(Business) Research Methods Part 1

It varies between

o People (e.g., cups of coffee you drank this morning)

o Locations (e.g., average temperature in June)

o Firms (e.g., yearly profit) -

...

• ...and we are interested in this variation.

• Cause
• Or: predictor variable

The independent variable (IV) has an impact on the dependent variable (DV), which

therefore depends on the IV.

o Effect

o Or: outcome variable

The independent variable (IV) has an impact on the dependent variable (DV), which

therefore depends on the IV.

Nominal: Name

Ordinal: Name and order

Interval: Name, order and equidistance

Ratio: Name, order, equidistance and a meaningfull zero

Examples:

Nominal: colours of cars

Ordinal: survey range from strongly disagree to strongly agree

Interval: temperature

Ratio: length

Equidistance = same distance between the different levels

Meaningful zero = nothing being there, a reference point

By checking validity, reliability, objectivity and actuality.

Validity: • The test or instrument measures what it is supposed to measure.

• Difficult to establish.
• Often solved by using measures that have been used by others before.

Reliability:

• Stability or consistency
• Are test or research findings repeatable?
• Attention: a reliable method is not automatically valid!

Example: a thermometer (reliably) shows 10 degrees more than the actual outside temperature

Objectivity:

• Did the researcher influence the outcomes of the investigation.

• While collecting data (e.g., some interviewers are more eager than others)
• While analyzing data (e.g., exam, two examiners having different opinions)?

Actuality:

• Only relevant if research question refers to current circumstances.

• Often problematic if secondary data are used.

• Older data can lead to wrong conclusions today.

Examples:

• Population density, map from 1980.
• Survey regarding laptop use in the year 2000.

• Mode

• Median

• Mean

• All these measures refer to some kind of 'average.'

• The score that occurs most frequently in the dataset

• The tallest bar in the histogram

• Unimodal distributions have one mode (the normal distribution is unimodal)

• Bimodal distributions have two modes.

• Multimodal distributions have 3 or more modes.

Can be determined for metric, ordinal & nominal data

• The middle score when scores are ranked in order of magnitude.

• Can be determined for metric and ordinal data.

• Not for nominal data

• Because they are categories.
• There is no 'middle' when you look at green, red, and blue.

Example:

• 11 Facebook users, each with a specific number of friends.

For the median, with an even number of scores: take the average of the middle two values.

• Most common measure of central tendency.

• Usually, when talking about the 'average', people refer to the mean.

• Add up all scores, then divide by the total number of scores.

• Only for metric (also known as continuous) variables.

• Not for ordinal and nominal data.

• There is no mean without equal distances.
• There is no mean when you look at green, red, and blue.

Dispersion refers to the extent to which data values in a dataset are spread out or scattered around a central value (such as the mean or median). It provides a measure of the variability or diversity in the data. Dispersion is important because it helps us understand the distribution of data and whether values are closely clustered or widely spread.

• Spread of scores

• 'From here to there'

• Different measures

• Range
• Deviance
• Sum of squared errors (SS)
• Variance
• Standard deviation (SD)

• Difference between the largest and the smallest score

• The smallest score subtracted from the largest.

• Only for metric values.

• Example

• The highest number of Facebook friends is 234, and the lowest number is 22
• The range is 234 − 22 = 212

• Measure is dramatically affected by extreme scores (therefore you might be interested in different measurements).

-Quartiles (4 parts of data between 3 points).

-The three values that split the sorted data into four equal parts.

• Second quartile = median
• Lower quartile = median of lower half of the data
• Upper quartile = median of upper half of the data

• Less affected by extreme score

Deviance measures the difference between the likelihood of the observed data under the fitted model and the likelihood of the data under a perfect model (saturated model).

We can calculate the spread of scores by looking at how different each score is from the centre of of a distribution (e.g., the mean).

point.

The total deviance is the sum of the deviances for each data point.

• Square the deviances so they will not cancel each other out, then sum them up.

you can read off the SS under the column: squared deviation

The sum of squares, variance, and standard deviation represent the same thing.

(= the average dispersion = the average spread)

• It is more useful to work with the average (not total) dispersion, known as the variance.

• You use the sum of errors and divide it by the number observations minus 1.

The sum of squares, variance, and standard deviation represent the same thing.

Variance (𝒔𝟐) = average error between the mean and the observations that were made.

• But: measure is given in units squared.

• Solution: square root of the variance, known as the standard deviation (𝒔).

The sum of squares, variance, and standard deviation represent the same thing.

• Frequency distributions also reveal information about how likely it is that a score

would occur (probability).

• We can use the frequencies of different scores and the area of a frequency

distribution to estimate the probability that a particular score will occur.

• Remember: a probability of 0.1 = 10% (calculation to percent’s)

X-axis has the values of observations

Y-axis has the number of occurances

symmetrical

Refers to the tail of a distribution

Refers to the measurement of how steep the peek is. Leptokurtic and platykurtic are terms to use to say how peek it is.

When the mean is 0 and the standard deviation of 1

the value of an observation expressed in standard deviation units. It is calculated by taking the observation, subtracting the mean of all observations from it and dividing the result by the standard deviation of all observations. By converting a distribution of observations into z-scores a new distribution is created that has a mean of 0 and a standard deviation of 1.

numerical value calculated from sample data that is used in a statistical hypothesis test. It measures the degree of agreement between the sample data and the null hypothesis. The test statistic helps determine whether to reject or fail to reject the null hypothesis by comparing it to a critical value or by using its corresponding p-value.

• used to describe the data at hand
• gives a nice overview of what you are dealing with
• checking for potential problems
• measures of central tendncy and dispersion

Bias is some kind of distortion that affects your data and the reults of your analyses.

Sources of bias:

• outliers (flawed data collection)
• violations of assumptions

a probability-probability plot

• investigate the assoviation between two metric (continuous) variables
• to which extent are these variables related?
• systematic connection
• degree of correspondence

Investigate through scatterplots, covariance and correlation

A positive covariance indicates that the two variables tend to increase or decrease together (e.g., height and weight).

A negative covariance indicates that one variable tends to increase as the other decreases (e.g., hours spent studying and time spent on leisure).

A covariance of zero suggests no linear relationship between the variables.

• lies between -1 and +1
• negative values indicate a negative correlation
• positive values indicate a positive correltation
• a value close to zero indicates no or radom correlation