LECTURE 1 INTRODUCTION
The principles of hypothesis testing “Women are more intelligent than men”
N=2, men score 108 and women score 109
Is my hypothesis supported or not? What if N=10, 100? 100?
Point of departure -> assumption that there is no difference.
This gives a point of comparison
If no difference, than IQ(women) – IQ(men) = 0
We can predetermine: if I measure in 1000 persons, and the mean difference between men and
women is larger than 5IQ-points, then it is very unlikely that this difference is coincidence.
Types of hypothesis
Null hypothesis, H0 this is the one we try to reject
There is no effect expected (most of the time)
This is generally the outcome
For example: “woman are equally likely as men to wear a skirt or dress” or “there is no
relationship between age and the number of wrinkles you have”
The alternative hypothesis, H1 Woman are more likely to wear a skirt or dress than man
If we can reject H0, this one is supported by the data but not proven.
“There is a positive relationship between age and the number of wrinkels you have.”
In Statistics, we try to reject the null hypothesis. If we can reject H0, this one is supported by the data
but not proven. Shoe size example. if we have a class of 100 people and the average size is 40. We try
to predict the future. Only two people have a size 46. How likely is it that the first person who comes
in has as size 46?
Statistics offer u a means to determine exactly how (un-)likely it is that we would observe a set of data if
the null hypothesis is true. In other words, we examine the chance the null hypothesis is true. If it is very
unlikely (smaller than 5%) we may conclude that the alternative hypothesis is not true.
Experiment
- You manipulate something
- This is supposed to have an effect
- In other words: cause -> effect.
- The manipulated variable is the independent variable.
- The effect is the dependent variable.
I want to study the effect of colour clothing on how hot you feel. -> you can manipulate this.
Independent is the colour of the shirt
Dependent is how hot you feel.
Correlational design
You measure/observed perceived reality. For example: Do people get more wrinkles as they grow older?
-> you cannot manipulate this.
1. Examine association
Is depression associated with poor health?
2. Predictor -> outcome variable
Does lecture attendance predict grade?
Terminology to use depends on the variable you are talking about.
, Independent variable Dependent variable
If experiment, the proposed cause which If experiment, the proposed effect
is manipulated
If survey, a predictor variable If survey, an outcome variable
Both measured not manipulated
Variables
A variable varies. It has different values.
“Women who spend a lot of time following fitgirls are less satisfied with their body than woman who
spend less time following fitgirls”
Time spent following fitgirls is independent variable
Body satisfaction is the dependent variable
So, to summarize the use of dependent and independent variables in experimental or correlational
designs.
Independent variables
- If experiment, the proposed cause, which is manipulated
- If correlational design, a predictor variable
Dependent variable
- If experiment, the proposed effect
- If correlational, the outcome variable
- Measured not manipulated
There are two main categories to be found within all types of variables. Categorical and continuous
variables. Categorical variables are entities divided into distinct categories, like gender/animal person.
continuous variables are entities which got a distinct score. Like age, leisure ranking.
Categorical entities
1. Binary or dichotomous variable: there are only two categories.
For example, dead or alive.
2. Nominal variables: there are more than two categories.
For example, whether someone is omnivore, vegetarian or vegan or fruitarian.
3. Ordinal variables: there are more than two categories but have a logical order.
Ordinal variables allow you to say something about the order of things.
They also allow you to say whether something equals something or not.
For example, whether people fail, pass, merit or have a resit for their exam.
For example, whether people completely agree, agree, disagree or completely disagree with a
statement.
Continuous variables
1. Interval variables: Equal intervals on the variable represent equal differences in the property
being measured.
Interval variables allow you to say something about the distance between units/(distance):
They also allow you to say something about the order of things (order)
They also allow you to say whether something equals something or not (equality)
Interval ratio’s don’t have a “real” 0 point. Year 0 does not mean the absence of time, just
like 0 degrees also does not mean there is no temperature at that point.
For example, 1940 – 1945 is a five year period, just as 2005 – 2010 (distance).
1945 comes later than 1940 (order)
, 1945 ≠ 1940 (equality)
2. Ratio variable : the same as an interval variable, but the ratios of scores on the scale must also
make sense.
Ratio variables allow you to say something about the ratio between measurements (ratio):
Ratio variables have a true zero point. Like zero calories, or zero kilo´s.
Interval variables allow you to say something about the distance between units/(distance):
They also allow you to say something about the order of things (order)
They also allow you to say whether something equals something or not (equality)
Notes chapter 2 4-9-2023
A useful concept in distinguishing different types of variables is what’s known as the scale of
measurements.
Nominal Scale
Within nominal scale variables there are no relationships between the variables. For these kinds of
variables it doesn’t make any sense to say that one of them is bigger of better than the other variable. The
classical example is eye colour. Eyes can be blue, green or brown, amongst other possibilities, but none of
them is any “bigger” than any other one. As a result, it would feel really weird to talk about an “average
eye colour”. Similarly, gender is nominal too: male isn’t better or worse than female.
In short, nominal variables are for those which the only thing you can say about the different possibilities
is that the are different. That’s it.
, So, what’s the average transportation type? Obviously, the answer here is that there isn’t one. It’s a silly
question to ask. You can say that travel by car is the most popular method, and travel by train is the least
popular method, but that’s about all. Similarly, notice that the order in which I list the options isn’t very
interesting.
Ordinal Scale
Ordinal scale variables are a bit more structured compared to the nominal variables; but not by a lot. An
ordinal variable is one in which there is a natural, meaningful way to order the different possibilities. The
usual example given is the ‘finishin position in a race’. You can say who finished first was faster than the
one who finished second, but we don’t know how much faster. That said, notice that while we can use the
natural ordering of these items to construct sensible groupings, what we can’t do is average them.
Interval scale
In contrast to nominal and ordinal scale variables, interval scale and ratio scale variables are variables for
which the numerical value is genuinely meaningful. In the case of interval scale variables the differences
between the numbers are interpretable, but the variable doesn’t have a “natural” zero value. A good
example of an interval scale variable is measuring temperature in degrees celsius. For instance, if it was 15
yesterday and 18 today, then the 3 difference between the two is genuinely meaningful. Moreover, that
3 difference is exactly the same as the 3 difference between 7 and 10. In short, addition and subtraction
are meaningful for interval scale variables.2
However, notice that the 0 does not mean “no temperature at all”. It actually means “the temperature at
which water freezes”, which is pretty arbitrary.
- There is no 0 in interval scales.
- It is weird to give them some kind of ratio.
Ratio scale
The fourth and final type of variable to consider is a ratio scale variable, in which zero really means zero,
and it’s okay to multiply and divide. A good psychological example of a ratio scale variable is response
time (RT). In a lot of tasks it’s very common to record the amount of time somebody takes to solve a
problem or answer a question, because it’s an indicator of how difficult the task is. Suppose that Alan
takes 2.3 seconds to respond to a question, whereas Ben takes 3.1 seconds. As with an interval scale
variable, addition and subtraction are both meaningful here. Ben really did take 3.1 - 2.3 = 0.8 seconds
longer than Alan did. However, notice that multiplication and division also make sense here too: Ben took
3.1/2.3 = 1.35 times as long as Alan did to answer the question. And the reason why you can do this is that
for a ratio scale variable such as RT “zero seconds” really does mean “no time at all”.
- There is a 0 in ratio which means something.
