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Obsah : Technick² popis: Hlavnφ nabφdka: Statistika: Anal²za
Anal²za procesu uΦenφ

Dialogov² panel dostupn² z Tools: Statistics: Analysis v SuperMemo poskytuje matice a grafy, kterΘ ilustrujφ aktußlnφ stav procesu uΦenφ v prßv∞ otev°enΘm systΘmu v∞domostφ. N∞kterΘ z t∞chto graf∙ je mo₧no chßpat i bez znalosti Algoritmu SM-8; avÜak v∞tÜina z nich vy₧aduje vÜeobecnΘ znalosti o tom, jak SuperMemo vypoΦφtßvß optimßlnφ intervaly mezi opakovßnφm.
Na nabφdce Analysis jsou dostupnΘ nßsledujφcφ karty:

Distributions (Rozd∞lenφ)

  • Interval distribution (Rozd∞lenφ interval∙) - rozd∞lenφ interval∙ mezi opakovßnφmi u danΘho systΘmu v∞domostφ

    A-Factor distribution (Rozd∞lenφ A-faktor∙) - rozd∞lenφ A-Faktor∙ v danΘm systΘmu v∞domostφ (vÜimn∞te si, ₧e rozd∞lenφ samotnΘ se v Algoritmu SM-8 nepou₧φvß, pouze v²sledky z n∞ho)

    Repetitions distribution (Rozd∞lenφ opakovßnφ) - rozd∞lenφ poΦtu opakovßnφ v danΘm systΘmu v∞domostφ (berou se v ·vahu jen probranΘ prvky, tj. neexistuje kategorie s nulov²m poΦtem opakovßnφ)

    Lapses distribution (Rozd∞lenφ selhßnφ) - rozd∞lenφ poΦtu selhßnφ (zapomenutφ) jednotliv²ch prvk∙ systΘmu v∞domostφ (v ·vahu se berou jen probranΘ prvky).

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    Curves (K°ivky) - pro v²poΦet matice RF je nezßvisle vyneseno Φty°i sta k°ivek. Ty odpovφdajφ dvaceti kategoriφm poΦtu opakovßnφ vynßsoben²ch dvaceti kategoriemi A-Faktor∙ (vÜimn∞te si, ₧e pro prvnφ opakovßnφ jsou sloupce matice RF indexovßny podle poΦtu selhßnφ pam∞ti mφsto A-Faktoru). Volbou sprßvnΘ karty na spodnφm okraji grafu m∙₧ete vybrat k°ivku zapomφnßnφ, o kterou se zajφmßte. Vodorovnß osa p°edstavuje Φas vyjßd°en² jako: (1) U-Faktor, tj. pom∞r po sob∞ nßsledujφcφch interval∙ mezi opakovßnφm nebo (2) poΦet dn∙ (jen v p°φpad∞ prvnφho opakovßnφ). Svislß osa p°edstavuje retenci v∞domostφ v procentech.

    ModrΘ krou₧ky p°edstavujφ opakovßnφ (Φφm v∞tÜφ je krou₧ek, tφm v∞tÜφ je poΦet opakovßnφ). ╚ervenß k°ivka koresponduje s nejlΘpe odpovφdajφcφ k°ivkou zapomφnßnφ zφskanou exponencißlnφ regresφ.
    Vodorovnß zelenß Φßra koresponduje s     po₧adovan²m indexem zapomφnßnφ, kde₧to svislß zelenß Φßra zobrazuje Φasov² okam₧ik, v n∞m₧ se aproximovanß k°ivka zapomφnßnφ protφnß s Φarou po₧adovanΘho indexu zapomφnßnφ. Tento Φasov² okam₧ik urΦuje hodnotu p°φsluÜnΘho faktoru R. Hodnoty O-faktoru a R-faktoru jsou zobrazeny v hornφ Φßsti grafu. Za nimi nßsleduje poΦet p°φpad∙ opakovßnφ pou₧it² pro vynesenφ grafu.
    VÜimn∞te si, ₧e na zaΦßtku procesu uΦenφ neexistuje ₧ßdnß historie uΦenφ a ₧ßdnß data opakovßnφ, kterß by bylo mo₧no vyu₧φt pro v²poΦet R-faktor∙. Z toho d∙vodu se poΦßteΦnφ hodnoty matice RF berou z Wozniakova modelu pam∞ti a odpovφdajφ parametr∙m pam∞ti podpr∙m∞rnΘho studenta (model pr∙m∞rnΘho studenta nebyl pou₧it, proto₧e konvergence od slabΘhostudenta nahoru je rychlejÜφ ne₧ konvergence v opaΦnΘm sm∞ru).

    Grafy

  • G-FI graph - G-FI graph correlates the expected forgetting index with the grade obtained at repetitions. You can imagine that the forgetting curve graph might use average grade instead of retention on its vertical axis. If you correlated this grade with the forgetting index (which is 100% minus retention), you arrive at the G-FI graph

    G-AF graph - G-AF graph correlates the first grade obtained by an item with the ultimate estimation of its A-Factor value. At each repetition, the current element's old A-Factor estimation is removed from the graph and the new estimation is added. This graph is used by the Algorithm SM-8 to quickly estimate the first value of A-Factor at the moment when all we know about an element is the first grade it has scored in its first repetition

    DF-AF graph - DF-AF graph shows decay constants of power approximation of R-Factors along columns of the RF matrix. The horizontal axis represents A-Factor, while the vertical axis represents D-Factor (i.e. Decay Factor). D-Factor is a decay constant of power approximation of curves that can be inspected with the Approximations tab of the Analysis dialog box

    First interval graph - the length of the first interval after the first repetition depends on the number of times a given item has been forgotten. Note that the first repetition may also mean the first repetition after forgetting. In other words, a twice repeated item will have the repetition number equal to one after it has been forgotten (i.e. the repetition number will not equal three). The first interval graph shows exponential regression curve that approximates the length of the first interval for different numbers of memory lapses (including the zero-lapses category that corresponds with newly memorized items).

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    Matrices

  • O-Factor matrix - matrix of optimal factors indexed by the repetition number and A-Factor (only for the first repetition, A-Factor is replaced with memory lapses)

    R-Factor matrix - matrix of retention factors

    Cases matrix - matrix of repetition cases used to compute the corresponding entries of the RF matrix (double click an entry to view the relevant forgetting curve). This matrix can be edited manually

    Optimal intervals - matrix of optimum intervals derived from the OF matrix

    D-Factor vector - vector of D-Factor values for different A-Factor values (also repetition cases used in computing particular D-Factors)

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    3-D Graphs - 3-D graphs that visually illustrate the changes to OF, RF and Cases matrices

    Approximations - twenty power approximation curves that show the decline of R-Factors along columns of the RF matrix. For each A-Factor, with increasing values of the repetition number, the value of R-Factor decreases (at least theoretically it should decrease). Power regression is used to illustrate the degree of this decline that is best reflected by the decay constant called here D-Factor. By choosing the A-Factor tab at the bottom of the graph, you can view a corresponding R-Factor approximation curve. The horizontal axis represents the repetition number, while the vertical axis represents R-Factor. The value of D-Factor is shown at the top of the graph. The blue polyline shows R-Factors as derived from repetition data. The red curve shows the fixed-point power approximation of R-Factor (fixed-point approach is used as for the repetition number equal two, R-Factor equals A-Factor). The green curve shows the fixed-point power approximation of R-Factor taken from the OF matrix. This is equivalent to substituting the D-Factor obtained by fixed-point power approximation of R-Factors with D-Factor obtained from DF-AF linear regression.