Modalities and Scales

If I conduct a Khi² analysis, what should be my hypothesis?

• H0: independence ; H1: dependence.

• H0: dependence ; H1: independence.

• H0: same means ; H1: different means.

• H0: different means ; H1: same means.

Answer explanation

Keep in mind that H0 means 0 difference. The alternative hypothesis H1 then means the opposite: there is a difference.

Khi² works with frequencies and evaluates the degree of (in)dependency between variables (the difference in means is observed with t-test and anova).

When the result of my test leads me to accept H0 but, in reality, it is H1 which is true. What kind of error am I making?

• The error type I

• The error type II

Answer explanation

Type I error refers to a situation where my test leads me to conclude that there is a difference (or dependency between variables), but in reality, this difference is not observed.

Type II error is the opposite: my test leads me to conclude that there is no difference, whereas in reality, a difference does exist.

A way of remembering this: Type I error (1) means that accepting H1 (1) is an error.

I conduct a Khi² analysis, with the two following variables: site color theme (blue; green; red; purple) and amount of the purchase. What is my degree of freedom?

• 2

• 4

• 6

• I can't run the test.

Answer explanation

Khi² should be used when we are working with two qualitative variables.

Here, the "site color theme" is indeed a qualitative variable, with the following modalities (labels) : 1 = blue; 2 = green; 3 = red; 4 = purple. However, the variable "amount of the purchase" seems to be a quantitative variable (respondent will answer "100€" or "19,99€", etc.).

For this type of situation, ANOVA would be more suitable (multimodal qualitative variable as the independent variable and quantitative variable as the dependent variable).

I conduct a Khi² analysis, with the two following variables: site color theme (blue; green; red; purple) and amount of the purchase (below 50€; between 50-100€; below 100€). What is my degree of freedom?

• 2

• 4

• 6

• 8

Answer explanation

To calculate the degree of freedom of a Khi², we need to use the following formula: (number of modalities of variable 1 - 1) multiplicated by (number of modalities of variable 2 - 1).

Here, we have "site color theme" with 4 modalities (blue; green; red; purple) and "amount of the purchase" with 3 modalities (below 50€; between 50-100€; below 100€).

Hence, to find my df, I should do: (4-1)(3-1) = 6

After conducting a Khi² test, which result had led me to conclude that the two variables are dependent?

• p-value > ⍺, so H0 is accepted.

• p-value < ⍺, so H0 is accepted.

• p-value > ⍺, so H1 is accepted.

• p-value < ⍺, so H1 is accepted.

Answer explanation

These two informations are important to know: 

1. (1) if p-value < 0.05, then I should accept H1. This result means that I have less than a 5% chance of being wrong by saying that the variables are connected. In other words, I am 95% sure that the result that I have found (ie: the variables are connected) will occur in reality. 

3. (2) if p-value > 0.05, then I should accept H0. This result means that, if I say that the variables are connected, I have more than 5% chance of being wrong. In order to avoid this situation, it is more reasonable to conclude that there is no relationship between the variables (then accepting H0. 

0.05 (5%) is ⍺. In general, we select the standard boundary ⍺ = 5% (0.05). But ⍺ can be different, for instant 1%. This means that I will be 99% regarding teh results that I have found (particularly important in the case of healthcare industries, for example).

After conducting a t-test, which result had led me to conclude that the independent variable has an effect on the dependent variable?

• T(calulated) > T(critical)

• T(calulated) < T(critical)

Answer explanation

With the former question, p-value < 0.05 is the information given by the SPSS software (the “significativity” or “sig.”). Here, we did the test by hand. To do so, we need first to calculate the test associated with our results [= T(calculated)], and compare this result with the critical boundary we find in the associated statistical table [= T(table)]. Then, we conclude thank to the following rules: 

1. (1) If I win against the table, then I validate H1. In other words: T(calcl.) > T(table) leads me to support H1.

2. (2) If the table wins against me, then I validate H0. In other words: T(calcl.) < T(table) leads me to support H0. 

The logic is a bit different to the one with the p-value, but leads to the same conclusion. In the situation where T(calcl.) > T(table), this means that the difference is so big between what I have found and what I should find under the probability curve, that this difference can only be explained by a difference between my variables (and so, that my variables are interacting with each other), leading me to validate H1. On the other hand, if T(table) > T(calc.), this means that my results are more or less where they should be under the probability curve: nothing amazing happens. If so: status quo! I validate H0.

After conducting a khi², which result had led me to conclude that the two variables are independent?

• • Khi²(calulated) < Khi²(critical)

• Khi²(calulated) > Khi²(critical)

Answer explanation

Idem as the former question (we are just working with another formula, and so, another statistical table):

1. (1) X²(calcl.) > X²(table) leads me to support H1.

2. (2) X²(calcl.) < X²(table) leads me to support H0. 

After conducting an ANOVA, which result had led me to conclude that the independent variable has an effect on the dependent variable?

• F(calulated) < F(critical)

• F(calulated) > F(critical)

Answer explanation

Idem as the former question:

1. (1) F(calcl.) > F(table) leads me to support H1.

2. (2) F(calcl.) < F(table) leads me to support H0. 

If p-value > 5% (assuming that the risk has been defined at ⍺ = 0.05), then H1 is validated.

• True

• False

Answer explanation

It's important to keep these two points in mind:

(1) if p-value < 0.05 ==> H1 validated

(2) if p-value > 0.05 ==> H0 validated

If p-value < 5% (assuming that the risk has been defined at ⍺ = 0.05), then H0 is validated.

• True

• False

Answer explanation

On more time...:

(1) if p-value < 0.05 ==> H1 validated

(2) if p-value > 0.05 ==> H0 validated