure the relationship between two factors by altering the direction adn the strength of an observed correlation. An outlier is a score that falls substantially above or below most other scores in a data set.

Front 42

The restriction of range problem

Back 42

This occurs when the range of data measure in a sample is restricted or smaller than the range of data in the general population. To avoid this problem, the direction and the strength of a significant correlation should only be generalized to a population within the limited range of measurements observed in the sample.

Front 43

There are 4 measurements for ways in which we can describe the variability, what are these?

Back 43

1. Range

2. Interquartile range

3. Variance

4. Standard deviation

Front 44

Range

Back 44

The easiest measurement, it is the range of scores that you get so the distance between the lowest and highest scores. Can only be calculated for variables that are at least ordinal because of the fact that a nominal variable does not have an order and you cannot calculate the rage.

Front 45

Characteristics of the range

Back 45

1. It is easy to understand.

2. It is informative because it tells us what the lowest and highest scores are.

3. It is very responsive to outliers . Because it simply looks at the lowest and highest scores. So it can be that you add one outlier that the range becomes much much higher then it was before.

Front 46

Interquartile range

Back 46

It has to do with the median, the thing is when you have the median you can also calculate the 25th and 75th percentile. It is useful because it tells you something about the middle group. You can visualize the IQR with a boxplot, with this you can show the range and the IQR. It can only be calculated for variables that are at least ordinal because of the fact that a nominal variable does not have an order and you cannot calculate an IQR because it does not have an order.

Front 47

The formula for variance

Back 47

Write it down.

Front 48

Variance

Back 48

Is a calculation that we use that is based on the sum of squares. It means that we are using the square distances from the mean. Variance is a little bit of a meaningless value, it becomes meaningless in comparison so if you are comparing different countries for example with each other then if you compare the variance it becomes meaningful. So then you can see that there is more variance arounm the mean. It allows for comparison.

Front 49

How do you calculate a variance in a population?

Back 49

1. Calculate all distances from the mean.

2. Square all these individual numbers.

3. You add these numbers together.

4. Divide it by the number of people on the population.

Front 50

Standard deviation

Back 50

This is the most complicated to calculate, it is a measure of variabilite. It is the average distance frome the mean. It is the square root of the variance. So basically if we have a mean in the distribution than the SD is how muhch people on avergae differ from the mean.

Front 51

A normal distribution

Back 51

Is a distribution that is symmetrical. Where one answers the most given answer, in these distribution the mean, median and mode are all the same. BUt skewed distribution, (ones that are not symmetrical) there is a difference between a mean, median and mode.

Front 52

The mu sign

Back 52

Is a population mean

Front 53

sigma

Back 53

Standard deviation in a population

Front 54

M

Back 54

Mean in a sample

Front 55

s

Back 55

SD in a sample

Front 56

x

Back 56

A specific score on a variable or a unit of analysis score on a variable.

Front 57

Bivariate statistics

Back 57

Statistics dealing with the correlation adn relation between two variables.

Front 58

When we are building models based on theory we distinguish between two types of variables. What are these?

Back 58

Independent variables and dependent variables.

Front 59

Independent variables

Back 59

The variables we expect to influence the other variables in the model. Referred to as X.

Front 60

Dependent variables

Back 60

The variables we expect to be influenced by at least one independent variable in the model. Referred to as Y.