CFA Level I: Quan­ti­ta­ti­ve Methods, Sta­tis­ti­cal Con­cepts and Mar­ket Returns, Mea­su­re­ment Scales

We mea­su­re data on dif­fe­rent scales:

  • nomi­nal scales,
  • ordi­nal scales,
  • inter­val sca­les, and
  • ratio sca­les.

On nomi­nal sca­les, data can only be cate­go­ri­zed; it can­not be ran­ked. In other words, the­re are dif­fe­ren­ces on nomi­nal sca­les, but no ran­king is possible.

Examp­le:

The­re are dif­fe­ren­ces bet­ween dif­fe­rent natio­na­li­ties, but the­re is no way to rank them. Natio­na­li­ty A is not bet­ter than natio­na­li­ty B, only dif­fe­rent. The­re­fo­re, natio­na­li­ties are mea­su­red on nomi­nal scales.

On ordi­nal sca­les, we can sort data into cate­go­ries (some­thing we can not do on nomi­nal scales).

Examp­le:

Four stu­dents sit a math exam at their school and get gra­des of D, C, B, and B.

The gra­des can be orde­red, e.g. as B, B, C, D or as D, C, B, B. But the distan­ces are not com­pa­ra­ble: the distance bet­ween gra­de D and C is much grea­ter than that bet­ween C and B.

On inter­val sca­les, the distan­ces bet­ween sca­le values are equal. The pro­per­ties of nomi­nal and ordi­nal sca­les are also found on inter­val scales.

Examp­le:

Tem­pe­ra­tures in °F and °C are mea­su­red on inter­val scales.

Ratio sca­les have all the cha­rac­te­ris­tics of the other sca­les; they also have a true zero point.

Examp­le: 

Distan­ces mea­su­red in miles or kilo­me­ters have a true zero point, becau­se we can­not chan­ge them.

THE LAMBERT METHOD

It’s very important to under­stand the dif­fe­ren­ces bet­ween the various sca­les, becau­se the type of ana­ly­sis per­for­med on the data dif­fers from one sca­le to the next. Put dif­fer­ent­ly, mea­su­re­ment sca­les are vital, becau­se using the right mean, disper­si­on and cor­re­la­ti­on dif­fers on dif­fe­rent sca­les:

Sca­leMeanDisper­si­onCor­re­la­ti­on
nomi­nal scalemodenot rele­vantnot rele­vant
ordi­na­ry scalemedi­anran­geSpear­man cor­re­la­ti­on coefficient
inter­val scalearith­me­tic meanvari­an­ce, stan­dard deviationcor­re­la­ti­on coef­fi­ci­ent of Bra­vais and Pearson
rati­on scalearith­me­tic meanvari­an­ce, stan­dard deviationcor­re­la­ti­on coef­fi­ci­ent of Bra­vais and Pearson

The important aspects of Sta­tis­ti­cal Con­cepts and Mar­ket Returns can be seen on this Mind­Map (click on it to get a lar­ger picture).

Did you find the Mind­map hel­pful? All of Lam­bert Education’s Mind­Maps for CFA Level I and CFA Level II can be found here:

https://daniel-lambert.de/produkt-kategorie/chartered-financial-analyst/

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