There are many different tests you can use in statistics.

Sometimes it can be quite difficult to know which is the correct test to use.

This video will talk about seven tests you are likely to use.

involving means proportions and relationships.

When you are trying to work out which is the most appropriate test

there are three questions you should ask

One. What level of measurement was used for the data we are analyzing.

2. How many samples do we have?

3. What is the purpose of our analysis?

I will now explain each of these questions

1. Data or level of measurement

Is our data nominal or interval/ratio?

Nominal data is also called categorical, qualitative

or nonparametric

Examples of nominal data are color

whether parts are defective or not,

or preferred type of chocolate.

Nominal summary values are usually stated as frequencies, proportions or

percentages.

The tests that involve nominal data are:

Test for a proportion

Difference of two proportions

and chi-squared test for independence

The other type of data

is interval/ratio

also called quantitative

Examples of interval/ratio data are

daily sales figures for choconutties

weight of peanuts or temperature

the most common summary value for interval/ratio data is a mean.

Tests that involve interval/ratio data are:

Test for a mean

difference of two means - independent samples

difference of two means - paired

and regression analysis.

For more help on levels of measurement see our video:

"Types of data nominal, ordinal, interval/ratio"

Ordinal data can be classified with nominal or interval/ratio

depending on the circumstances.

2. Samples

Next we ask how many samples are involved

Is there one sample for which we are testing the relevant statistic

against a hypothesized value

or are there two samples

which are being compared with each other

or

is the one sample but each observation has a measure or score

for more than one variable?

The same sample is measured twice.

If we wish to compare a proportion or a mean against a given value,

this will involve one sample.

If we're comparing two different lots of people or things such as men and women

or people from two different departments

then we would have two samples.

If we have two sets of information on the same people of things

we would say we have one sample with two variables.

An example is one set of days and information on how many choconutties

are sold and what the temperature was.

Or - one set of people and information on their gender and preferred type of chocolate.

Finally we ask

What is the purpose of the analysis?

We can be testing against the hypothesized value

comparing two statistics

or looking for a relationship.

Chi-squared test for independence and regression are similar

in that they are looking at the relationship between two variables

The difference between them is in the kind of data.

If you would summarize the data in s table,

we would use a chi-squared test fo independence

whereas if you would put it on a scatter plot

you would use regression analysis.

Here iss an example for each of these tests.

They relate back or out other videos teaching about hypothesis testing.

After each description of the scenario pause the video

and see if you can identify the correct test before we tell you the answer.

Helen is still selling choconutties.

Example one:

sufficient nuts.

Helen was concerned whether the quantity of nuts was sufficient in her choconutties.

She took a sample of twenty packets and found the weight of nuts in

each packet

Pause the video

1. Data

The weight was interval/ratio data.

2. Samples

There was just one sample of twenty packets of choconutties.

3. Purpose. Helen was comparing against given value

Thus, the test she needs to use is Test for a mean.

Example Two

Prize tickets

In a promotional campaign twenty percent of all packs of choconutties should

include tickets for free prizes.

Helen takes a sample of fifty packets and finds that seven of them

have winning tickets

Pause the video

1. Data: For each bar we are saying yes or no, only to be lumped whether or not

there is a ticket.

This is nominal data from which we get a sample proportion of seven out of fifty

Or 0.14

Samples

There is one sample of fifty packets

Purpose.

Helen is comparing the sample value against a given value: twenty percent

We conclude that the test she needs to use is test for a proportion.

Example three

Bar longevity compared with nuttabars.

Helen thinks her choconutties last longer than the competition, nuttabars.

She gets 36 people to eat one of each, and records their eating times.

Pause now

1. Data. Helen collects times taken in seconds

so this is interval/ratio data.

2. Samples

There is one sample of thirty-six people but with two scores for each person

the time for the choconuttie and the time for the nuttabar.

3. Purpose

She is looking at whether there iss a difference in the amount of time taken

for each of the bars.

Thus the test is difference of two means, paired sample.

Example four

Defective wrapping from two wrapping machines

Helen thinks there is a difference in performance between

the two wrapping machines in her factory. She checks 200 bars from

one machine and 150 bars from the other.

For each bar she is seeing if the wrapping is satisfactory or not

She finds that ten out of two hundred bars from the first machine

and nine out of 150 bars from the second machine

are badly wrapped.

Pause the video

Data. The information for each bar is OK or not ok

This is nominal data.

It has been summarized as frequencies.

2. Samples there are two independent samples

one sample from each of the two machines

3. Purpose

Helen is comparing the proportions from the two samples

We can see that the test is

difference of two proportions.

Example five

Do stickers help sales?

Helen is exploring whether having free stickers makes a difference to sales.

She has the sales figures for thirteen days when she did offer free stickers

and ten days when she did not. Pause and decide on the test

Data. For each day Helen has a number or value corresponding to the sales for that day

This is interval/ratio data

It is summarized as a mean member of sales.

2. Samples

There are two samples one sample for days with stickers

and one sample for days without.

3. Purpose

Helen is comparing the average sales figures for the two treatments

we conclude that the test to use is...

Difference of two means independent samples

Example six

Are sales affected by temperature?

Helen wants to see if there is a relationship between the daily

temperature and sales of choconutties.

She has data on sales and temperature

for thirty weekdays of sales

Pause!

Data. Sales and temperature at both interval variables

Samples

There is one sample of thirty days with two measures or scores for each day.

Purpose.

Helen is interested in the relationship between sales and temperature

This leads us to decide that the test is regression.

Example seven

Men and women and chocolate preference

Helen is thinking of selling dark chocolate, milk chocolate and white chocolate

choconutties.

She thinks that men and women might have different preferences with regard to type.

She collects data from fifty customers, noting down if they are men or women

and asking them which variety they prefer.

Pause the video and decide.

Data. Helen records the type of chocolate and sex of person.

These are both nominal variables.